Question

Suppose that a firm's demand curve is D (P) = Q = 80 - P while its cost function is C (Q) = 64 -2Q. The demand and costs are the same for both the entrant and incumbent. If you are an incumbent in this industry, find the limit price (i.e., the price that the market should have in order to deter entry?

Answer 1

The limit price to deter entry into the market is $39, as this is where the incumbent firm earns zero economic profit, which does not attract new entrants.

Step-by-step explanation:

Calculating the Limit Price to Deter Entry

To calculate the limit price that will deter entry into a market, we will examine the demand curve D(P) = Q = 80 - P and the cost function C(Q) = 64 - 2Q. The limit price is where economic profits are zero, thus deterring entry because new entrants would not expect to make a profit. First, we set the marginal revenue (MR) equal to marginal cost (MC) to find the profit-maximizing quantity Q*. The demand curve can be written as P = 80 - Q, so the marginal revenue for this linear demand curve would be MR = 80 - 2Q. The marginal cost from the cost function is MC = dC/dQ = -2. Setting MR equal to MC gives us:

80 - 2Q = -2

This implies Q* = 41. To find the corresponding price, we substitute Q* back into the demand equation:

P = 80 - Q*

P = 80 - 41 = 39

This price of $39 is the limit price, the highest price the incumbent can charge without attracting new entrants, assuming costs are the same for all firms.