27.3 Everyday Application: Sandwiches, Chess Clubs, Movie Theaters, and Fireworks: In the introduction, we mentioned that while

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27.3 Everyday Application: Sandwiches, Chess Clubs, Movie Theaters, and Fireworks: In the introduction, we mentioned that while we often treat public and private goods as distinct concepts, many goods actually lie in between the extremes because of “crowding.”

A. We can think of the level of crowding as determining the optimal group size for consumption of the good, with optimal group size in turn locating the good on the continuum between purely private and purely public goods.

a. One way to model different types of goods is in terms of the marginal cost and marginal benefit of admitting additional group members to enjoy the good. Begin by considering a bite of your lunch sandwich. What is the marginal benefit of admitting a second person to the consumption of this bite? What is therefore the optimal “group size,” and how does this relate to our conception of the sandwich bite as a private good?

b. Next, consider a chess club. Draw a graph with group size N on the horizontal axis and dollars on the vertical. With additional members, you’ll have to get more chessboards, with the marginal cost of additional members plausibly being flat. The marginal benefit of additional members might initially be increasing, but if the club gets too large, it becomes impersonal and not much fun. Draw the marginal benefit and marginal cost curves and indicate the optimal group size. In what way is the chess club not a pure public good?

c. Consider the same exercise with respect to a movie theater that has N seats (but you could add additional people by having them sit or stand in the aisles). Each customer adds to the mess and thus the cleanup cost. What might the marginal cost and benefit curves now look like?

d. Repeat the exercise for fireworks.

e. Which of these do you think the market and/or civil society can provide relatively efficiently, and which might require some government assistance?

f. Why do you think fireworks on national holidays are usually provided by local governments, but Disney World is able to put on fireworks every night without government help?

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