question archive 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)
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)
Subject:EconomicsPrice: Bought3
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 discount factor ?δ? ?∈? (0, 1). Given these firms compete repeatedly, they may be able to earn higher
profits by engaging in tacit collusion. Let ??δ∗? be the minimum discount factor that sustains 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 thus need to optimally choose both prices.)
(b) How can the two firms use tacit collusion in the repeated game to jointly earn 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 ?δ∗?, the minimum discount factor that sustains this collusive outcome.
(d) Suppose that instead of updating quantities each period, the firms are only allowed to update them in odd-numbered periods (the choice made then persists for two periods). Find the new threshold discount factor, ?δ∗∗? ?
Is collusion now easier or harder to sustain than in the baseline case?
