3. Suppose that two firms produce a pair of imperfectly substitutable goods at the same

constant marginal cost c=16 and compete la Bertrand (firm 1 chooses P1 and firm 2

chooses P2). There are no fixed costs. The market demands that the firms face each

period (q1 for firm 1 and q2 for firm 2) are given by

q1=24-3p1+2p2

q2=24-3p2+2p1

The horizon is infinite (T=), and all firms discount the future by the same discountfactor (0, 1). Given these firms compete repeatedly, they may be able to earn higher

profits by engaging in tacit collusion. Let be the minimum discount factor thatsustains collusion.

(a) Calculate the (per-period) prices, quantities, and profits in the one-shot(non-collusive) Bertrand equilibrium and in the case when both act as a monopoly.(Hint: Note that a monopoly firm will need to produce both goods and will thusneed to optimally choose both prices.)

(b) How can the two firms use tacit collusion in the repeated game to jointlyearn the same profit that a monopoly firm would earn from part (a)?That is, what are the grim trigger strategies that the firms follow to achieve this?

(c) Given your answer to part (b), determine , the minimum discount factorthat sustains this collusive outcome.

(d) Suppose that instead of updating quantities each period, the firms areonly allowed to update them in odd-numbered periods (the choice made then persists for two periods). Find the new threshold discount factor,

Is collusion now easier or harder to sustain than in the baseline case?