Cheap Tuesdays and the Demand for Cinema

∗

Nicolas de Roos

†

Sydney University

Jordi McKenzie

‡

Sydney University

Abstract

Many movie markets are characterised by extensive uniform pricing practices, ham-

pering the ability to estimate price elasticities of demand. Australia presents a rare

exception, with most cinemas oﬀering cheap Tuesday ticket prices. We exploit this

feature to estimate a random coeﬃcients discrete choice model of demand for the

Sydney region in 2007. We harness an extensive set of ﬁlm, cinema, and time-

dependent characteristics to build a rich demand system. Our results are consistent

with a market expansion eﬀect from the practice of discounted Tuesday tickets,

and suggest that cinemas could proﬁt from price dispersion by discounts based on

observable characteristics.

Keywords: Motion pictures, cinema demand, discrete choice model, market ex-

pansion.

JEL Classiﬁcation: L13, L82

∗

We would like to thank the editor, Julie Holland-Mortimer, and two anonymous referees for valuable

comments. We would also like to thank Phillip Leslie, Kathryn Graddy, Darlene Chisholm and David

Prentice for comments on earlier drafts of this paper. We are grateful for the research assistance of Akshay

Shanker and Paul Tiﬀen. We are also grateful to participants at the Screen Economics Research Group

Symposium (Sydney, June 2009), European Science Days Summer School (Steyr, July 2009), Australian

Conference of Economists (Adelaide, September 2009), Macquarie University (Sydney, February 2010),

International Conference on Cultural Economics (Copenhagen, June 2010), Suﬀolk University (Boston,

October 2010), Mallen/UCLA Scholars and Practitioners Workshop in Motion Picture Industry Studies

(Los Angeles, November 2010), University of Tasmania (Hobart, February, 2011), University of Western

Australia (Perth, May 2011), Conference of the European Association for Research in Industrial Organi-

zation (Stockholm, September 2011), and University of Melbourne (Melbourne, October 2012). Finally,

we would like to thank the Motion Picture Distributors Association of Australia and Rentrak Australia

(formerly Nielsen EDI) for supplying data used in this study, and Paul Aubery from Greater Union

Cinemas for useful comments and insights.

†

Corresponding author: Faculty of Arts and Social Sciences, Merewether Building H04, The University

of Sydney, nicolas.deroos@sydney.edu.au

‡

Faculty of Arts and Social Sciences, The University of Sydney, jordi.mckenzie@sydney.edu.au

“One of the more perplexing examples of the triumph of convention over rationality

is movie theatres, where it costs you as much to see a total dog that’s limping its way

through its last week of release as it does to see a hugely popular ﬁlm on opening night.”

James Surowiecki (The Wisdom of Crowds, 2004, p.99).

1 Introduction

Product diﬀerentiation in movies is self-evident to even the most casual enthusiast. How-

ever, as Orbach and Einav (2007) discuss in detail, to the puzzlement of many observers,

the practice of (almost) uniform pricing is a long-standing feature of the market for movies

screened in cinemas.

The Australian cinema market oﬀers a rare partial exception. For

example, in Sydney almost all cinemas oﬀer discounted tickets every Tuesday for the entire

day.

Based on typical multiplex prices, this reduces the price of an adult ticket by about

40%, a student ticket by about 25%, and a child ticket by about 20%. We exploit this

rare (and arguably exogenous) price variation in the Sydney cinema market to estimate

the demand for cinema using a comprehensive data set of daily ﬁlm revenues for cinemas

in the greater Sydney region over the year 2007.

Our ﬁrst goal is to investigate whether this experiment with discounting has been

successful. Has it led to an increase in cinema attendance, or has it simply induced

consumers to switch the timing of their attendance? The purpose of discounted pricing

is typically to lure consumers into the market and away from competitors. In the case

of the Sydney cinema market, discounting is quite well coordinated across cinemas with

almost all cinemas engaging in “cheap Tuesday” pricing. In aggregate then, cinemas are

likely to beneﬁt only if discounting leads to a market expansion.

To tackle this problem, we consider two alternative market deﬁnitions in our demand

speciﬁcation. Our daily market deﬁnition includes all ﬁlms exhibited on a speciﬁc day in

the choice set of each consumer. An outside good is also available, permitting consumers

to opt out of the movie market. Discounting can then lead to substitution away from

the outside good or other movies oﬀered on the same day, but not substitution away

from movies on other days of the week. By not allowing such temporal substitution, this

deﬁnition could overstate the market expansion due to cheap Tuesday pricing. Our weekly

market deﬁnition is designed to address this problem by including all ﬁlms screening over

the week within the choice set of each consumer.

Using this deﬁnition, we can examine

whether discounting has led to substitution away from the outside good or substitution

away from other ﬁlms oﬀered during the week.

Orbach and Einav (2007) provide detail that during the pre-Paramount era (i.e. before 1948) variable

pricing strategies were used with respect to ﬁlms categorised by quality. This practice subsequently

continued into the 1950s and 1960s where ‘event’ movies were often priced above other movies. Price

variation between weekends and weekdays and by type of seat within an auditorium was also evident.

This kind of price variation has more recently been largely absent in most markets. Orbach and Einav

(2007) conclude that exhibitors could increase proﬁts if they practiced variable pricing strategies.

In the U.S. on certain days matinee performances may be priced lower, but not the evening sessions

where there is likely to be more demand.

We thank Philip Leslie for suggesting this alternative market deﬁnition.

Our second goal is to examine the potential proﬁtability of additional price dispersion.

Despite weekly discounting, a remarkable degree of price uniformity remains in the Syd-

ney market. In particular, we observe the two pricing puzzles discussed by Orbach and

Einav (2007): i) the ‘movie puzzle’ (why diﬀerent movies attract the same price); and

ii) the ‘show-time puzzle’ (why diﬀerent times, days, and seasons are priced uniformly).

Armed with our demand estimates, we simulate optimal pricing for diﬀerent types of ﬁlms,

ranging from a ﬁlm in the middle of its run to an opening week ﬁlm to a blockbuster in

opening week. This allows us to examine the returns to price adjustments for diﬀerent

categories of ﬁlms.

Price uniformity itself hampers attempts to formulate an optimal pricing strategy.

Without variation in price, demand elasticities cannot be inferred from the data, and the

enterprise is destined for failure. An additional contribution of our work is then to obtain

demand estimates in a setting with substantial price variation. We observe prices that

vary by around 30% in every week of the sample for each cinema-ﬁlm pair. We also make

use of a rich data set, enabling us to estimate a detailed characteristics-based demand

system. In particular, we control for ﬁlm characteristics (e.g. genre, budget, advertising,

reviews, cast appeal), theatre characteristics (e.g. location, number of screens), the day

of observation (e.g. day of week, public/school holidays, weather), and the demographics

of the local population (e.g. age, income).

We adopt a random coeﬃcients discrete choice model of demand. We deﬁne a product

as a combination of a ﬁlm, a theatre and day of screening. There are a large number

of such products in our sample, making a characteristic-based estimation strategy the

only feasible means of extracting the full set of cross-price elasticities. To accommodate

heterogeneous preferences for movie oﬀerings, our strategy is based on the empirical model

of Berry et al. (1995) (hereafter, “BLP”). Following Nevo (2001), we permit heterogeneity

in “observable” characteristics (local region-speciﬁc demographic characteristics) as well

as “unobservable” characteristics; and we include movie-speciﬁc ﬁxed eﬀects. Following

Davis (2006), we incorporate a spatial dimension to product characteristics that accounts

for travel costs. In the spirit of Imbens and Lancaster (1994) and Petrin (2002), we include

additional moment conditions based on external population demographic data.

Our estimation strategy relies on the assumption that the demand for movies on Tues-

days is essentially the same as for regular weekdays. That is, we assume the choice of

Tuesday (as opposed to Monday, Wednesday or Thursday) as the cheap ticket day is not

related to demand conditions.

Under this assumption, an indicator variable for Tuesdays

represents a valid instrument for prices.

Moreover, it is an important instrument, ac-

counting for much of the variation in prices. We note that we are unable to explicitly test

this assumption. Because the vast majority of weekly price variation is due to Tuesday

discounts, we are unable to separately identify variation in attendance on Tuesdays from

Our correspondence with industry participants has not yielded a conclusive explanation for the emer-

gence of “Cheap Tuesdays”. However, the propensity for public holidays to fall on Mondays and new

movies to be released on Thursdays suggests a narrowing down of the available days for an oﬀ-peak

discount that is unrelated to demand (once we control for public holidays and opening days).

In fact, in estimation we include a ‘cheap day’ dummy variable as four independent cinemas actually

oﬀer a cheap Monday ticket and one cinema oﬀers a cheap Thursday ticket in our sample. Further details

are provided in Section 4.

variation in price on Tuesdays. However, we have no reason to suspect demand diﬀers

systematically between Mondays, Tuesdays, Wednesdays, and Thursdays. A consequence

of this choice of instrument is that much of the identiﬁcation of the price elasticity of

demand stems from temporal variation in prices as opposed to cross-sectional variation.

The proﬁt maximisation problem of a cinema is a complicated one. In particular, we

see the consideration of ancillary sales to be an important issue. We are not armed with

data to rigorously tackle this problem.

Accordingly, we do not introduce supply side

moment conditions, but rely only on our demand model to estimate demand parame-

ters. Instead, given our estimated demand parameters, we consider the cinema’s revenue

maximisation problem in the absence of concerns about ancillary sales. Given the likely

positive relationship between cinema attendance and concession sales, we argue that this

places an upper bound on the cinema’s proﬁt-maximising prices.

As in most applied settings, our data constrain the performance of our estimation

strategy. In particular, we rely on repeated observations of a single (large) geographic

market. This provides cross-sectional variation between connected local markets, but

not between geographically separated markets. Our data exhibit intra-week temporal

variation in price, but no other systematic time-series price variation; and cinemas charge

the same price for all movies screened on a given day. Hence, it is intra-week temporal

variation in price coupled with cross-sectional variation at the level of a cinema (rather

than a ﬁlm) that identiﬁes our demand estimates. Further, ﬁlms tend to be introduced

simultaneously across multiple cinemas, constraining our ability to identify heterogeneity

in preferences for ﬁlms. We return to these issues in the discussion of our results.

To preview our results, consistently across the set of speciﬁcations we consider, we

observe that: cinema demand is relatively elastic, with the median own-price elasticity of

a ﬁlm-at-theatre around 2.5 or higher; cross-price elasticities are quite low, leading us to

believe that much substitution takes place with the outside good; and there are intuitive

relationships between cinema attendance and a range of ﬁlm-, cinema-, and time-speciﬁc

characteristics. Both our daily and weekly models suggest that the eﬀect of discounting

has been not only a market expansion, but an increase in revenue. Finally, our revenue-

maximisation problem is consistent with systematic overpricing for a substantial subset

of cinema tickets. For a typical ﬁlm in our dataset, our demand estimates suggest that

a price reduction would raise revenue without stretching screening capacity. However,

for a subset of ﬁlms (such as opening week ﬁlms with wide release), it is plausible that

screening capacity could be constrained in the presence of substantial discounting.

Our research bears most similarity in its method to the studies of Davis (2006), Einav

(2007) and Moul (2007, 2008) in that we adopt a discrete choice approach to modeling de-

mand. Einav (2007) and Moul (2007) both employ nested logit models on weekly revenue

data (observed at the national level), exploring seasonality of demand and word-of-mouth

By contrast, Davis (2006) and Moul (2008) attempt to overcome this problem by imposing assump-

tions about the relationship between these variables based on aggregate industry data.

It is worth noting that we perform a demand estimation exercise rather than a forecasting exercise.

Cinema managers are likely to have additional information at their disposal – such as ﬁlm- and session-

speciﬁc attendance information as it develops. If our demand study reveals opportunities to proﬁtably

vary price based on observable information, a forecasting exercise could be even more revealing. However,

an important complicating factor is the role of word-of-mouth.

eﬀects, respectively, whilst Moul (2008) uses similar data to explore distributor conduct

in terms of rental pricing and advertising. Our data and method, however, most closely

resembles Davis (2006) in that we use daily ﬁlm-at-theatre revenues and follow the ap-

proach of Berry (1994) and Berry et al. (1995) by employing a random coeﬃcients model.

Like Davis (2006), we exploit information about the spatial distribution of consumers

and theatres in our empirical strategy. Relative to the dataset harnessed by Davis, our

data has a more extensive time-series dimension (365 days compared to seven), but a

more limited cross-section dimension (we only observe one distinct (geographic) market,

in contrast to his 36).

