SECTION A

Answer all four questions from this section (12.5 marks each).

1. Two players pick a number in [0,1 I. The player whose number is closest to halt the average of the two numbers gels +1. the other player gets -1. If both players are equally close. they get zero.

a) Suppose player 1 picks x (0 < x 5 1). What is the set of best responses for Player 2?

b) What is the Nash equilibrium for this game?

2. Consider a market in which 90 people would like to sell their used cars. Out of these cars, 30 are good, 30 are in moderate shape. and 30 are bad. Each seller values a good car at £7,000, a moderate car at £3.000. and a bad car at £0. There are many people interested in buying these cars. so sellers have all the bargaining Over. Each potential buyer is willing to pay up to £10.000 for a good car. £6,000 for a moderate car. and £2.000 for a bad car.

a) Suppose that both buyers and sellers can observe the quality of each car before they trade. How many cars would be sold and at what prices?

b) Now suppose that buyers cannot distinguish between goods. moderate and bad cars although sellers know the quality of their cars. How many cars would be sold and at what prices?

3. A monopolist has demand given by p = a – QB. The marginal cost is zero.

a) Find the profit-maximizing quantity and price.

b) An aid Valorem tax is introduced. Find the profit-maximizing quantity and price.

4. Consider the production function xi -ix, “1 where y es units of output. and x and x2 are units of inputs 1 rind 2. respectively. al If the unit input factor costs of input I and 2 am 1 and 16. rowed: every, what are the conditional factor demands for each input? Is) What is the long-run total cost function for a firm producing using INS technology when the factor coat of input 1 is 1 and the factor cost of Input 2 Is 16?