Question

A firm sells its product in a perfectly competitive market where other firms charge a price of $100 per unit. The firm estimates its total costs as C(Q) = 40 + 10Q + 3Q2. In addition to numerical solutions below, please use a graph to illustrate and explain the underlying logic for each question. a) How much output should the firm produce in the short run? Why? b) What price should the firm charge in the short run? c) What are the firm’s short-run profits? d) What adjustments should be anticipated in the long run? Why?

Answer 1

In the short run, the firm should produce 15 units and charge a price of $100 per unit, resulting in short-run profits of $725. In the long run, we can anticipate a decrease in profits.

Step-by-step explanation:

a) In the short run, the firm should produce the quantity at which marginal cost (MC) equals marginal revenue (MR) to maximize profits. This occurs when MC = MR = price.

To find the quantity, we find the derivative of the total cost function and set it equal to price:

MC = dC(Q)/dQ

= 10 + 6Q.

Setting this equal to $100, we solve for Q and find Q to be 15. So, the firm should produce 15 units in the short run.

b) Since the firm is in a perfectly competitive market, it must charge the market price of $100 per unit.

c) The firm's short-run profits can be calculated by subtracting total cost from total revenue. Total revenue is price multiplied by quantity, so

TR = $100 * 15 = $1500.

Total cost can be calculated by plugging in the quantity into the cost function:

TC = 40 + 10(15) + 3(15)^2

= $775.

Short-run profits are

TR - TC = $1500 - $775

= $725.

d) In the long run, other firms may enter the market to take advantage of the profits being made. This increase in supply will cause the market price to decrease. Additionally, the firm may also see an increase in its costs due to changes in input prices or technology. Therefore, in the long run, we can anticipate a decrease in the firm's profits.