1) In the hoteling's location model, consumers are uniformly distributed along the line segment [0,1] and each consumer buys a scoop of ice cream. Suppose firm A is locatedat 0 and charges price at P, while firm B is situated at 1 and charges price P*for a scoopof ice cream. Furthermore, the transportation cost for each consumer is c per unitlength, and the marginal cost to making one scoop of ice cream for both firms is m.

a) Derive the demand function for firms A and based on the informationprovided above. [5 marks]

b) Next, derive the profit of each firm bearing in mind that both firms are identical.[5 marks]

2) Identical firms compete a la Salop in a circle city whose residents are uniformly distributed along the city and each resident buys one unit of the good.

a) Suppose the city can support two firms; characterise a Nash equilibrium of the game. [5 marks]

b) Recently the population of the city has increased because of migration so that the city can now support four firms. If the residents remain uniformly distributed, characterise a Nash equilibrium of the game. [5 marks]