Question

1. The demand for a firm’s product is estimated by the equation Q = 20 - P, and its total cost function is TC = Q2 + 8Q + 2. Marginal cost is MC = 2Q + 8, and marginal revenue is MR = 20 - 2Q.

a. Given this information, what is the firm’s profit-maximizing output and price?

b. What is the firm’s profit at this level of output?

c. Is the firm operating in a perfectly competitive price taker or price searcher market? How do you know?

d. If the firm was operating in a perfectly competitive market, what would be its long-run quantity and price?

Answer 1

a) Profit maximizing quantity and price are calculated by equating the marginal revenue and marginal cost function.

So, equating marginal revenue and marginal cost,

2Q + 8 = 20 - 2Q

2Q + 2Q = 20 - 8

4Q = 12

Q = 12 / 4 = 3 is the answer.

P = 20 - Q

P = 20 - 3 = 17 is the answer.

b) Profit = Total Revenue - Total Cost

Profit = (price x quantity) - (Q² + 8Q + 2)

Profit = (17 x 3) - [(3)² + 8(3) + 2]

Profit = 51 - (9 + 24 + 2)

Profit = 51 - 35 = 16 is the answer.

c) The firm operating in this case is not a price taker as we can see from the marginal revenue and price functions that as quantity decreases, both price and marginal revenue also decrease which is a feature of monopoly and price maker firm and not perfect competition. In this case, the quantity calculated is low whereas price is too high which is again a feature of monopoly.

d) If this firm operates in a perfectly competitive market, then the long run price and quantity are calculated by equating price and marginal cost.

So, P = MC

20 - Q = 2Q + 8

2Q + Q = 20 - 8

3Q = 12

Q = 12 / 3 = 4 is the answer.

P = 20 - Q

P = 20 - 4 = 16 is the answer.