Question

Suppose that demand in a given market is given by P = 439 - Q and marginal costs are constant, with MC = 147. Assume that fixed costs are zero (so ATC also are constant at 147). If there are only two firms in the market, one can construct a matrix as shown below representing the payoffs to strategies: Firm 2 Collude (92=73) Compete (92=97) Collude (qı=73) 10658, 10658 8906, 11834 Firm 1 Compete (qi=97) 11834, 8906 9506, 9506 a.) Solve for the monopoly profit-maximizing quantity, price, and profits in this situation and show that the profits you solved for are exactly equal to the sum of the profits earned when both firms play the collude strategy. The marginal revenue formula for this demand curve is given by MR = 439 – 2*Q. b.) Identify whether either firm has a dominant strategy. c.) Which combination of strategies leads to the highest level of total profit between the two firms, and why? What challenges might be faced in reaching this outcome? d.) Can you think of any commitment devices that can help solve the problem you identified in part (c)? Keep in mind that overt collusion could draw unwanted attention from antitrust lawyers.

Answer 1

A) Monopolist equilibrium occurs at where MR= MC

MR=439-2Q

MC=147

439-2Q=147

Q=292/2=146

P=439-146=293

Profit=(293-147)*146=146*146=21,316

B)given firm 2 move collude, best move for firm 1 is to compete.

Given firm 2 move compete ,best move for firm 1 is to compete.

So firm 1 has a dominant strategy of to compete.

Similarly ,firm 2 has also a dominant strategy of to compete.

C)when both firm choose to collude, then joint profit maximize and equal to 21,316.

It is because ,both firms jointly produce Monopoly output,that maximize profit.

Challenge

Given one firm me ve collude , other firm always has an incentive to increase output and choose to compete , and increase its individual payoff.

D)The commitment should be like this.

If any firm choose to increase output than collude output, then in next period ,other firm will play grim strategy and also choose to increase output and will stay at that level. Thus this result in Decrease in both firm profit.

Knowing this no firm would try to increase output from collude level.