Consider the following inverse demand function, p(Q) = a-bQ, Q = q1 +q2, where a and...

Consider the following inverse demand function, p(Q) = a-bQ, Q = q1 +q2, where a and b are positive parameters and q_i denotes firm i's output, i = 1, 2. Assume that the total cost of firm i is cq_i²/2, with c > 0. Firms choose quantities simultaneously and non cooperatively (Cournot competition). The Cournot game described above is infinitely repeated. Firms use grim trigger strategies (infinite Nash reversion). Firms discount future profits at a rate r > 0.

a) Derive the critical discount factor above which full cartelization (joint profit maximization) is sustainable as a Subgame Perfect Nash Equilibrium (SPNE) of the infinitely repeated game.

b) Compute the impact of c on the critical discount factor and provide a brief comment.

Solutions

Expert Solution

The given question is solved as below:

b. Equating the inequality putting the value of monopoly profit and cournot profit we get the relation between discount rate r and the marginal cost c. Marginal cost is negatively related to the discount rate lower marginal costs makes the firm impatience.

Rahul Sunny answered 1 year ago

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