The paper is organised as follows. In section 2 we provide a brief background of the

Australian industry and the speciﬁc market we consider. In section 3 we outline the

discrete choice demand framework. In section 4 we describe the data set. In section 5 we

describe the estimation procedure. In section 6 we discuss the results, and in section 7

we conclude.

2 Industry background and market characteristics

As in many other countries, distribution and exhibition are both highly concentrated in

the Australian industry, with concentration of exhibition especially pronounced as the two

largest theatre circuits (Hoyts and Greater Union) account for more than 77% of sales

in our sample.

Theatrical distribution is dominated by the six major U.S. based studio

distributors who account for 75% of turnover in our sample.

This is also reﬂected in the

number of U.S. productions released relative to the local content. Of the 314 ﬁlms which

opened in 2007, 172 of these were of U.S. production origin whilst only 26 were recorded

as Australian by the Motion Picture Distributors Association of Australia (MPDAA).

Although the cinema industry may be regarded as small by other industry standards, it

is by far the largest of the cultural sectors of the economy and in 2007 took over 895m

Australian dollars (A$) in box oﬃce receipts (MPDAA).

The relationship between ﬁlm distributors and cinema exhibitors operating in the Aus-

tralian market is in many respects similar to the U.S. model. As in the U.S., distributors

and exhibitors operate at ‘arms length’, and the typical exhibition contract resembles

those observed in many other countries with a share division of box oﬃce revenues which

shifts in favour of the exhibitor in the later weeks of a ﬁlm’s run.

In Australia, the

general rate of ‘ﬁlm rental’ (the portion of box oﬃce remaining with the distributor) is

commonly acknowledged to be in the region of 35-40%.

As is the case in most other countries, Australian distributors are legally precluded

from specifying an admission price in the exhibition contract, but can choose not to

In our sample, the Hirﬁndahl-Hirschmann index is 0.33 for exhibition and 0.11 for distribution.

This ﬁgure also includes Roadshow who, whilst not a U.S. studio, operate a joint distribution ar-

rangement with Warner Bros. Roadshow is also jointly owned by major exhibition companies Village

and Greater Union.

Unlike many U.S. exhibition contracts, however, Australian exhibition contracts do not usually in-

clude the exhibitor’s ﬁxed costs known commonly as the ‘house-nut’. The ﬁrst week splits are therefore

usually in the order of 60/40 revenue for the distributor/exhibitor rather than as much as 90/10 as is

often the case in the U.S.

supply a cinema should they deem the admission price too low to be proﬁtable for them.

Exhibitors naturally prefer a lower session price than a distributor given that they receive

high proﬁt margins from the sales of popcorn, drinks and other snacks.

3 Model

3.1 Demand

We employ a random coeﬃcients discrete choice model to estimate demand (see, for

example, Berry (1994); Berry et al. (1995); and Nevo (2001) for a detailed discussion

of this class of model). Our model most closely resembles that of Davis (2006), and

we follow his exposition. Consumer choices depend on ﬁlm and theatre characteristics.

The indirect utility enjoyed by consumer i by attending ﬁlm f ∈ {1, . . . , F

} at theatre

(house) h ∈ {1, . . . , H

} on day t ∈ {1, . . . , T } is given by

ifht

= α

+ x

fht

− λd

+ φ

+ ξ

fht

+ 

ifht

(1)

where p

is an average price that varies by cinema and time

; and x

fht

is a vector of

product characteristics. In particular, x

fht

includes time-varying ﬁlm characteristics (e.g.

an opening day indicator and week of run indicator variables), theatre characteristics

(e.g. number of screens, shopping centre location), and the time of screening (e.g. day of

week, public or school holiday, weather). In the spirit of Davis (2006), consumers incur

travel costs, with d

=k L

− L

k measuring the driving distance between consumer

i and theatre h. Film-speciﬁc ﬁxed eﬀects are captured by φ

. Time-invariant ﬁlm

characteristics (e.g. budget, advertising, reviews, cast, genre) are then recovered in an

auxiliary regression in the manner of Nevo (2001). The remaining error structure includes

a common component, ξ

fht

, capturing remaining unobserved product heterogeneity once

ﬁlm ﬁxed eﬀects, φ

, have been accounted for; and an idiosyncratic term, 

ifht

, with a

type-I extreme value distribution.

Consumer heterogeneity is embedded in our deﬁnition of a consumer type, τ

, D

, ν

, 

), where L

is the consumer’s location, D

is a K

× 1 vector of (potentially

observable) demographic variables, ν

is a K

×1 vector of unobservable characteristics

and 

is a vector of the idiosyncratic disturbances. Heterogeneity in consumer types yields

heterogeneity in preferences over price (α

), other product characteristics (β

), and theatre

location (d

). We deﬁne θ

= [α

, β

] as the vector of individual-speciﬁc parameters, and

= [α, β] as the common component. Following Nevo (2001), we further deﬁne

= θ

+ ΠD

+ Σν

, ν

∼ N(0, I

) (2)

where Π is a K

× K

matrix of coeﬃcients which measures how the idiosyncratic indi-

vidual demographics relate to the product characteristics parameters, and Σ is a diagonal

As discussed in Section 4, we are not able to observe ticket prices paid by individuals. We have created

a (weighted) average ticket price based on the industry information of admission type percentages.

In principle, we could permit heterogeneity in preferences over all K

product characteristics. In

practice, we restrict this to a much more limited set.

scaling matrix. Empirical distributions based on Census data are used for the demographic

characteristics, D

The model is completed with the speciﬁcation of an outside good. The indirect utility

of forgoing cinema attendance can be written

it0

= ξ

+ π

+ σ

+ 

it0

, (3)

where we normalise the mean utility of the outside good, ξ

, to zero.

We deﬁne the scope of the market to be the greater Sydney region within 30km of a

cinema, yielding a market size of just over 4 million people.

We consider two separate

deﬁnitions of a market. Our ﬁrst deﬁnition equates a market with a day: consumers

choose between all available ﬁlms (plus the outside good) on a given day. This deﬁnition

presumes that consumers see at most one movie each day. More restrictively, it prevents

substitution between ﬁlms on diﬀerent days. Under this deﬁnition, the set of consumer

types who choose ﬁlm f at theatre h on day t is

fht

, p

, L

, ξ

; θ) = {τ

| u

ifht

> u

iglt

∀ f, h, g, l s.t. (f, h) 6= (g, l)}, (4)

where x

and ξ

are the (J

×1) observed and unobserved product characteristics, respec-

tively; p

are the (H

×1) observed theatre prices; L

are the (H

×1) theatre locations;

and θ = (α, β, λ, Π, Σ) is a vector of parameters. Our second deﬁnition equates a market

with a week. This permits substitution between ﬁlms on diﬀerent days of the week, while

imposing a maximum of one ﬁlm per week on our consumers. With the majority of new

releases occurring on Thursdays, we deﬁne a week as the period Thursday to Wednesday.

Equation (4) is analogously deﬁned in this context.

The market share of ﬁlm f at theatre h on day t is then given by

fht

, p

, L

, ξ

; θ) =

f ht

∗

(L, D, ν, ) =

f ht

∗

()dP

∗

(ν)dP

∗

(D|L)dP

∗

(L), (5)

where the notation P

∗

(·) describes population distribution functions. The second part of

the equality in equation (5) follows from Bayes’ rule and the assumption of independence

of the error terms (, ν) with location, L, and demographics, D. Again, equation (5) can

be deﬁned in either the daily or weekly market context.

3.2 Simulation of revenue-maximising prices

Plausibly, the marginal cost of the attendance of an additional patron at a capacity

unconstrained cinema is zero. A cinema manager could thus focus on maximising revenue

if a session is not expected to sell out. However, the manager must also account for the

important role played by concession sales.

We do not have data on concession sales or

session-speciﬁc attendance rates. Accordingly, we do not attempt the joint estimation of

parameters of the cinema’s proﬁt maximisation problem. Instead, we simulate revenue-

maximising prices given our estimated demand parameters. Eﬀectively, this delivers us

Additional details are contained in Section 4.3.

See McKenzie (2008) for an entertaining discussion of the relationship between cinema ticket pricing

and concession sales.

the ﬁlm- and theatre-speciﬁc proﬁt-maximising price for capacity unconstrained sessions

were cinema managers to be unconcerned with concession sales. In our sample, average

attendance rates are low (we discuss this in more detail in Section 6). Thus, we view the

omission of concession sales to be the more serious limitation. If sales of concession items

are positively related to cinema attendance (as we would expect), then our simulation

exercise places an upper bound on proﬁt-maximising prices given our estimated demand

parameters.

For exposition, let us start by assuming the manager of cinema h seeks to maximise

the static proﬁt of cinema h. She then solves the following problem at time t:

max

f ht

}

f =1

f=1

fht

, p

, L

, ξ

; θ)p

fht

, (6)

where M is the size of the market. This leads to a set of ﬁrst order conditions for all ﬁlms

at all theatres:

fht

g=1

∂s

ght

∂p

fht

ght

= 0, t = 1, . . . , T, h = 1, . . . , H

, f = 1, . . . , F

, (7)

where we omit the arguments of s

fht

and its partial derivative for convenience. Rewriting

equation (7) in matrix notation, we have

+ Ω

.∗ D

= 0 (8)

where Ω

is an ownership matrix, discussed below; [X .∗ Y ] indicates element-by-element

multiplication; and D

represents a matrix of partial derivatives of market shares with

respect to prices with typical element D

(a, b) =

∂s

∂p

. We can rewrite equation (8) to

form the basis of a simple recursive algorithm to simulate proﬁt-maximising prices:

k+1

= −



Ω

.∗ D

)



−1

). (9)

Initialising p

to be a J

× 1 zero vector, we iterate equation (9) until convergence. See,

for example, Davis (2010) for details.

We consider four alternative deﬁnitions of the ownership matrix Ω

, corresponding to

four forms of theatre competition. First, we consider the possibility outlined above that

theatre managers seek to simply maximise proﬁts of their own theatre: Ω

(f, g) = 1 if

ﬁlms f and g are exhibited at the same theatre at time t, and 0 otherwise. Next, we

account for the ownership structure of theatres by assuming that each theatre manager

seeks to maximise the proﬁts of the “circuit” (owner) to which her theatre belongs. That

is, Ω

(f, g) = 1 if ﬁlms f and g are exhibited at theatres belonging to the same circuit

at time t, and 0 otherwise. Third, we consider market structure at the distributor level

by assuming that distributors choose prices to maximise the proﬁts of their basket of

exhibited ﬁlms. That is, Ω

(f, g) = 1 if ﬁlms f and g are associated with the same

distributor, and 0 otherwise. Finally, we also examine the joint-revenue maximisation

problem of the industry by deﬁning Ω

as a matrix of ones.

It should be noted that in reality, optimal price setting from the exhibitor or distributor perspective

4 Data

4.1 Film characteristics and other explanatory variables

The data used in this study are primarily derived from Nielsen Entertainment Database

Inc. (EDI). We observe every ﬁlm at every cinema in the greater Sydney region playing

from January 1, 2007 until December 31, 2007. Nielsen EDI track daily revenues of all

ﬁlms playing at all 61 cinemas in this region. This sample is reduced to 50 cinemas

by excluding Sydney’s Darling Harbour IMAX theatre, a number of open-air (seasonal)

cinemas, drive-ins, and occasional theatres on the grounds that they provide something of

a diﬀerent product to the typical cinema experience. Of these 50 cinemas, 13 are owned

by Hoyts, 12 by Greater Union, four by Palace, three each by Dendy and United, with the

remainder being independents. One theatre (Merrylands, an eight screen Hoyts cinema

complex) closed midway through the sample on June 21, meaning we only observed 49

cinemas in the second half of the year. The locations of the 50 cinemas across the greater

Sydney area are shown in Figure 1. Across these 50 theatres 373 distinct titles were

recorded. From these, a further 59 ﬁlms were dropped because they were either re-releases

(45 ﬁlms), or had 6 or less screenings in 2007 (14 ﬁlms). In total we observe 148,680 daily

ﬁlm-at-theatre revenue data points over the 365 days of 2007. The daily ﬁlm-at-theatre

revenue data consistently reﬂect large levels of skew and (excess) kurtosis. In our sample,

the average (median) daily ﬁlm-at-theatre revenue was A$1,288 (A$569), with the top

earning ﬁlm, Harry Potter and the Order of the Phoenix, making A$65,052 on its opening

day at Macquarie Megaplex.

Table 1 provides summary statistics of the 314 ﬁlms used in estimation. Data is

incomplete in relation to some of these variables (in particular advertising, budgets, and

reviews).

