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## Exercise: Spatial Competition

###### (faculty.washington.edu/krumme/207/exercises/bigsmall.html)

Due: Tuesday, May 6
Additional Help (Click!) | and here!

Wal-Mart ("Big") and True Value Hardware ("Small", equivalent to this one) selling similar products are considering opening a new store in one of four towns located on a given highway somewhere in Kitsap County. The total population of the four towns is 50,000 (as distributed on the graph below); the towns are equally distant from each other (10 miles).

#### Distribution of Total Population ( = Market):

 ``` A Town B Town C Town D Town ______ ______ ______ ______ | | 10 miles | | 10 miles | | 10 miles | | | 20%|----------| 20%|----------| 40%|----------| 20%| |____| |____| |____| |____| ```

Expecting community opposition and/or competitive responses, the two companies are keeping their plans secret until it is too late to respond to the competitor's eventual location disclosure. Where (in which of those 4 towns) would you expect the two to locate their respective store given the following, generally known information?

1. If Wal-Mart's store is located closer to a town, it will capture 80% of the market.
2. If Value Hardware is nearer, then the Walmart will capture 40%.
3. If both companies' stores are equally distant, including being located in the same town, then Walmart will capture 60%.

Suggested Tasks: [1 & 2 are necessary; select from 4-6 those questions which you feel might help you in the interpretation of your results.]

1. set up the matrix of the "game" (fill in only that part of the table which you feel is needed to answer the question and justify your answer. See example of such a combined payoff matrix
2. find optimal strategies for the two competitors and interpret your results
3. How, in general, might your results change if you would introduce some distance elasticity of demand?
4. briefly discuss the social (welfare) implications of the case without distance elasticity of demand.
5. Would the locational results have been different had Walmart and Value known about their respective plans earlier?

Wal-Mart in the News: