Question

3) [9 pts] Recall the Hotelling “hotdog stand model” from class in which two hotdog vendors must independently decide where to locate their hotdog stand.

a) [3 pts] Assume that people are uniformly distributed along the beach, and that everyone buys a hotdog from the closest vendor. What is the Nash equilibrium location of each profit-maximizing vendor?

b) [3 pts] Under the same assumptions as part (a), what is the socially optimal location for each vendor?

c) [3 pts] Do the results from (a) and (b) change when the beach encircles an island? If so, how? (Assume there’s a mountain in the middle of the island so that hotdog stands must be located on the beach.)

Answer 1

a) Suppose the vendor 1 places himself in the middle, he will guranteed to get half the business becasue if vendor 2 locates himself to the left of vendor 1, everything on the right and some middle portion will go to v1 and similarly if he places himself on the right,still the vendor 1 will get all the left and some middle portion.

so, The Nash equilibrium property of each profit-maximizing vendor would be as follows:

Taking 0,1 as the extremes of the beach,

b) The socially optimal location for each vendor would be the middle to get exactly half the business.

c)The results will remain same even if beach encircles an island.

Because if both vendors locate themselves at equidistance from one another., still the consumer in the middle of both extremes will go to either V1 or V2 which will require the other one to move closer as the vendors cannot place themselves in the middle of the island because of the mountain,they will place themselves together to get exactly half the market.