Data on total box oﬃce revenue, opening week screens, and advertising were

sourced from the Motion Picture Distributors Association of Australia (MPDAA). At the

national box oﬃce level, the average ﬁlm earned just over A$3.65m, but the median is

less than A$1m. As observed in the daily ﬁlm-at-theatre revenues, the ‘hit’ ﬁlms skew

the revenue distribution markedly as is apparent by the top ﬁlm earning A$35.5m (Harry

Potter and the Order of the Phoenix )—more than ﬁve standard deviations above the

calculated mean.

The average opening week number of screens is also highly skewed,

with the largest opening ﬁlm (Pirates of the Caribbean: At World’s End) taking up 608

screens. Budget data, derived from IMDb, Box Oﬃce Mojo, and Nielsen EDI, are also

skewed, with the most expensive ﬁlm of the sample costing US$300m (Pirates of the

is likely to be confounded by a number of other considerations beyond the simple ownership structure

we have posited. For example, the exhibitor likely considers sales of popcorn, drinks and other snack bar

items in her objective function, while the distributor likely considers ancillary (potentially substitute)

markets related to DVD/Blu-ray sales or on-demand viewing. In addition, many exhibitors practice more

subtle forms of price discrimination with respect to loyalty programs and promotions which would aﬀect

optimal price setting behaviour. Also, the repeated interaction between large distributors and exhibitors

might impact on the nature of price setting. This last consideration is a potential motivation for our

market-level deﬁnition of the ownership matrix Ω

. We are indebted to a referee for drawing our attention

to some of these possibilities.

We, in part, address this problem by the use of ﬁlm ﬁxed eﬀects in estimation.

De Vany and Walls (1996) examine the kurtotic nature of box oﬃce distributions which they attribute

to the leveraging eﬀects from word-of-mouth information transmission.

Caribbean: At World’s End).

Reviews were compiled from weekly Thursday, Friday and Saturday editions of The

Sydney Morning Herald—the second largest circulation newspaper in Sydney and with the

most comprehensive set of ﬁlm reviews available—based on a ﬁve star system. Although

there are many other review sources available to consumers, we argue this particular

source is likely to be amongst the most visible to Sydney ﬁlmgoers and provide the best

proxy for the potential eﬀect of critical reviews. Also, because of the fact reviews from this

source generally appear before, on, or the day after release, this source is likely to capture

any potential ‘inﬂuence’ (beyond simply a ‘prediction’ eﬀect) as discussed by Eliashberg

and Shugan (1997) and Reinstein and Snyder (2005). Review ratings were obtained for

257 out of the total 314 ﬁlms of the sample.

We include a number of ﬁlm-speciﬁc dummy variables to account for the eﬀects of

sequels, stars, awards, genre, and rating. Sequel data were obtained from MPDAA and

Nielsen EDI and represent approximately 6 per cent of the sample. The ‘Star’ variable

was constructed using James Ulmer’s Hollywood Hot list, Volume 6, which rates stars

according to their ‘bankability’ as derived from survey results of numerous industry pro-

fessionals. We classify a star according to whether any of the leading actors were rated as

an A+ or A actor on the Ulmer list. Star ﬁlms represent approximately 13% of all ﬁlms

in our sample.

We also include two dummy variables for the eﬀect of Academy Award nominations

and awards in the categories Best Picture, Best Actor in a Leading Role, and Best Actress

in a Leading role. For the 14 unique ﬁlms which were nominated in these categories, we

assign a value of one to observations for dates equal to and beyond 23rd of January for

nominations, and a value of one to the three winners (The Departed, The Last King of

Scotland, and The Queen) for dates equal to and beyond the 25th of February. We include

three dummy variables for the main genre categories: action, comedy, and drama. The

numeraire category is the composite of all other genres.

Finally, rating is classiﬁed

under G, PG, M, MA15+, and R18+ as deﬁned by the Oﬃce of Film and Literature

Classiﬁcation.

In addition to the award-nomination/-win variables, which are obviously time-variant,

we consider other time-variant variables relating to what point of the run the ﬁlm was at

the speciﬁc cinema of observation. We consider ﬁlms at preview stage (mostly one week

prior to actual release), opening day at theatre, and week-of-run at theatre. As expected,

(unreported) average daily revenues decline at higher weeks of release. We account for

week-of-run in a relatively ﬂexible manner by including individual dummy variables for

weeks 1-10.

We also consider school/public holidays and daily weather as important time-variant

explanatory variables in the local Sydney market. Consistent with Einav (2007), we

observe that ﬁlms typically earn more on public and school holidays. Relative to Einav

(2007), our daily data suggests the additional insight that the peaks are most obvious

in the weekdays rather than the weekend days. We control for weather by including

measures of temperature and rainfall. Our temperature measure is the diﬀerence between

The full data set actually deﬁnes genre over 20 categories. We focus on the largest three. These

collectively account for 73% of all observations.

Only a very small fraction of ﬁlms (1.1%) last longer than 10 weeks in our sample.

the daily maximum temperature and the monthly average, while rainfall is measured by

the daily rainfall. Both temperatures and rainfall are measured at Sydney’s Observatory

Hill weather station as recorded by the Bureau of Meteorology. We are only aware of

two recent studies (Dahl and DellaVigna (2009) and Moretti (2011)) that have considered

weather in broader models of movie demand.

4.2 Theatre characteristics, ticket prices, and admissions

Table 2 summarises the characteristics of the 50 theatres in our sample. There is con-

siderable heterogeneity across cinemas. The largest cinema, George St. in the heart of

Sydney CBD, has 17 screens and seating capacity in excess of 4,100, while the smallest

has just 64 seats. Cinemas located in shopping centres (known as multiplexes) account

for 21 of the theatres, with an average size of just under 10 screens.

Table 2 also includes pricing information by theatre. Our price and quantity data are

constructed from 3 sources. Dataset 1, our primary dataset, described above, contains

daily revenues by theatre and ﬁlm. Dataset 2 contains pricing information disaggregated

by ticket type for each theatre. Most theatres in our dataset had a ﬁxed menu of prices

throughout our sample, with prices varying by ticket type. In most instances, a sepa-

rate menu of prices operated on Tuesdays. Ticket price information was collected either

directly from the cinema, or from the Australian Theatre Checking Service (ATCS). In

instances where there had been a change in ticket price over the year, the highest price

was used.

Dataset 3 comprises annual revenue for the Greater Union national chain,

disaggregated by ticket type. In 2007, within their national chain, the revenue share

of ‘Adults’, ‘Students’, ‘Seniors’, and ‘Children’ was 44.7%, 13.1%, 10.9%, and 3.1%,

respectively.

Our primary revenue data are aggregated across ticket types while our price data are

disaggregated by ticket type. We therefore construct daily weighted average prices and

admissions by theatre and ﬁlm. We use supplementary data on revenues for Greater Union

(Dataset 3), which is disaggregated by ticket type, to construct weights for diﬀerent ticket

types. We then use these weights to calculate weighted average prices and quantities at

the theatre level, aggregated across ticket types.

More precisely, we use the following procedure. We use superscripts to specify datasets

and subscripts to indicate the dimension of variation, and abuse our earlier notation

slightly.

1. Calculate a set of theatre weights by dividing theatre-speciﬁc annual revenue by

aggregated annual revenue from our primary dataset, w

= R

;

2. use these theatre weights and our disaggregated ticket prices to construct weighted

average ticket prices by ticket type, p

hkt

, where the time subscript

indicates intra-weekly variation (e.g. cheap Tuesdays) and k indexes ticket type;

Unfortunately cinema managers were unable to report when these price changes occurred exactly

leading us to use the higher price.

The remainder are made up of group tickets, gift vouchers, promotional tickets and the like.

3. use our Greater Union revenue data to construct quantity-based weights by ticket

type, with quantities calculated as the ratio of revenue to our ticket-type price index,

= R

and weights given by w

= q

);

4. use these weights to construct theatre-speciﬁc prices, aggregated across ticket types,

hkt

; and

5. use our constructed weighted average prices and the revenue data to construct ad-

missions (quantity) data, q

fht

= R

fht

Using this method, the weights we apply are 0.56 to the price of an adult ticket, 0.21

to the price of a student ticket, 0.18 to the price of a child ticket, and 0.05 to the price of

a pensioner ticket. The weighted average ticket price ranged from $5.82 at Campbelltown

Twin-Dumares ($6 adult ticket), to $14.90 at Academy Twin ($16.50 adult ticket). The

nature of temporal variation in prices is highlighted by Table 2. With the vast majority

of theatres oﬀering Tuesday discounts, the theatre-average price is substantially lower on

Tuesdays than for most other days. Four theatres oﬀer cheap Monday tickets (all owned

by Palace) and one theatre oﬀers cheap Thursday tickets (Mt. Victoria Flicks). Of the

remaining 45 theatres, only three independents do not oﬀer cheap tickets.

Using our (weighted) average cinema ticket prices, the top panel of Table 3 provides

summary statistics of aggregated estimated daily admission across all cinemas by day of

week. The estimates suggest, on average, approximately 42,000 people (about 1% of the

population) attend a cinema each day in the greater Sydney area, and that Saturday is the

most popular day of the week followed by Sunday then Friday and Tuesday, which have

approximately equal average (and median) attendance rates. In fact, Tuesday records the

highest attendance in a single day across the sample period on January 2, 2007 where

almost 140,000 individuals were estimated to have patronised a cinema.

One of our critical assumptions in identiﬁcation relies on the fact that weekdays

(Monday-Thursday) are implicitly treated the same by consumers. The top panel of

Table 3 suggests that Monday and Wednesday generate similar levels of attendance but

Thursday tends to attract more attendance. In Australia, however, ﬁlms typically open on

a Thursday. In fact, of the 4,542 openings recorded in this sample, 3,988 (88%) opened on

Thursday. Once the opening day eﬀect is removed from the week day summary statistics,

Thursday attendance is very similar to Mondays and Wednesdays as shown in the bot-

tom panel of Table 3. This is consistent with consumers treating all weekdays (excluding

Fridays) as equal. As discussed in more detail in Section 5, we exploit this observation in

our estimation strategy.

4.3 Market deﬁnition, demographics, and survey data

Our discussion of the data is complete with details of our market size, demographic infor-

mation, and the additional industry survey data we employ as extra moment conditions

in estimation. Table 4 reports summary statistics of the demographic variables we use,

based on Australian Bureau of Statistics (ABS) Census data from 2006. We include “col-

lection districts” (see Figure 2) whose centroid latitude and longitude coordinates place

We use non-Tuesday prices in this construction. That is, p

≡ p

, t 6= T uesday.

it no further than 30kms from a theatre location. We use Google Earth to “geo-code” the

latitude and longitude of each cinema, and use this to create a distance variable from each

collection district to each cinema. All distances are calculated as driving distances. Using

our 30km deﬁnition, the total population of our market (the greater Sydney region) is a

little over 4 million people. Given that the oﬃcial ABS population count is a little over

4.3 million, this gives us approximately 93% coverage of the market. Over this area, there

are a total of 6,587 collection districts with an average of 613 people in each. In our ﬁnal

model, we restrict attention to demographic information on income and age. For these

variables we are able to construct an empirical distribution conditional on location. In

particular, the empirical distribution of age conditional on location, P (a|L), and the em-

pirical distribution of income conditional on age and location, P(y|a, L), are both available

from the Census. This allows us to construct P (D|L) = P (a, y|L) = P (y|a, L)P (a|L).

Finally, we exploit additional information on the proﬁle of the cinema going audience.

In particular, we obtain cinema attendance rates by age in 2007 from Roy Morgan and

Co. Pty Ltd., and cinema attendance rates by income in 2006 from the ABS based on

the Attendance at Selected Cultural Venues and Events (cat no 4114.0). As discussed in

Section 5, we use this information to introduce an additional set of moment conditions.

The Morgan and ABS statistics suggest higher cinema attendance rates for younger people

and higher income earners.

5 Estimation

Our estimation strategy must account for the joint determination of prices and market

shares. Following Berry (1994) and BLP, we adopt a generalised method of moments

(GMM) estimator.

Our ﬁrst set of moment conditions requires the existence of a set

of instrumental variables, Z = [z

, . . . , z

], that are correlated with market price, but

uncorrelated with the unobserved product characteristics, ξ:

(θ) ≡ E (Z

ξ(θ

)) = 0, (10)

where θ

represents the true parameter vector. For a candidate parameter vector, θ, we

solve for ξ(θ) in the usual way. First, we solve for the vector of mean utilities, δ

fht

β + αp

fht

+ φ

+ ξ

fht

, using the market share inversion trick of Berry (1994). Given

fht

, we can then solve directly for ξ

fht

Our second set of moment conditions derives from external information about cinema

attendance patterns:

(θ) ≡ E



ifht

(θ) − s

∗

ifht

|i ∈ D



= 0, m = 1, . . . , L

(11)

where s

ifht

(θ) is the predicted attendance probability of individual i given the parameter

vector, θ; s

∗

ifht

is the attendance probability of individual i, obtained from our external

source; D

is a set of demographic characteristics indexed by m; and expectations are

Further details about the estimation procedure are provided in the appendix.

