Bart Wurst runs the only hot-dog stand in a large park in a large boring town. O

Question

Bart Wurst runs the only hot-dog stand in a large park in a large boring town. On Sundays people in this town all sit in the park and sunbathe. For any t between 0 and 30, the number of people who are sitting within t minutes of Bart’s stand is 15t 2 . People in Bart’s town are lazy and hate to walk. They think that every minute of walking they do is as bad as spending $0.10. Everybody in the park has a reservation price of $1 for a hot dog, where the cost of a hot dog includes the subjective cost of walking as well as the money price they have to pay when they get there. (Nobody has ever thought of fetching a hot dog for someone else.) Find a formula for the market demand for Bart’s hot dogs. Explain how you got it.

Explanation / Answer

If Bart charges p where 0 <p< 1; his extensive margin is the customers who are at distance t* from Bart

where p + .10t = 1. Then t = 10-p and the demand for hot dogs at prices p is the number, (10-p)^2; of people within t* of Bart.

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