Question

1) In a monopolistically competitive industry, the typical firm has fixed cost of 20 and constant marginal cost of 1. The average cost curve of the typical firm is then AC = 1 + 20/Q. Prior to trade each firm has the following demand curve, Q = 60 - 20P.

a. Find the profit maximizing level of output and the price charged by the typical firm prior to trade. Determine average cost and profits.

b. After trade is opened, each firm has a demand curve given by Q = 105 - 45P. Find output per firm and price after trade is opened. Determine average cost and profits.

Answer 1

1(A)

Profit maximization condition for a monopolistically competitive firm occurs when its marginal cost equals its marginal revenue.

To derive the marginal revenue (MR) function, we need to find total revenue function first.

TR = P * Q

Given the demand function Q = 60 - 20P

P = 3 - 0.05Q

So, TR = 3Q - 0.05Q²

So, MR = d(TR) / dQ = 3 - 0.1Q

Now, from the question we have marginal cost (MC) equals to 1.

So, MR = MC means,

3 - 0.1Q = 1

0.1Q = 2

Q = 20.

Now, if we put Q = 20 in the demand function, we will get the profit-maximizing price.

20 = 60 - 20P

20P = 40

P = 2.

Now, if we put Q = 20 in the AC function, we will get average cost.

AC = 1 + (20 / 20) = 2.

Now, Profit = TR - TC

TR = 3Q - 0.05Q²

TR = (3 * 20) - 0.05 * (20 * 20) = 60 - 20 = 40.

TC = AC * Q = Q + 20 = 20 + 20 = 40.

So, Profit = 40 - 40 = 0.

So, the profit-maximizing level of output is 20 units, the price charged is $2. And average cost is $2 and profit is 0.

(B).

Now, when trade opens up, demand function changes to Q = 105 - 45P

So, P = 2.33 - 0.02Q

TR = 2.33Q - 0.02Q²

MR = 2.33 - 0.04Q

MC is given as 1.

So, 2.33 - 0.04Q = 1

0.04Q = 1.33

Q = 33.25.

Now, if we put Q = 33.25 in demand equation, we will get

P = 2.33 - (0.04 * 33.25)

P = 1.

So, average cost = 1 + (20 / 33.25) = 1.60.

Now, TR = (2.33 * 33.25) - 0.02 * (33.25 * 33.25) = 55.36

TC = 33.25 + 20 = 53.25

So, profit = (55.36 - 53.25) = 2.11

So, the output per firm is 33.25 units, the price charged is $1. And average cost is $1.60 and profit is $2.11.