For a detailed discussion of the integration of such moment conditions into estimation see Imbens

and Lancaster (1994), and for an early application closely related to our context, see Petrin (2002).

taken with respect to ﬁlm, cinema, time, and individual characteristics. This set of

moment conditions thus places discipline on the model’s predicted conditional attendance

probabilities of diﬀerent demographic groups.

Deﬁning ˆg(θ) = [ ˆg

(θ) ˆg

(θ)]

as a vector of sample equivalents of our population

moment conditions, we can write our GMM estimator as

θ = arg min

G(θ) = ˆg(θ)

−1

ˆg(θ), (12)

where

Φ is a consistent estimate of E[g(θ)g(θ)

]. Intuitively, the weighting matrix, Φ

−1

gives less weight to moments with higher variance. Because we include the ﬁlm ﬁxed

eﬀects, φ

, in equation (1), our GMM estimator does not identify the role of time-invariant

ﬁlm characteristics in consumer choice. Following Nevo (2001), we perform an auxiliary

regression to recover these additional parameters.

An important component of the empirical strategy is the choice of instrumental vari-

ables. A great deal of intertemporal price variation stems from the common cinema

practice of oﬀering discounted ticket prices on Tuesdays. We include a dummy variable

for the cheap ticket day in our instrument set. For most cinemas in our sample the cheap

ticket day is a Tuesday, for a small minority of four it is a Monday, and for a single theatre

it is a Thursday. Average attendance is relatively constant during the week with the ex-

ception of Fridays, weekends and opening days. We include dummy variables for Friday,

Saturday, Sunday, and opening day in our set of explanatory variables. Eﬀectively then,

our maintained assumption is that the choice to oﬀer cheap tickets on Tuesdays instead

of Mondays, Wednesdays, or Thursdays, is unrelated to demand conditions. BLP suggest

that rival product characteristics may provide useful instruments. Davis (2006) considers

the characteristics of rival theatres within ﬁve miles of the theatre, such as consumer

service, DTS, SDDS, Dolby Digital, Screens, THX, weeks at theatre, ﬁrst week of na-

tional release, and local population counts (of diﬀerent deﬁnitions). Accordingly, we also

include a range of other instruments which relate to i) the characteristics of the nearest

rival cinema including number of seats, number of screens and distance from the reference

cinema; and ii) the characteristics of all rival cinemas within a certain distance of theatre

h (e.g. total number of cinema screens, seats, or shopping centre theatres within [0,5],

and [0,10] kms of h).

For our additional moment conditions, we use information about attendance rates

conditional on age and income. In particular, we match attendance rates for the age

brackets {15-24}, {25-34}, {35-49}, and {≥ 50}; and the weekly income brackets {<

400}, {400-600}, {600-800}, {800-1000}, {1000-1300}, {1300-1600}, {1600-2000}, and

{≥ 2000}, where all ﬁgures are in Australian dollars.

We close this section by brieﬂy discussing the nature of variation in our data that

identiﬁes our parameter estimates. In principle, we can exploit time-series variation,

cross-section variation within the greater Sydney market, and, because consumers face

transport costs, some variation between local markets within Sydney. In practice, the

variation in price takes a restricted form. The primary source of time-series variation is

the common practice of oﬀering cheap Tuesday tickets. There is very little other time-

series variation in price, with a small number of small theatres oﬀering cheap tickets on

Mondays instead. This time series variation allows identiﬁcation of the average price

sensitivity, α. However, to separately identify heterogeneity in preferences toward price,

we need variation in relative prices. For this we rely on cross-section variation in relative

prices of similar movies at neighbouring theatres in diﬀerent areas.

There is suﬃcient heterogeneity in ﬁlm oﬀerings in our sample to identify mean pref-

erences towards ﬁlm characteristics. We need variation in the mix of ﬁlms to identify

heterogeneity in preferences towards ﬁlm characteristics. In our sample, most new ﬁlms

are introduced simultaneously in many theatres, limiting such heterogeneity. Accordingly,

we struggled to separately identify heterogeneity parameters relating to ﬁlm characteris-

tics. We brieﬂy return to this issue in the discussion of our results.

5.1 Identiﬁcation

Our parameter estimates are identiﬁed by time-series variation, cross-section variation

within the greater Sydney market, and, because consumers face transport costs, some

variation between local markets within Sydney. In practice, the variation in price takes a

restricted form. Most cinemas oﬀered a ﬁxed menu of prices over our sample, with prices

varying by ticket type and day of the week. The primary source of time-series variation

is the common practice of oﬀering cheap Tuesday tickets. In addition, a small number of

small theatres oﬀered cheap tickets on Mondays instead. Cross-section variation is limited

by uniform pricing practices. Cinemas charge the same price for all oﬀerings on a given

day. The source of cross-section variation is then price diﬀerences across cinemas.

The above price variation is suﬃcient to identify the average price sensitivity, α. In

fact, the depth and regularity of price discounting permits precise estimates of α. How-

ever, to separately identify heterogeneity in preferences toward price, we need variation in

relative prices. For this we rely on variation in relative prices of similar movies at neigh-

bouring theatres in diﬀerent areas. The existence of a small number of cinemas oﬀering

discounted prices on Mondays aids identiﬁcation. As we discuss in the next section, we

found our estimates of heterogeneity to be sensitive to speciﬁcation.

There is suﬃcient heterogeneity in ﬁlm oﬀerings in our sample to identify mean pref-

erences towards ﬁlm characteristics. We need variation in the mix of ﬁlms to identify

heterogeneity in preferences towards ﬁlm characteristics. This variation was somewhat

limited, leading to challenges in identifying heterogeneity parameters. Accordingly, we

restricted attention to heterogeneity with respect to the week of run of a ﬁlm. Variation

in week of run identiﬁes mean preferences for recent movies, while we need variation in the

mix of ﬁlm vintages to identify heterogeneity in such preferences. With the coordinated

release of new ﬁlms, such variation was somewhat limited. We brieﬂy return to this issue

in the discussion of our results.

Heterogeneity in movie attendance conditional on product characteristics identiﬁes the

random coeﬃcient on the constant. With regard to our demographic characteristics, we

require variation in attendance rates across cinemas surrounded by local regions exhibiting

diﬀering demographic distributions. With a sample of 50 cinemas, we found that our

supplementary moment conditions (equation (11)) did much of the work in identifying

our age and income parameters, while similar moment conditions were not available to

assist in identifying our travel cost parameter.

Features of our data also had more fundamental implications for our demand model.

As an alternative to our random coeﬃcients model, we also considered a variety of nested

logit models. The nested logit model incorporates heterogeneity by permitting substitu-

tion patterns to diﬀer within and between groups. Relative to the MNL model, estimation

of the (single-level) nested logit model requires inclusion of an inside share variable as an

explanatory variable, where the inside share is the market share of a product within its

product grouping. The principal empirical challenge lies with the potential endogeneity

of this inside share variable; the inside market share of a product is likely related to unob-

served characteristics of the product. Instrumental variables are a common solution; for

example, Ho et al. (2012) and Einav (2007) use this strategy to estimate nested logit mod-

els in similar contexts. In these settings, the presence of multiple markets is an important

element of the instrumental variables strategy. In our setting, we are restricted to a single

market, hampering our ability to devise valid instrumental variables. Consequently, we

do not present estimates of the nested logit model.

6 Results

Parameter estimates are contained in Tables 5 and 6. Table 5 presents estimates of equa-

tion (1), while Table 6 presents the results of an auxiliary regression to recover parameter

estimates for time-invariant ﬁlm characteristics. Columns 1-3 of Table 5 consider our daily

market deﬁnition, while columns 4-6 relate to our weekly market deﬁnition. Columns 1

and 4 present estimates of a simple multi-nomial logit (MNL) model in which our hetero-

geneity parameters are absent, while the remaining columns present estimates from our

random coeﬃcients (RC) model. In our MNL model, demographic variables are included

as additional product characteristics and are considered as ‘distance rings’ around each

theatre following Davis (2006). For example, ‘Pop[0,5]’ and ‘Pop(5,10]’ measure the pro-

portion of the total population (approximately 4 million) living within 5 kilometres of

theatre h, and living between 5 and 10 kilometres from theatre h, respectively. An exam-

ple distance ring is provided in Figure 2. ‘log(Age)[a,b]’ and ‘log(income)[a,b]’ measure

the (log) weighted-averages of the median age and median income, respectively, of each

collection district within the distance ring [a,b], where weights are population proportion

of each collection district within the distance ring. Columns 2 and 5 contain estimates

of the RC model where we allow heterogeneity with respect to consumer location, age

Notice that our empirical setting presents diﬀerent challenges for the nested logit and random co-

eﬃcients models. In particular, the endogeneity problem that surfaces in the nested logit model is less

relevant for the random coeﬃcients model. To see this, compare closely related versions of each model.

The nested logit model with two groups consisting of the outside good and all “inside” goods has similar

economic implications to the random coeﬃcients model in which consumer heterogeneity is limited to

the constant term. Speciﬁcally, both models could generate the same substitution patterns. However,

the econometric challenges presented by each model are diﬀerent. In the nested logit model, the nesting

parameter which determines substitution patterns is identiﬁed by the relationship between the normalised

market share of a product and its inside share. Inferring this relationship is complicated by the likely

correlation of the inside share with unobserved product characteristics. By contrast, with the random

coeﬃcients model, the heterogeneity parameter is determined by the variance in the outside share condi-

tional on product characteristics. The relationship between unobserved product characteristics and the

variance in the share of the outside good is likely to be much weaker, and the same endogeneity problem

does not arise.

and income, and heterogeneity in preferences for the outside good and attendance in the

opening week of a ﬁlm. In columns 3 and 6, we include, in addition, heterogeneity in

preferences over price.

The coeﬃcients on price suggest that demand is relatively elastic. In the MNL model

and the RC model that omits the price heterogeneity term, the price sensitivity parameter

is in the vicinity of −0.2 for each speciﬁcation.

This translates to a median ﬁlm-level

own-price elasticity of around 3.34 for the daily RC model (column 2) and 2.45 for the

weekly RC model (column 5). This magnitude is similar to other (mostly time series)

studies which have found elastic own price demand.

Our estimates of mean preferences

towards price were sensitive to the inclusion of heterogeneity in price preferences, and this

is particularly evident in our daily model estimates of column 3. However, the implied

estimates of demand elasticities are somewhat less sensitive. We estimate median ﬁlm-

level own-price elasticities of 3.91 and 1.72 for the daily (column 3) and weekly (column 6)

models, respectively. In (unreported) ﬁrst stage regressions for our MNL model, our cheap

ticket indicator variable plays an important role, accounting for much of the variation in

price.

We include time-variant theatre-speciﬁc ﬁlm variables relating to previews and opening

day sessions, and we include indicator variables (unreported) for each week of the run of

a ﬁlm. Consistent with Davis (2006), Einav (2007), and Moul (2007), consumers prefer

to see a ﬁlm earlier in its run with opening day being particularly attractive. Interest in

movie attendance declines approximately linearly with the week of the run, particularly for

the ﬁrst 8 weeks of a movie’s run (which accounts for the bulk of our data). The numeraire

is a ﬁlm running beyond week 10 of its release, and the Preview coeﬃcient is consistent

with interest similar to a mid-run ﬁlm. Academy Award nominations have a mixed

relationship with attendance, but the eﬀect of a win is estimated to be negative. This is a

likely manifestation of the fact that the eventual winners had all spent considerable time

in cinemas prior to their wins.

Saturday followed by Sunday, followed by Friday are the most popular days, with

coeﬃcients relative to a non-Friday weekday numeraire. Public and school holidays also

attract movie goers. Weather also plays a role, with rainy days and cooler days tending

to draw larger attendances. Turning to theatre characteristics, we see that location in

a shopping centre and the number of cinema screens (at the theatre location) are both

associated with greater attendance.

In the MNL model, the fact that the coeﬃcient of ‘Pop[0,5]’ is substantially greater

than that of ‘Pop(5,10]’ is consistent with travel costs associated with cinema attendance

as in Davis (2006). Against a-priori expectations, we see that an increase in the median

age increases attendance, and consistent with a-priori expectations an increase in median

weekly income is associated with increased attendance, with these relationships being

In unreported OLS estimation, when price was not instrumented the price coeﬃcient was found to

be in the region -0.15 to -0.17, i.e. less elastic in all speciﬁcations. This is consistent with expectations

given that price endogeneity creates an upward bias on the OLS estimator.

