Blockbusters and market expansion: evidence from the motion picture industry

Abstract

Like other cultural industries, the theatrical film industry is subject to the ‘blockbuster effect’, where popular products often dominate their competition by orders of magnitude over relatively short-run time horizons. This paper investigates this particular feature of the industry and the implication for overall market size. Using simple regression analysis, a positive relationship between (product-level) market concentration and market size is established using weekly box office revenue data from the US motion picture industry. This empirical evidence supports a simple theoretical model of heterogeneous consumers who selectively participate in the market.

Appendix

The theoretical model detailed below provides a simple illustration of how (product-level) market concentration might be positively related to market size in the short run. Assume two groups of consumers face a choice between n movies that are screened in a given week. Without loss of generality, assume that there are $N_1$ consumers, who are part of the first group, and that they are distributed across n movies according to the distribution $\alpha _1\le \alpha _2\le \cdots \le \alpha _n$ where $\alpha _i$ is the proportion of the group watching movie i (or the attractiveness of movie i) and $\sum _{i=1}^n \alpha _i=1$.⁸ Consumers from the first group always choose to watch some movie but only one. The demand for movie i from the first group is given by

$$\begin{aligned} x_{i,1}=\alpha _i N_1. \end{aligned}$$

(2)

There are $N_2$ consumers of the second type, who attend some movie in a given week only when there are movies with attractiveness above some threshold $\overline{\alpha }$. We refer to movies that satisfy this criterion as ‘blockbusters’. If more than one movie is a blockbuster, consumers select the movies proportional to their attractiveness. The demand for movie i from the second group is given by

$$\begin{aligned} x_{i,2}=\left\{ \begin{array}{ll} \frac{\mathbf{{1}}(\alpha _i>\overline{\alpha }) N_2\alpha _i}{\sum _{j=1}^n \mathbf{1}(\alpha _j>\overline{\alpha })\alpha _j}, &\quad \text{ if } \max _i\{\alpha _i\}> \overline{\alpha }; \\ 0, &\quad \text{ otherwise }. \end{array} \right. \end{aligned}$$

(3)

The total demand for movie i is the sum of demands from two groups. Consequently,

$$\begin{aligned} x_i=x_{i,1}+x_{i,2}=\left\{ \begin{array}{ll} \alpha _i\left( N_1+\frac{\mathbf{{1}}(\alpha _i>\overline{\alpha }) N_2}{\sum _{j=1}^n \mathbf{1}(\alpha _j>\overline{\alpha })\alpha _j}\right) , &\quad \text{ if } \max _i\{\alpha _i\}> \overline{\alpha }; \\ \alpha _i N_1, &\quad \text{ otherwise }. \end{array} \right. \end{aligned}$$

(4)

We assume that the price of attending any movie is the same and for simplicity normalise it to 1. The total box office as a result is given by

$$\begin{aligned} B=\left\{ \begin{array}{ll} N_1+N_2, &\quad \text{ if } \max _i\{\alpha _i\}> \overline{\alpha }; \\ N_1, &\quad \text{ otherwise }. \end{array} \right. \end{aligned}$$

(5)

As one can see, the existence of consumers of the second type increases the box office from $N_1$ to $N_1+N_2$ when there are blockbuster movies.

Proposition 1

The existence of consumers of the second type is consistent with higher total box office when there are blockbuster movies.

To measure market concentration we introduce the standard Gini coefficient

$$\begin{aligned} G=\frac{2\sum _{i=1}^nix_i}{n\sum _{i=1}^nx_i}-\frac{n+1}{n}, \end{aligned}$$

(6)

where we continue to assume attractiveness in non-decreasing order, i.e. $\alpha _i \le \alpha _{i+1}$.

We now prove the following Proposition:

Proposition 2

The existence of consumers of the second type is consistent with a higher Gini coefficient when there are blockbuster movies.

Let us compare Gini coefficients for the following two cases. The first case is when only consumers of the first type are present. The second case is when both types are present. The Gini coefficient in the first case is given by $G_1=\frac{2\sum\nolimits _{i=1}^ni\alpha _i}{n\sum _{i=1}^n\alpha _i}-\frac{n+1}{n}$, while the Gini coefficient in the second case is given by $G_2=\frac{2\sum\nolimits _{i=1}^nix_i}{n\sum _{i=1}^nx_i}-\frac{n+1}{n}$. This results in the following comparison

$$\begin{aligned} \frac{\sum _{i=1}^ni\alpha _i}{\sum _{i=1}^n\alpha _i}\sim \frac{\sum _{i=1}^nix_i}{\sum _{i=1}^nx_i}. \end{aligned}$$

(7)

To simplify, define $\beta =1+\frac{\mathbf{{1}}(\alpha _i>\overline{\alpha }) N_2}{\sum _{j=1}^n \mathbf{1}(\alpha _j>\overline{\alpha })\alpha _jN_1}$ and movie $k\in \{1,2,\ldots ,n\}$ such that $\alpha _k\le \overline{\alpha }$, while $\alpha _{k+1}> \overline{\alpha }$. Comparison (7) transforms to

$$\begin{aligned} \frac{\sum _{i=1}^ni\alpha _i}{\sum _{i=1}^n\alpha _i}\sim \frac{\sum _{i=1}^ki\alpha _i+\beta \sum _{i=k+1}^ni\alpha _i}{\sum _{i=1}^k\alpha _i+\beta \sum _{i=k+1}^n\alpha _i}, \end{aligned}$$

(8)

which can be simplified to

$$\begin{aligned} \frac{\sum _{i=1}^ni\alpha _i}{\sum _{i=1}^n\alpha _i}\sim \frac{\sum _{i=k+1}^ni\alpha _i}{\sum _{i=k+1}^n\alpha _i}. \end{aligned}$$

(9)

The left-hand side is E(i), while the right hand side is $E(i|i>k)$. This proves $G_2>G_1$. $\square$