Suppose that the market demand for steel in Australia is rep

Suppose that the market demand for steel in Australia is represented by: Qd = 90 - 5P. It is also assumed that there is only one firm producing steel (i.e., monopoly) and the firm’s marginal cost is $5 per unit.

a) Assume that the monopolist can practice perfect price discrimination. What is the minimum price the firm would charge to maximize its profit? Calculate consumer surplus, producer surplus, and deadweight loss. Demonstrate the results on a graph.

b) Now assume that the monopolist can engage in second-degree price discrimination (instead of first-degree price discrimination). More specifically, it charges $10 for the first 40 units, then $7 for any additional unit. Calculate consumer surplus, producer surplus, and deadweight loss.

c) Now assume that this steel industry is dominated by a large firm with a constant marginal cost of $5 per unit, and this firm does not practice price discrimination. There also exists a competitive fringe of 100 firms, each of which has a marginal cost given by MC =3 + 10q, where q is the output of a typical fringe firm. Suppose the market demand curve for steel is still the same as above. Derive the equation of the supply curve for the competitive fringe, and the equation of the dominant firm’s residual demand curve.

d) Continue from part (c), what is the profit-maximizing price set by the dominant firm? How does this price change if the number of fringe firms falls to 50?

Solution

Q_D =20?1/5P On rearranging; P = 100 - 5Q

Tr = PxQ = 100Q - 5Q²

^{MR = Change in TR per unit change in Q , MR= 100 -10Q}

^{At equilibrium, MR = MC ; 100-10Q = 10}

^{Q = 90/10 = 9}

Monopolist Price at 9 units, 100 - 5x9 => 55$

In a perfectly competitive firm, Price is same as MR i.e., 100-10x9 =10$

Output by a competitive firm at 10$; Q = 20 - 1/5x10

= 18

Output by 72 firms = 72x18 =>1296

Yes the monopoly sells less output than a perfectly competitive firm.

Dead weight loss = 1/2 x Difference in P x Difference in Q

= 1/2 x (55-10) x (!8-9) => 1/2x45x9

202.5

Perfectly competitive firm is more efficient