For example, Dewenter and Westermann (2005) ﬁnd the own price elasticity of demand to be in the

range of 2.4-2.76 using annual German data between 1950 and 2002.

Notice that, while our speciﬁcation of the dynamic path of attendance is quite ﬂexible, it is still

restrictive: we impose the same dynamic pattern of attendance for all ﬁrms. Our results suggest that the

dynamic path of attendance is diﬀerent for these successful ﬁlms.

weaker or even negative at greater distances (i.e. 5 to 10 kilometres away). This suggests

that the demographic proﬁle further away from a cinema has little direct bearing on

cinema performance. These observations are consistent with the existence of travel costs

in cinema attendance.

Table 6 presents coeﬃcient estimates on time-invariant ﬁlm characteristics. As we

might expect, there is a positive relationship between attendance and a ﬁlm’s budget and

advertising spending (with the exception of our daily model allowing for price heterogene-

ity), while screening a ﬁlm at a greater number of locations dilutes the audience at any

one theatre. Sequels, and ﬁlms attracting favourable reviews are associated with larger

audiences. We observe a negative relationship between attendance and the presence of

stars in a ﬁlm. A possible explanation is that the ﬁlm’s budget and advertising already

controls for the appeal of marquee cast. Coeﬃcients on our genre and ratings indicator

variables suggest that attendance is greater for comedies, action movies, and ‘M’ and ’PG’

rated movies, and is lower for dramas.

Consider next the parameters related to consumer heterogeneity in Table 5. Recall

that travel costs enter with a negative sign. In all speciﬁcations, the distance coeﬃcient

is highly signiﬁcant, but estimated to be quite small, particularly for the weekly spec-

iﬁcations. Compared to the eﬀect of a one dollar increase in ticket price, travelling an

additional kilometre to a movie venue appears a relatively minor imposition. This is

consistent with the idea that consumers decide ﬁrst on the ﬁlm they intend to see before

considering the most appropriate venue.

Heterogeneity in the constant term suggests

consumers diﬀer in their propensity to substitute between movies rather than forego movie

attendance altogether. Columns 2 and 5 permit heterogeneity in preferences for opening

week ﬁlms, and columns 3 and 6 allow, in addition, heterogeneity in preferences towards

price. We observe heterogeneity in preferences for opening oﬀerings. However, for our

weekly models, the extent of heterogeneity identiﬁed is quite sensitive to speciﬁcation

changes. We also identify heterogeneity in price sensitivity, but we found the magnitude

of this parameter to be relatively sensitive in alternative speciﬁcations we considered.

Finally, in each of these speciﬁcations, we also consider the relationship between cinema

attendance and local demographic characteristics. We do not ﬁnd a consistent relation-

ship between attendance and the local proportion of young adults (those aged 15-30),

while we do ﬁnd a positive relationship between log income and attendance.

As we presaged in Section 5.1, our empirical setting constrains our ability to identify

heterogeneity parameters and this led to sensitivity in our estimates. The restrictive na-

ture of price variation in our sample limited our ability to separately identify the mean

and variance of preferences for price.

The tendency of cinemas to coordinate the release

of new ﬁlms hampered the identiﬁcation of the random coeﬃcient on opening week ﬁlms.

Similar considerations led us to rule out more ﬂexible speciﬁcations of consumer hetero-

Indeed, according to a Cinema and Video Industry Audience Research survey (conducted by the

Cinema Advertising Association) the majority of people decide which ﬁlm to see in advance of their

visit (CAVIAR Consortium, 2000). An additional complication is that some movie goers may see movies

near their workplace rather than near their home. We calculate distances relative to the distribution of

residential rather than commercial locations.

For example, we note that, while the random coeﬃcient on price is precisely estimated in the models

presented, this coeﬃcient is quite sensitive to changes in speciﬁcation. We have omitted other hetero-

geneity parameters for this reason.

geneity. For the results that follow, we focus attention on the random coeﬃcients model

contained in columns 2 and 5. This speciﬁcation allows heterogeneity over preferences for

opening week attendance but not over price.

6.1 Elasticities

Our demand estimates yield ﬁlm-level median and mean elasticities of 3.34 and 3.13,

respectively, for the daily model, with a standard deviation of 0.45. Elasticities for the

weekly model are somewhat lower, with a median, mean, and standard deviation of 2.45,

2.30, and 0.33, respectively. These suggest that ﬁlm-level demand is relatively elastic. At

the market level, estimated elasticities are lower but less than one. We obtain market-level

median elasticities for the daily and weekly models of 2.27 and 1.26, respectively.

Tables 7-10 detail a selection of demand elasticities, disaggregated by week of run and

by cinema.

Table 7 presents summary information on ﬁlm-level own-price elasticities

for the daily and weekly models. The daily (weekly) model is presented in the columns on

the left (right). In the top panel, we show elasticities by the week of a movie’s run. Our

speciﬁcation allows heterogeneity in preferences for opening week ﬁlms, but does not ad-

mit additional heterogeneity over the life of a ﬁlm. The variation in own-price elasticities

beyond week one of a ﬁlm then stems from changes in the mix of ﬁlms and cinemas con-

ditional on week. The bottom panel presents analogous information indexed by cinema.

We see a greater degree of variation in own-price elasticities, reﬂecting heterogeneity in

preferences across cinemas with diﬀerent locations and local demographic conditions.

Table 8 presents median ﬁlm-level cross-price elasticities by week of run. Estimates

for the daily (weekly) model are presented in the top (bottom) panel. The ﬁrst two rows

and columns represent previews and opening days, with the remainder increasing in week

of run. Element (j, k) contains the median price elasticity of a ﬁlm screening in week j −2

with respect to the price of a ﬁlm screening in week k−2. As we can see from the diagonal

for both market deﬁnitions, elasticities tend to fall with week of run as more consumers

switch to the outside good. The weekly market deﬁnition admits a larger set of substitute

products. The propensity to substitute to any speciﬁc product is then reduced, leading

to lower estimated cross-price elasticities for the weekly model.

Table 9 presents analogous information with cross-price elasticities disaggregated by

cinema. Again, we see predominantly lower elasticities in the weekly model, reﬂecting

the greater number of substitute products. The higher estimated travel costs of the daily

model are also reﬂected in the substitution patterns. We observe a greater sensitivity to

location in the daily model. In particular, cross-price elasticities for ﬁlms within the same

cinema are markedly higher in the daily model, but not the weekly model.

Table 10 presents cinema-level cross-price elasticities. Diagonal elements represent

own-price elasticities, and oﬀ-diagonals contain cross-price elasticities. At the cinema

level, demand is still elastic, with own-price elasticities in the vicinity of 3 - 3.5 for most

cinemas in the daily model and in the range 2 - 2.5 for most cinemas in the weekly model.

This ﬁnding is consistent with our conjecture that the daily model may overstate the

extent of market expansion due to the daily model not permitting substitution between

See, for example, Nevo (2000) for details on the calculation of demand elasticities in a similar context.

days—by deﬁnition. Once we aggregate to the cinema level, we see noticeable substitution

across cinemas. In the daily model, the higher estimated travel cost parameter is again

reﬂected in elasticities that are more sensitive to location.

6.2 Market expansion or cannibalisation?

The eﬀect of the entry of a new product into a market can be decomposed into a mar-

ket expansion eﬀect (attracting new customers to the market), a market stealing eﬀect

(poaching customers from rival ﬁrms), and cannibalisation (diverting customers from one

of your existing products to the new product). We could think of the eﬀect of a decrease in

price in similar terms. In this section, we discuss the extent to which our estimates point

to a market expansion eﬀect arising from the policy of cheap Tuesday cinema pricing.

More pertinently, we are interested in whether discount pricing has led to an expansion

in revenues.

The major source of price variation in our data set is the discounts oﬀered on ﬁlms

shown on Tuesdays at most theatres. Our daily model, by deﬁnition, does not permit

substitution across days; the only products in the consumer’s choice set are the movies of-

fered on a given day (and the outside good). Hence, when prices are lowered on Tuesdays,

the increase in consumption is at the expense of other movies shown on Tuesdays and the

outside good. With most movies receiving discounts on Tuesdays, the aggregate eﬀect is a

decrease in the market share of the outside good; that is, a market expansion. In practice,

some consumers might substitute away from movie consumption on a Wednesday when

they decide to see a movie on a Tuesday. By ignoring this, our daily model overstates the

market expansion eﬀect of a decrease in prices.

Our weekly market deﬁnition is designed to overcome this limitation. Our weekly

model incorporates in the choice set all ﬁlms at all theatres showing in the week. Con-

sumers are therefore able to substitute between movies shown on diﬀerent days of the

week. This opens up the possibility that the “cheap Tuesday” policy has led to substi-

tution away from other days in the week. In fact, in this speciﬁcation, consumers see at

most a single movie over the week. That is, any consumer attending a movie on a Tues-

day cannot also attend on Wednesday. This speciﬁcation may therefore also place too

much restriction on consumer behaviour. In practice, some consumers who are attracted

to cheap Tuesday movies may decide not to visit the cinema on other days in the week,

but some consumers may be willing to attend more than once in the week. Consequently,

our weekly market deﬁnition has the potential to overstate the degree of cannibalisation

and/or market stealing.

Because we are unable to account for all of the sources of preference heterogeneity

for movies, whether our weekly model overstates or understates the extent of market

expansion is ambiguous. In particular, we do not allow for heterogeneity in preference

towards the day of screening of a ﬁlm. To see why this may be important, consider the

extreme case provided by the simple MNL with our weekly market deﬁnition. It is well

known that under the MNL, substitution patterns are driven by market shares: consumers

substitute to products in proportion to their market share. Consider the preferences of

a consumer contemplating seeing ﬁlm f shown at theatre h on a Tuesday. In the weekly

model, also included in her choice set are ﬁlm g shown at theatre h on a Tuesday and

ﬁlm g shown at theatre h on a Wednesday. Her substitution patterns to either of these

ﬁlms will be identical because they share the same characteristics (except possibly price)

and thus have the same market share. We may suspect that in practice consumers will be

more willing to substitute to ﬁlms screening on the same day. The implications for our

estimates of the market expansion eﬀect are ambiguous, but we have no reason to suspect

market expansion is substantially overestimated in our weekly model.

Both our daily and weekly models suggest that the eﬀect of discounting policies on

Tuesdays has led to an increase in revenue. Demand elasticities are greater than 1 at

the ﬁlm, cinema, and market level with both market deﬁnitions. In both speciﬁcations

the outside good has a large market share, and much of the substitution is away from

the outside good. In the next section, we examine the implications for proﬁt-maximising

prices.

6.3 Revenue-maximising prices

In Table 11, we present revenue-maximising prices for a selection of cinemas based on our

demand estimates. We present results from both the daily and weekly models. Results

are based on a selection of cinemas for screenings taking place on January 4.

The ﬁrst

column presents the actual price oﬀered at a speciﬁc cinema. The left (right) hand side

of the table contains revenue-maximising prices for the daily (weekly) model. Revenue-

maximising prices are calculated for a range of ownership structures. Columns (1-4)

for each market deﬁnition present optimal prices based on cinema-level, circuit-level,

distributor-level, and market-level ownership, respectively. In each speciﬁcation, revenue-

maximising prices are below actual prices. Optimal prices are higher for the weekly model,

consistent with our lower elasticity estimates for the weekly model. Optimal prices are

also higher for more concentrated market structures, with optimal prices under monopoly

ownership in the weekly model approaching the observed level of prices. Optimal prices at

the circuit level are similar but sometimes higher than at the distributor level, reﬂecting

greater concentration of ownership at the circuit level. Consequently, our results do not

suggest a substantial conﬂict between distributors and exhibitors.

Recall from the discussion in Section 3.2 that we implicitly impose two main assump-

tions: cinemas are capacity unconstrained, and concession sales do not enter the proﬁt-

maximisation problem. Under these assumptions, optimal prices are quite low relative

to prevailing cinema prices. In light of this result, it is worth brieﬂy interrogating our

maintained assumptions.

To investigate the importance of capacity constraints, we focus on a selection of our

data for which we have more detailed information. We have session time information

for the 13 largest multiplex cinemas in our sample over four complete weeks in April

2007.

This dataset comprises 21,206 session times covering 4,821 daily ﬁlm-at-theatre

data points across 41 unique ﬁlms, and represents approximately 3.3% of our full sample.

