Question

8. A firm has the following short-run inverse demand and cost functions for a particular product:

P = 45-0.2Q
TC = 500+5Q

1. At what price should the firm sell its product?
2. If this is a monopolistically competitive firm, what do you think would happen as the firm moves towards the long run? Explain.

Answer 1

Given the demand and cost functions for a particular product.

The firm should sell the product at the equilibrium price and quantity.

The equilibrium of the firm is given by the price and output where we have MC = MR

TC = 500 + 5Q

or MC = 5

P = 45 - 0.2Q

TR = P * Q = (45 - 0.2Q) * Q

or TR = 45Q - 0.2Q²

MR = 45 - 0.4Q

Now, equating MR = MC

45 - 0.4Q = 5

or 0.4Q = 40

or Q = 100

and P = 45 - 0.2Q = 45 - 0.2 * 100 = 45-20 = 25

Thus, price at which the firm should sell the product at a price of 25 per unit.

b. If the firm is a monopolistically competive firm, then in the long run it will produce the goods at a point where long run marginal cost curve is equal to MR. Also, the price will be set at a level where the quantity produced falls on the average revenue (AR) curve. Thus, firm, in the long run, will be in break-even situation.