Ecns 300, Intermediate Microeconomic Theory Group Project 1

Ecns 300, Intermediate Microeconomic Theory
Group Project 1.

Along a stretch of beach 'down the shore' there are 500 children in five clusters of 100 each. They are clustered in this fashion due to the location of the lifeguard stands. The stands are labeled A, B, C, D, E. Each child buys one ice cream cone per day.

There are two rival ice cream vendors named Ben and Jerry. Each morning they roll their wagons down to the beach for business at 10 AM. They must locate their wagon at the exact location of one of the clusters. The children always go to the nearest vendor. If there is a vendor in a cluster then all 100 children buy from that vendor. For clusters without a vendor, 50 of the children will walk to an adjacent cluster with a vendor for ice cream, only 20 will walk as far as two clusters, none will walk three or more clusters for ice cream. If both Ben and Jerry are located in the same cluster then they each get 50% of the demand for ice cream at that location. If Ben and Jerry locate in different clusters then children that are equidistant from both of them will be equally split.

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1. Fill in the missing cells in the payoff matrix. To get you started: If Ben chooses B and Jerry chooses C, then Ben will sell 150 cones (100 from his own cluster and 50 walking over from A) and Jerry will sell 170 cones (100 from his own cluster plus 50 walkers from D and 20 walkers from E).

2. Suppose that Jerry plays B. What is Ben's best response?

3. How many dominant solutions are there in this game? What are they? (If there are, explain how you derived the solution(s).)

4. How many Nash equilibria are there? List any.

5. Are there Pareto Optimal outcomes in this game? List any.

6. Does this example help explain why Home Depot located across the street from Lowes. Explain why or why not*. (Note: Lowes, originally doing business as Eagle, was at the West End location for several years before Home Depot located across the street. Use that fact.)

• If this example does NOT explain the close location, what additional assumptions or considerations might you add to the second paragraph above to change the payoffs so that the outcome of the game would explain the observed phenomenon? Note: Lowes and Home Depot are pretty close to each other in Bozeman and too many other cities to be mere coincidence.