With screens (seats) ranging from 10 to 17 (1,980 to 4,112), these cinemas are larger than

average in our dataset. The average seats-per-screen at these 13 locations ranges from

A more detailed discussion of this issue is available from the authors on request.

Results are not sensitive to our particular selection of cinemas and date.

Session time information was collected from old newspapers using an optical reader.

168 to 270, with the average cinema screen among these catering for 217. We calculate

average daily capacity for a ﬁlm-at-theatre by multiplying the average seats-per-screen

by the average number of daily screenings-per-ﬁlm. On average each ﬁlm screened 4.4

times per day with a standard deviation of 2.48. Naturally, new release and more popular

ﬁlms tend to be allocated a greater number of sessions each day. Restricting attention to

opening week ﬁlms, the average number of daily sessions increased to 5.37. A number of

popular ﬁlms had signiﬁcantly more screenings than this average. For example, the ﬁlm

300 occupied 15 sessions per day in its opening week at two locations. Accordingly, we

consider further subsets of our data contingent upon national opening week screen count.

Conditioning in this manner we observe average (opening week) daily sessions for ﬁlms

opening on more than 200 and 300 screens as 7.38 and 8.95, respectively, which would be

regarded as a large (wide) release in the Australian industry.

This capacity information is contained in the far right column of Table 12.

The

remaining columns contain information about actual and simulated attendance for our

April selection of cinemas and ﬁlms. Columns from left to right contain, respectively,

information based on actual attendance, model simulated attendance based on actual

prices, and model simulated attendances based on cinema-, circuit-, distributor-, and

market-based revenue maximisation. The top (bottom) panel contains information based

on our daily (weekly) model. Rows contain information about diﬀerent cuts of this data:

the ﬁrst row uses this full dataset; the second row restricts attention to ﬁlms in their

opening week; and the next two rows, respectively, further restrict attention to ﬁlms

opening on more than 200 and 300 screens nationally.

The ﬁrst row (“All Sessions”) of each panel suggests that there is substantial excess

capacity on average in the data. Further, our model simulations suggest excess capacity

for a sizeable selection of screenings even if cinemas were to substantially reduce prices.

However, once we restrict our attention to more popular ﬁlms, capacity constraints start

to bind. Taken together, these results paint a picture of an industry with substantial

excess capacity for the vast majority of screenings, but with binding capacity constraints

for a small selection of screenings.

We are unable to bring direct evidence to our second maintained assumption; that

cinema managers do not consider concession sales. If concession sales are positively related

to attendance (as we would expect), then our results place an upper bound on optimal

prices for the vast majority of sessions which are anticipated to be capacity unconstrained.

This suggests non-trivial gains from deviating from the practice of uniform pricing across

ﬁlms.

Across the full sample of 314 ﬁlms, opening screens above 200 and 300 represent approximately the

75th and 85th percentiles, respectively, of this variable.

We do, of course, realise that cinema operators manage with-in theatre auditoria as well as number

of sessions during the course of a ﬁlm’s run but do not attempt to integrate this into our exercise. Given

the likely allocation of larger capacity auditoria for new ﬁlms, this would subsequently increase capacity

even further than our estimates.

Note that these sample selections are based only on (a minimal set of) observable information for

cinema managers. The week of a ﬁlm’s run is clearly an important determinant of attendance, while the

number of opening week screens will be related to the industry’s forecast of attendance.

7 Conclusion

In this paper, we develop a random coeﬃcients discrete choice model of cinema demand

using a large sample of daily ﬁlm-at-theatre box oﬃce revenues from the Sydney region

over the 365 days of 2007. With price uniformity across ﬁlm and session a common feature

of movie markets, a critical component of our identiﬁcation strategy derives from the

cheap Tuesday ticket prices which characterise the Sydney market. We ﬁnd an intuitive

relationship between attendance and a range of characteristics which relate to the ﬁlm,

theatre, and timing of consumption.

We ﬁnd that movie demand is price elastic. This suggests that the “cheap Tuesday”

discounting experiment has been successful at raising revenue. This conclusion survives

several robustness checks. Elasticities are greater than one at the ﬁlm-, cinema-, and

market-level. This result holds both using our daily market deﬁnition in which substitu-

tion across days of the week is not permitted, and using our weekly market deﬁnition in

which such substitution is mandated.

Our results imply that cinemas could increase proﬁts by oﬀering more oﬀ-peak pricing,

and by employing variable ﬁlm pricing practices. This doesn’t necessarily imply that the

pricing strategy should be particularly complex – it could be as simple as categorising

certain ﬁlms as ‘blockbusters’, or oﬀering a ‘new release’ and ‘old release’ price contingent

upon some (commonly known and pre-speciﬁed) week of the run. For example, our

simulations suggest mid-run ﬁlms could be discounted without running into screening

capacity constraints.

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Appendix

In this appendix, we provide additional detail on our demand estimation algorithm. Much

of the material is drawn from Berry et al. (1995) and Nevo (2000, 2001), where additional

discussion can be found. We break the demand estimation details into several components.

We ﬁrst outline the calculation of the GMM objective function for a given parameter

vector. Next, we discuss the gradient of the vector of moment conditions, required both for

the application of gradient-based optimisation algorithms, and the calculation of standard

errors. We also outline the calculation of the variance-covariance matrix of the objective

function.

First, let us brieﬂy introduce some additional notation. Let J =

t=1

h=1

the number of observations in the dataset, with J

h=1

the number pertaining to

period t. We deﬁne S to be the J ×1 vector of observed market shares and S

the J

×1

vector of observed period t market shares. Similarly, s(x, p, L, ξ; θ) is the J × 1 vector

of predicted market shares from our model, and ˜s(τ, x, p, L, ξ; θ) is the J × NS matrix

of purchase probabilities of NS simulated individuals drawn from P

∗

(L, D, ν). Following

Nevo (2001), we partition the parameter vector into two components, θ = (θ

, θ

). An

important interim step in estimation is the calculation of the vector of mean values, δ.

Given S, the parameter vector θ

= (λ, Π, Σ) enters δ = δ(S, θ

) in a nonlinear manner.

By contrast, the vector θ

= (α, β) can be extracted as a linear function of δ(S, θ

The GMM objective function

Calculating the GMM objective function, G(θ), involves several steps:

1. given the vector of non-linear parameters, θ

, and a vector of observed market shares,

S, solve for the vector of mean values (deﬁned below) of each product, δ(S, θ

);

2. given θ

and δ(S, θ

), solve for the vector of linear parameters, θ

;

3. calculate the moment conditions, ˆg

(θ) and ˆg

(θ), and the GMM objective function,

G(θ).

We decompose the indirect utility enjoyed by consumer i by attending ﬁlm f ∈

{1, . . . , F

} at theatre (house) h ∈ {1, . . . , H

} on day t ∈ {1, . . . , T } into three com-

ponents:

ifht

= δ

fht

+ µ

ifht

+ 

ifht

(13)

fht

= x

fht

β + αp

fht

+ γ

+ ξ

fht

(14)

ifht

= x

fht

(ΠD

+ Σν

) − λd

, (15)

where δ

fht

is the mean value that is common to all consumers, µ

ifht

describes how ob-

servable (D

) and unobservable (ν

) characteristics of consumer i aﬀect her preferences,

and 

ifht

is the familiar type-1 extreme value idiosyncratic unobservable.

Our ﬁrst exercise is to calculate δ, which is implicitly deﬁned by the relationship

(δ

, θ

) = S

. (16)

In turn, we calculate the market share vector, s, by aggregating over the individual

purchase probabilities of consumers. We simulate NS consumers, with consumer i’s

characteristics (L

, D

, ν

) drawn from P

∗

(L, D, ν). The purchase probabilities of consumer

i are given by

˜s

ifht

(δ, θ

) =

f ht

+µ

if ht

, 4

= 1 +

glt

+µ

iglt

, (17)

with the market share vector then determined by

fht

(δ

, θ

) =

˜s

ifht

(δ

, θ

). (18)

To solve for the vector of mean values, we exploit the contraction mapping of BLP,

k+1

= δ

+ ln s

(δ

, θ

). (19)

Our next step is to solve for the linear parameters, θ

. These can be obtained from

the ﬁrst order conditions of our GMM objective function,

ˆg(θ)

−1

∂ˆg(θ)

∂θ

= 0. (20)

Restrict attention to the linear parameters, θ

, and note that

∂ˆg

(θ)

∂θ

= 0. Under the

assumption that our two sets of moment conditions, g

(θ) and g

(θ), are independent, we

can then write the linear parameters as a function of the mean value vector:



−1



−1

δ(S, θ

), (21)

where

−1

is a L

×L

partition of the weighting matrix, corresponding to the covariance

matrix of the set of moment conditions, g

(θ).

Given the vector of mean utilities, δ(S, θ

), we can use equation (14) to solve for the

structural error term, ξ(θ). Our ﬁrst set of moment conditions is then given by

ˆg

(θ) =

ξ(θ). (22)

Let Υ be a L

× NS matrix of inclusion in demographic groups, with typical element

= 1{i ∈ D

}. Our second set of moment conditions is given by

ˆg

(θ) = Υ

t=1

h=1

f=1

˜s

.fht

(θ)

i=1

− s

∗

, (23)

When we deﬁne a market as the set of ﬁlms screened over a week, we must of course sum over the

ﬁlms shown during the week.

where ./ indicates element-by-element division, and (abusing notation slightly) s

∗

is a

×1 vector of annual cinema attendance probabilities of each of our demographic groups.

Combining the moment conditions, ˆg(θ) = [ ˆg

(θ) ˆg

(θ)]

, we can write our objective

function for given parameter vector, θ,

G(θ) = ˆg(θ)

−1

ˆg(θ), (24)

where

Φ is a consistent estimate of E[g(θ)g(θ)

Our method for dealing with our ﬁlm ﬁxed eﬀects follows Nevo (2001). We proceed in

two stages. First, we obtain our GMM estimator,

θ, by minimising G(θ) using equation

(24). This requires removing from x any explanatory variables that are speciﬁc to each

ﬁlm and time invariant, and including a set of ﬁlm indicator variables. We then perform an

auxiliary regression of our ﬁlm-ﬁxed explanatory variables on the estimated ﬁxed eﬀects,

yielding



−1



−1

, (25)

where X contains the ﬁlm-speciﬁc time-invariant explanatory variables,

is the vector

of coeﬃcients on the ﬁlm-ﬁxed eﬀects, and V

is the variance-covariance matrix of

The gradient of the moment vector

The gradient of the moment vector is required for calculation of the variance covariance

matrix of the parameter vector, θ, and for the use of gradient based optimisation methods.

The gradient is given by

∂ˆg(θ)

∂θ



∂ˆg

(θ)

∂θ

∂ˆg

(θ)

∂θ



, (26)

where the gradient of our ﬁrst set of moment conditions is

∂ˆg

(θ)

∂θ



∂δ(S, θ

)

∂θ



(27)

and the gradient of our second set of moments is

∂ˆg

(θ)

∂θ

t=1

h=1

f=1

∂˜s

.fht

(θ)

∂θ

i=1

. (28)

The gradient of the mean value vector,

∂δ(S,θ

)

∂θ

, is obtained implicitly by diﬀerentiation of

equation (16):

∂δ(S, θ

)

∂θ

= −



∂s(δ, θ

)

∂δ



−1

∂s(δ, θ

)

∂θ

. (29)

We can simplify the terms on the right as follows:

∂s

fht

(δ, θ

)

∂δ

glt

i=1

˜s

ifht

(1{(f, h) = (g, l)} − ˜s

iglt

) (30)

∂s

fht

(δ, θ

)

∂λ

i=1

˜s

ifht

˜s

iglt

− d

(31)

∂s

fht

(δ, θ

)

∂σ

i=1

˜s

ifht

fht

−

˜s

iglt

glt

(32)

∂s

fht

(δ, θ

)

∂Π

i=1

˜s

ifht

fht

−

˜s

iglt

glt

, (33)

where σ

is the lth diagonal element of the scaling parameter matrix, Σ; x

is the lth prod-

uct characteristic; and Π

describes the impact of the interaction between demographic

characteristic d and the lth product characteristic. The term

∂˜s

.f ht

(θ)

∂θ

, required for the

gradient of our second condition is implicitly deﬁned above.

The variance-covariance matrix

Deﬁning ˜g(θ) =

∂ˆg(θ)

, the estimated variance-covariance matrix of the vector of GMM

parameter estimates,

θ, is given by

GMM

˜g(θ)

−1

˜g(θ)

−1

˜g(θ)

−1

˜g(θ)

−1

˜g(θ)

−1

, (34)

where

A is an estimate of the sampling variance of

√

Ng(θ) (see, for example, Greene

(2008) for additional details).

