Take a look at your student ID number (450549496). Define z as the sum of the first three digits of your S

For example, if your SID is 123456789, then z=1+2+3=6

3. Two firms compete in the market for a homogeneous product. Each firm has a capacity of k=5 units. Market demand is given by

where Q=91+q2. Each firm has a constant marginal costs of z and no fixed costs

C(q)=zq

where z is the number you calculated earlier based on your SID. The firms compete by simultaneously choosing price. The lowest priced firm captures the whole market(up to their capacity constraints), while the higher priced firm serves any residual demand

(a) Suppose a single firm operates in the market. Find the profit-maximising price and quantity of the monopolist. Label the monopoly price Pm. What are the monopolist's profits, Im?

(b) Suppose the two firms interact for a single period. Describe the reaction function for each firm

c)Two firms compete by simultaneously choosing prices over an infinite horizon. Both firm have the same discount factor, 8. We want to find the sustainability of collusion on the monopoly price using a variation of the grim trigger strategy. In particular, the firms consider the following collusive strategies

set p= pm in the first period OR if both firms set a price Pm last period OR if both firm set a price of zero last period

set p=otherwise.

These strategies involve a single period of harsh punishment in which both firms set a price of zero before returning to the monopoly price. Punishment is said to be credible if all players

have an incentive to carry out the punishment.

i. Assume that the punishment is credible. For what values of 8 do both players have an incentive to cooperate? Explain carefully how you derived your answer

ii. For what values of 8 is the punishment credible? Explain carefully how you derived your answer