Consider two ice cream sellers competing at a beach that is 1000 metres long. Ice cream prices are fixed by the ice cream company, but companies can choose their locations simultaneously. Customers are located uniformly (spread out evenly on the beach) and do not like walking. The cost of walking every metre is the same (i.e. linear cost).

a) Where will the ice cream stands be located in the Nash equilibrium if the locations are chosen simultaneously? (3)

b) What are the socially optimal locations, i.e. the best from society's point of view that minimise transportation cost? Are the locations in the Nash equilibrium different from the socially optimal locations? Explain. (3)

c) Suppose there are three ice cream sellers that locate simultaneously. Find the Nash equilibrium is there is one. Else, explain why there is none. (Focus on pure strategy Nash equilibria) (4)