Table 1: Film Summary Statistics

Obs. Mean Std. Dev. Min. Median Max

Total Box Oﬃce

300 3,652 6,369 1 904 35,500

Opening Week Screens 293 107 120 1 47 608

Advertising/Publicity

148 1,175 955 489 905 3,535

Budget

190 41,200 47,500 30 21,500 300,000

Review 257 3.15 0.71 1 3 5

Notes: Sources: Nielsen Entertainment Database Inc., MPDAA, IMDb, and Box Oﬃce

Mojo (see text for details).

Total box oﬃce and advertising/publicity are in thousands of

Australian dollars.

Budget is in thousands of US dollars.

Table 2: Theatre Summary Statistics

Obs. Mean Std. Dev. Min. Median Max

Screens 50 6.78 4.36 1 6.5 17

Seats 50 1,544 1,027 64 1,788 4,112

Ticket Price by Day of Week

Monday 50 12.35 1.90 5.82 13.07 14.79

Tuesday 50 9.93 1.63 5.82 10.00 14.90

Wednesday 50 12.74 1.67 5.82 13.49 14.90

Thursday 50 12.69 1.81 5.82 13.49 14.90

Friday 50 12.74 1.67 5.82 13.49 14.90

Saturday 50 12.74 1.67 5.82 13.49 14.90

Sunday 50 12.74 1.67 5.82 13.49 14.90

Notes:

Reported prices are weighted averages across ticket types. See text for details.

Table 3: Daily Total Admission, All Cinemas

Obs. Mean Std. Dev. Min. Median Max

All Days

Monday 53 23,584 20,625 8,730 13,914 97,320

Tuesday 52 47,338 27,725 23,348 35,394 138,903

Wednesday 52 25,471 23,749 9,627 15,327 117,070

Thursday 52 32,492 19,349 13,363 24,086 93,970

Friday 52 44,820 19,039 24,855 38,479 100,053

Saturday 52 65,699 16,235 37,333 61,018 111,511

Sunday 52 52,775 18,177 31,543 47,115 124,793

Total 365 41,690 25,243 8,730 37,034 138,903

Non-Opening Days

Monday 53 23,554 13,914 20,599 8,730 96,894

Tuesday 52 47,191 35,394 27,861 16,566 138,903

Wednesday 52 22,908 15,302 17,388 9,627 78,683

Thursday 52 20,542 13,419 18,392 5,726 90,848

Friday 52 44,476 37,595 19,107 24,249 99,780

Saturday 52 65,661 60,978 16,253 37,289 111,476

Sunday 52 52,758 47,115 18,129 31,543 124,223

Total 365 39,541 35,655 25,611 5,726 138,903

Notes: Daily total admissions are estimates based upon cinema-level weighted average

ticket prices. See text for details.

Table 4: Collection District and Demographic Summary Statistics

Obs. Mean Std. Dev. Min. Median Max

Collection District Population 6,587 613 256.7 0 578 2,765

Minimum Distance to Cinema (kms) 6,587 4.47 5.25 0.02 2.9 29.99

Median Age

6,587 36.58 5.99 17 36 84

Median Weekly Income

6,587 568.2 213.3 0 536 2,000

Notes:

Median age and median incomes are weighted by collection district population.

Table 5: Multinomial Logit and Random Coeﬃcients Model Results

Daily Model Weekly Model

(1) (2) (3) (4) (5) (6)

Price -0.179** -0.248** -1.807** -0.178** -0.182** -0.258**

(0.004) (0.004) (0.016) (0.004) (0.004) (0.004)

Time Variant Film at Theatre Variables

Preview 1.468** 1.501** 1.992** 1.479** 1.556** 1.916**

(0.096) (0.103) (0.161) (0.097) (0.108) (0.131)

Opening Day 0.190** 0.267** 0.861** 0.189** 0.193** 0.280**

(0.011) (0.014) (0.023) (0.011) (0.012) (0.015)

Oscar Nomination 0.080 0.057 -0.354** 0.065 -0.058 -0.056

(0.061) (0.068) (0.094) (0.061) (0.064) (0.104)

Oscar Award -0.489** -0.520** -0.992** -0.496** -0.640** -0.556*

(0.197) (0.211) (0.247) (0.197) (0.200) (0.268)

Week dummies Yes Yes Yes Yes Yes Yes

Day and Date Variables

Friday 0.605** 0.792** 1.875** 0.600** 0.585** 0.578**

(0.007) (0.008) (0.032) (0.007) (0.007) (0.008)

Saturday 1.058** 1.420** 3.545** 1.047** 1.015** 1.009**

(0.008) (0.011) (0.034) (0.008) (0.009) (0.009)

Sunday 0.819** 1.078** 2.528** 0.811** 0.787** 0.786**

(0.008) (0.010) (0.034) (0.008) (0.008) (0.009)

Public Holiday 0.403** 0.734** 1.918** 0.406** 0.490** 0.921**

(0.016) (0.021) (0.036) (0.016) (0.018) (0.029)

School Holiday 0.523** 0.656** 1.504** 0.550** 0.906** 1.164**

(0.017) (0.019) (0.030) (0.017) (0.019) (0.027)

Weather

Rainfall 0.005** 0.007** 0.017** 0.005** 0.006** 0.007**

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

Max to av. Diﬀ -0.020** -0.025** -0.051** -0.020** -0.021** -0.024**

(0.001) (0.001) (0.002) (0.001) (0.001) (0.002)

Theatre Variables

Shopping Centre 0.270** 0.162** 0.402** 0.269** 0.150** 0.144**

(0.024) (0.021) (0.025) (0.024) (0.020) (0.023)

Cinema Screens 0.102** 0.112** 0.144** 0.102** 0.102** 0.093**

(0.003) (0.003) (0.004) (0.003) (0.003) (0.004)

Demographics

Pop[0,5] 6.081** 6.088**

(1.011) (1.011)

Pop(5,10] -0.177 -0.170

(0.499) (0.499)

log(Age)[0,5] 1.119** 1.123**

(0.201) (0.202)

continued...

...continued

log(Age)(5,10] -0.785** -0.790**

(0.181) (0.181)

log(Income)[0,5] 0.440** 0.438**

(0.074) (0.074)

log(Income)(5,10] 0.176** 0.180**

(0.070) (0.070)

Travel Cost

Travel Cost 0.129** 0.114** 0.012** 0.044**

(0.002) (0.004) (0.001) (0.003)

Random Coeﬃcients (Std. Dev.)

Constant 2.397** 0.282** 0.521** 4.017**

(0.020) (0.157) (0.026) (0.050)

Price 0.613** 0.143**

(0.005) (0.002)

Week 2.543** 2.146** 0.207** 10.161**

(0.030) (0.114) (0.058) (0.078)

Demographics

Age*[Constant] -0.146** -0.228** 0.134** -0.067**

(0.001) (0.006) (0.000) (0.001)

log(Income)*[Constant] 0.308** 0.057** 0.598** 0.355**

(0.005) (0.016) (0.002) (0.004)

Constant -32.674** -24.630** -19.277** -32.761** -39.818** -33.263**

(0.191) (0.256) (0.294) (0.191) (0.211) (0.266)

N 148,680 148,680 148,680 148,680 148,680 148,680

Notes: MNL models (1) and (4) include distance ring demographic eﬀects; RC models

(2) and (5) include linear travel cost, and random coeﬃcients on constant and week; RC

models (3) and (6) include linear travel cost and random coeﬃcients on constant, price and

week. See text for full speciﬁcation details. Price is instrumented as discussed in text. All

models include ﬁlm ﬁxed eﬀects. Standard errors clustered at the ﬁlm and theatre level are

in parentheses. * and ** denote two tailed signiﬁcance at 5% and 1% respectively.

Table 6: Film Fixed Eﬀects on Time Invariant Covariates

Daily Model Weekly Model

(1) (2) (3) (4) (5) (6)

Time Invariant Film Variables

log(Budget) 0.738** 0.738** 1.127** 0.749** 0.732** 0.840**

(0.009) (0.012) (0.014) (0.009) (0.010) (0.013)

log(Adpub) 0.134** 0.169** -0.010 0.132** 0.269** 0.356**

(0.010) (0.014) (0.016) (0.010) (0.010) (0.013)

log(OpWkScrns) -0.242** -0.257** -0.501** -0.247** -0.369** -0.439**

(0.011) (0.016) (0.017) (0.011) (0.011) (0.015)

Star -0.481** -0.492** -1.284** -0.494** -0.453** -0.452**

(0.017) (0.023) (0.024) (0.017) (0.019) (0.024)

Sequel 0.193** 0.289** 0.103** 0.195** 0.278** 0.385**

(0.025) (0.032) (0.036) (0.025) (0.026) (0.033)

Review 0.267** 0.288** 0.444** 0.267** 0.299** 0.258**

(0.012) (0.016) (0.018) (0.012) (0.014) (0.017)

Action 0.127** 0.123** 0.393** 0.126** 0.108** 0.202**

(0.025) (0.031) (0.035) (0.025) (0.026) (0.033)

Comedy 0.479** 0.633** 1.304** 0.478** 0.475** 0.509**

(0.023) (0.029) (0.029) (0.023) (0.025) (0.031)

Drama -0.356** -0.380** -0.893** -0.364** -0.388** -0.618**

(0.023) (0.030) (0.032) (0.023) (0.026) (0.032)

M 0.467** 0.437** 0.767** 0.475** 0.452** 0.263**

(0.030) (0.039) (0.046) (0.030) (0.031) (0.040)

MA15+ -0.039 0.179** -0.051 -0.052 -0.008 -0.055

(0.033) (0.044) (0.048) (0.033) (0.036) (0.045)

PG 0.500** 0.612** 1.151** 0.513** 0.543** 0.597**

(0.031) (0.042) (0.048) (0.031) (0.032) (0.041)

R18+ 0.343** 0.365** 0.266** 0.344** 0.346** 0.132

(0.063) (0.072) (0.083) (0.063) (0.066) (0.080)

N 122 122 122 122 122 122

Notes: Estimates derive from auxiliary regression of ﬁlm ﬁxed eﬀects (derived from

models (1)-(6) reported in Table 5) on time-invariant ﬁlm covariates where the complete set

of ﬁlm covariates is observed. From the full set of 314 ﬁlm ﬁxed eﬀects, the complete set of

covariates is observed for 122 ﬁlms.

Table 7: Own-Price Elasticities

Daily Model Weekly Model

Obs Mean Median SD Mean Median SD

Week/Day of Run

Preview 1,508 -3.272 -3.371 0.288 -2.398 -2.471 0.211

Opening Day 4,618 -3.194 -3.323 0.365 -2.363 -2.450 0.268

Week 1 30,317 -3.087 -3.290 0.450 -2.284 -2.449 0.330

Week 2 29,641 -3.126 -3.345 0.450 -2.293 -2.450 0.329

Week 3 25,595 -3.133 -3.346 0.448 -2.296 -2.450 0.328

Week 4 20,768 -3.134 -3.346 0.452 -2.297 -2.450 0.331

Week 5 14,977 -3.141 -3.346 0.448 -2.301 -2.450 0.328

Week 6 10,219 -3.157 -3.363 0.435 -2.312 -2.466 0.319

Week 7 6,613 -3.156 -3.366 0.443 -2.312 -2.466 0.325

Week 8 4,005 -3.166 -3.367 0.435 -2.319 -2.466 0.318

Cinema

George St. 6,036 -3.331 -3.480 0.351 -2.445 -2.550 0.256

Bondi Jn. 4,281 -3.267 -3.402 0.322 -2.397 -2.493 0.236

Broadway 5,497 -3.239 -3.366 0.308 -2.375 -2.466 0.226

Campbelltown 3,975 -3.229 -3.374 0.317 -2.382 -2.476 0.230

Blacktown 4,248 -3.220 -3.344 0.300 -2.361 -2.450 0.220

Warringah 3,950 -3.232 -3.376 0.322 -2.391 -2.485 0.233

Fox Studios 4,786 -3.157 -3.271 0.274 -2.314 -2.396 0.201

Newtown 2,317 -2.900 -3.008 0.268 -2.125 -2.204 0.196

Academy 921 -3.499 -3.692 0.469 -2.565 -2.705 0.344

Cremorne 3,609 -3.273 -3.365 0.220 -2.402 -2.466 0.161

Notes: Own price elasticities derive from models (2) and (5) as reported in Table 5.

