Question

Amazon is a monopolist in the textbook market. Amazon is currently selling textbooks only in the US. The demand for textbook is given by: P = 210 − Q.

The marginal cost of producing textbook is MC = 5. there is no fixed cost.

1. (a) Compute the profit-maximizing price and quantity.

2. (b) Compute the deadweight loss due to monopoly power.

3. (c) If Amazon can use first-degree price discrimination, what is its profit? Is there any deadweight loss?

4. (d) Suppose that Amazon is deciding whether to also sell textbooks in Wakanda. The demand for textbook in Wakanda is given by: P = 70 − Q

   1. (i) If Amazon can price discriminate between US and Wakanda, what are the optimal prices

      and quantities?

   2. (ii) If Amazon cannot price discriminate between US and Wakanda, what are the optimal price and quantities?

   3. (iii) Using your answers in (i) and (ii), which country is better off with price discrimination? Which country is worse off?

   4. (iv) How would your answer to (i) change if the cost function is given by TC(Q) = 0.5Q2?

5. (e) Give an example of second-degree price discrimination.

Answer 1

(a) The demand for textbooks is P = 210 - Q. The total revenue will be then, P*Q = 210Q - Q^2.

So, the marginal revenue will be then, dPQ/dQ = 210 - 2Q (by differentiating both sides of total revenue).

MR = 210 - 2Q.

MC = 5.

Profit maximizing quantity will be at amount where, MR = MC.

210 - 2Q = 5

Or, 205 = 2Q

Or, 102.5 = Q*.

To know the profit maximizing price we need to substitute the value of Q* in the demand function.

P = 210 - Q

Or, P = 210 - 102.5

Or, P = 107.50

So, the profit maximizing price is 107.50 and quantity is 102.50.

(b) To findthe deadweight loss due to monopoly the formula for that would be,

1/2(P - MC)(Qc - Qm).

To find Qc we need to equate the demand curve with MC,

P = 210 - Q = 5

Or, 210 - Q = 5

Or, Qc = 205.

We already know Qm which is the monopoly quantity, ie Qm = 102.50 and P the monopoly price ie 107.50.

1/2(P - MC)(Qc - Qm)

= 1/2(107.50 - 5)(205 - 102.50)

= 1/2(102.50)(102.50)

= 21012.50

(c) If Amazon used first degree price discrimination then the profit would be P*Q - CQ = (210 - Q)Q - 5Q

= 210Q - Q^2 - 5Q

= 210*102.50 - 102.50^2 - 5*102.50

= 21525 - 10506.25 - 512.50

= 10506.25.

The profit will be 10506.25.

In case of first degree price discrimination there will be no deadweight loss.

(d)