Question

#1) Consider a market with demand curve given by P = 90 - Q . The total cost of production for one firm is given by TC(q) = (q²/2)+10 . The marginal cost of production is MC = q .

a) If the market is perfectly competitive, find the supply curve for one firm. Explain. b) If the market price was $10, how many perfectly competitive firms are in the industry if they are identical? Explain. c) Find an expression for the monopolists marginal revenue curve (hint: recall the relationship between the MR curve’s and the demand curve’s slopes.) d) If the market is monopolized by one firm, how many units will be sold and at what uniform price to maximize profits? Explain.

Answer 1

Consider a market with demand curve given by P = 90 - Q . The total cost of production for one firm is given by TC(q) = (q^2/2)+10 . The marginal cost of production is MC = q .

a) If the market is perfectly competitive, find the supply curve for one firm. Explain.

Supply curve for a single firm is its MC curve. Hence it is MC = P = q. This gives q = P.

b) If the market price was $10, how many perfectly competitive firms are in the industry if they are identical? Explain.

At P = 10, Qd (market demand) = 90 - 10 = 80 units. With one firm having P = q or q = 10 units as production, there are 80/10 = 8 firms in the short run.

c) Find an expression for the monopolists marginal revenue curve (hint: recall the relationship between the MR curve’s and the demand curve’s slopes.)

Demand is P = 90 - Q. TR is 90Q - Q^2. Hence MR = 90 - 2Q. (Twice the slope of demand).

d) If the market is monopolized by one firm, how many units will be sold and at what uniform price to maximize profits? Explain.

Monopoly uses MR = MC

90 - 2Q = Q

Qm = 90/3 = 30 units

Pm = 90 - Qm = 90 - 30 = $60 per unit.

This is the profit maximizing quantity and price