Table 8: Cross-Price Elasticities by Week of Run (Film Level)

1 2 3 4 5 6 7 8 9 10

Daily Model

1. Preview 0.000413 0.000278 0.000701 0.000802 0.000559 0.000476 0.000444 0.000477 0.000321 0.000376

2. Opening Day 0.000177 0.003786 0.003887 0.000213 0.000162 0.000122 0.000106 0.000077 0.000076 0.000059

3. Week 1 0.000150 0.003678 0.004129 0.000243 0.000179 0.000143 0.000125 0.000093 0.000090 0.000080

4. Week 2 0.000377 0.000478 0.000529 0.000561 0.000363 0.000283 0.000250 0.000215 0.000179 0.000171

5. Week 3 0.000391 0.000494 0.000539 0.000525 0.000405 0.000283 0.000250 0.000200 0.000187 0.000176

6. Week 4 0.000391 0.000477 0.000519 0.000529 0.000366 0.000321 0.000224 0.000210 0.000168 0.000164

7. Week 5 0.000329 0.000480 0.000521 0.000526 0.000391 0.000259 0.000293 0.000175 0.000198 0.000157

8. Week 6 0.000374 0.000485 0.000541 0.000514 0.000369 0.000319 0.000211 0.000244 0.000170 0.000192

9. Week 7 0.000390 0.000519 0.000556 0.000512 0.000417 0.000284 0.000298 0.000175 0.000173 0.000167

10. Week 8 0.000433 0.000518 0.000541 0.000524 0.000391 0.000317 0.000263 0.000272 0.000188 0.000159

Weekly Model

1. Preview 0.000168 0.000274 0.000333 0.000243 0.000167 0.000142 0.000132 0.000123 0.000093 0.000098

2. Opening Day 0.000161 0.000277 0.000329 0.000233 0.000175 0.000142 0.000121 0.000095 0.000086 0.000077

3. Week 1 0.000159 0.000271 0.000321 0.000231 0.000171 0.000141 0.000121 0.000095 0.000086 0.000077

4. Week 2 0.000160 0.000269 0.000325 0.000267 0.000180 0.000142 0.000128 0.000105 0.000091 0.000081

5. Week 3 0.000166 0.000279 0.000325 0.000253 0.000201 0.000139 0.000124 0.000098 0.000094 0.000083

6. Week 4 0.000166 0.000278 0.000320 0.000250 0.000177 0.000163 0.000112 0.000098 0.000088 0.000079

7. Week 5 0.000139 0.000266 0.000315 0.000251 0.000191 0.000131 0.000151 0.000088 0.000093 0.000076

8. Week 6 0.000136 0.000281 0.000327 0.000240 0.000172 0.000147 0.000103 0.000119 0.000082 0.000085

9. Week 7 0.000160 0.000268 0.000309 0.000246 0.000206 0.000146 0.000143 0.000088 0.000096 0.000074

10. Week 8 0.000161 0.000286 0.000318 0.000235 0.000179 0.000150 0.000130 0.000120 0.000085 0.000083

Notes: Cross price elasticities derive from models (2) and (5) as reported in Table 5. Cell entries i, j , where i indexes row and j

column, give the percent change in market share of i with a one-percent change in price of j . Each entry represents the median of the

elasticities.

Table 9: Cross-Price Elasticities by Cinema (Film Level)

1 2 3 4 5 6 7 8 9 10

Daily Model

1. George St. 0.002004 0.002246 0.001810 0.000034 0.000132 0.002725 0.001211 0.001665 0.001630 0.000447

2. Bondi Jn. 0.002133 0.001949 0.001680 0.000032 0.000115 0.002256 0.001104 0.001668 0.001416 0.000510

3. Broadway 0.002159 0.002129 0.001506 0.000040 0.000132 0.002181 0.001145 0.001647 0.001411 0.000656

4. Campbelltown 0.000046 0.000046 0.000044 0.003270 0.000064 0.000016 0.000033 0.000038 0.000019 0.000060

5. Blacktown 0.000247 0.000224 0.000205 0.000095 0.000696 0.000162 0.000140 0.000180 0.000167 0.000555

6. Warringah 0.003510 0.003153 0.002428 0.000015 0.000121 0.008669 0.001374 0.002847 0.004477 0.002113

7. Fox Studios 0.002183 0.002414 0.001707 0.000032 0.000112 0.002622 0.001124 0.001726 0.001558 0.000672

8. Newtown 0.001988 0.001992 0.001588 0.000044 0.000130 0.001740 0.000746 0.001524 0.001171 0.001242

9. Academy 0.002140 0.002170 0.001727 0.000035 0.000122 0.002673 0.001121 0.000420 0.001578 0.000263

10. Cremorne 0.002571 0.002408 0.001950 0.000023 0.000156 0.005724 0.001152 0.002046 0.002339 -0.000005

Weekly Model

1. George St. 0.000323 0.000362 0.000279 0.000227 0.000187 0.000224 0.000172 0.000203 0.000250 0.000194

2. Bondi Jn. 0.000337 0.000359 0.000278 0.000230 0.000191 0.000220 0.000171 0.000198 0.000255 0.000195

3. Broadway 0.000335 0.000364 0.000272 0.000229 0.000190 0.000216 0.000169 0.000199 0.000257 0.000194

4. Campbelltown 0.000322 0.000351 0.000268 0.000236 0.000194 0.000211 0.000162 0.000189 0.000242 0.000184

5. Blacktown 0.000322 0.000347 0.000263 0.000227 0.000185 0.000206 0.000159 0.000188 0.000244 0.000184

6. Warringah 0.000340 0.000368 0.000276 0.000228 0.000193 0.000211 0.000169 0.000195 0.000257 0.000194

7. Fox Studios 0.000339 0.000370 0.000279 0.000231 0.000192 0.000222 0.000168 0.000200 0.000259 0.000195

8. Newtown 0.000334 0.000362 0.000273 0.000231 0.000193 0.000222 0.000169 0.000184 0.000256 0.000192

9. Academy 0.000330 0.000353 0.000276 0.000222 0.000186 0.000223 0.000170 0.000198 0.000208 0.000192

10. Cremorne 0.000333 0.000366 0.000278 0.000230 0.000195 0.000231 0.000171 0.000195 0.000253 0.000189

Notes: Cross price elasticities derive from models (2) and (5) as reported in Table 5. Cell entries i, j , where i indexes row and j

column, give the percent change in market share of i with a one-percent change in price of j . Each entry represents the median of the

elasticities.

Table 10: Cross-Price Elasticities by Cinema (Cinema Level)

1 2 3 4 5 6 7 8 9 10

Daily Model

1. George St. -3.368187 0.069190 0.066112 0.008034 0.006657 0.080975 0.040610 0.012018 0.006310 0.033386

2. Bondi Jn. 0.095124 -3.327461 0.058108 0.006391 0.005115 0.065113 0.037192 0.010880 0.006132 0.029639

3. Broadway 0.097894 0.060934 -3.301929 0.010105 0.007110 0.063319 0.035443 0.011565 0.005874 0.027766

4. Campbelltown 0.015591 0.008500 0.013008 -3.169197 0.023900 0.000592 0.005193 0.002041 0.000244 0.000922

5. Blacktown 0.016250 0.008968 0.011595 0.032016 -3.297852 0.004154 0.005213 0.001991 0.000713 0.003021

6. Warringah 0.187646 0.104629 0.099427 0.000718 0.003878 -3.076050 0.069407 0.015131 0.009785 0.080700

7. Fox Studios 0.104572 0.068946 0.063763 0.007432 0.005684 0.077193 -3.222685 0.011264 0.006150 0.032105

8. Newtown 0.079199 0.048234 0.049967 0.006817 0.005222 0.042285 0.028186 -2.995928 0.005861 0.021350

9. Academy 0.087644 0.058814 0.056579 0.001624 0.004132 0.059799 0.034558 0.012340 -3.686736 0.027508

10. Cremorne 0.127760 0.076244 0.072116 0.001950 0.004899 0.141992 0.047827 0.012078 0.007150 -3.305150

Weekly Model

1. George St. -2.464277 0.061374 0.055934 0.037604 0.034652 0.033676 0.035011 0.013474 0.006801 0.024095

2. Bondi Jn. 0.086290 -2.431593 0.056449 0.037608 0.034642 0.033934 0.035128 0.013588 0.006826 0.024151

3. Broadway 0.085892 0.061581 -2.410617 0.037647 0.034645 0.033702 0.034982 0.013529 0.006790 0.023994

4. Campbelltown 0.081624 0.058066 0.053207 -2.436776 0.034442 0.031756 0.033232 0.012888 0.006416 0.022838

5. Blacktown 0.081557 0.058105 0.053243 0.037398 -2.415351 0.032085 0.033243 0.012829 0.006407 0.022930

6. Warringah 0.085276 0.060914 0.055583 0.036916 0.034298 -2.451404 0.034544 0.013344 0.006697 0.023926

7. Fox Studios 0.086378 0.061960 0.056140 0.037566 0.034616 0.033981 -2.360810 0.013583 0.006830 0.024117

8. Newtown 0.085629 0.061608 0.056545 0.037802 0.034730 0.033720 0.035130 -2.190355 0.006785 0.023898

9. Academy 0.085883 0.062169 0.056755 0.037658 0.034712 0.034059 0.035415 0.013595 -2.698693 0.024055

10. Cremorne 0.085234 0.060853 0.055883 0.037216 0.034346 0.033664 0.034774 0.013331 0.006750 -2.442678

Notes: Cross price elasticities derive from models (2) and (5) as reported in Table 5. Cell entries i, j , where i indexes row and j

column, give the percent change in market share of i with a one-percent change in price of j . Each entry represents the median of the

elasticities.

Table 11: Observed and Optimal Prices for Selected Cinemas

Observed Daily Model Weekly Model

Price Median Optimal Price Median Optimal Price

Cinema (1) (2) (3) (4) (1) (2) (3) (4)

George St. 14.042 4.259 5.135 4.509 7.194 5.748 7.511 6.405 12.471

Bondi Junction 13.730 4.256 5.103 4.489 7.068 5.682 7.515 6.410 12.490

Broadway 13.582 4.174 4.672 4.512 7.117 5.661 6.840 6.407 12.464

Campbelltown 13.633 5.485 5.778 4.532 6.357 5.632 7.466 6.385 12.269

Blacktown 13.489 4.235 4.917 4.481 6.451 5.607 6.813 6.384 12.264

Warringah 13.489 4.152 4.755 4.203 7.407 5.612 6.835 6.249 12.417

Fox Studios 13.193 4.127 4.708 4.496 7.186 5.610 6.845 6.409 12.492

Newtown Dendy 12.135 4.064 4.093 4.356 7.030 5.543 5.587 6.068 12.462

Academy Twin 14.897 4.059 4.169 4.137 7.171 5.534 5.671 5.662 12.477

Cremorne Orpheum 13.582 4.146 4.285 4.462 7.660 5.592 5.901 6.068 12.446

Notes: Daily and weekly estimates derive from models (2) and (5), respectively, as reported in Table 5. Optimal prices reported in (1),

(2), (3) and (4) refer to diﬀerent hypothetical cinema ownership arrangements. Speciﬁcally, (1) cinema-level ownership, (2) circuit-level

ownership, (3) distributor-level ownership, and (4) market-level ownership. Actual ownership and number of screens as follows: George

St., Greater Union, 17; Bondi Junction, Greater Union, 11; Campbelltown, Greater Union, 11; Blacktown, Hoyts, 12; Warringah, Hoyts,

9; Fox Studios, Hoyts, 12; Newtown, Dendy, 4; Academy Twin, Palace, 2; Cremorne Orpheum, independent, 6.

Table 12: Observed and Implied Daily Film-at-Theatre Demand

Optimal Price

Data Model (1) (2) (3) (4) Capacity

Daily Model

All Sessions 144 144 605 539 595 438 957

Opening Week 261 256 789 675 732 494 1,168

Opening Week (Screens > 200) 413 403 1,240 1,061 1,091 779 1,605

Opening Week (Screens > 300) 586 567 1,755 1,509 1,495 1,107 1,947

Weekly Model

All Sessions 144 145 279 241 268 175 957

Opening Week 261 263 495 425 463 308 1,168

Opening Week (Screens > 200) 413 412 773 663 695 480 1,605

Opening Week (Screens > 300) 586 585 1,085 931 962 672 1,947

Notes: Daily and weekly estimates derive from models (2) and (5), respectively, as

reported in Table 5. Optimal prices reported in (1), (2), (3) and (4) refer to diﬀerent

hypothetical cinema ownership arrangements. Speciﬁcally, (1) cinema-level ownership, (2)

circuit-level ownership, (3) distributor-level ownership, and (4) market-level ownership. Cal-

culation of capacity information is discussed in text.

Figure 1: Cinema Locations

Figure 2: Collection Districts

Representative cinema (example), [0,5] distance ring, (5,10] distance ring