Question

Crazy Harry, a monopolist, has a total cost curve given by TC = 4Q + 12. He sets two prices for his product, a regular price, P_H, and a discount price, P_L. Everyone is eligible to purchase the product at P_H. To be eligible to buy at P_L, it is necessary to present a copy of the latest Crazy Harry newspaper ad to the salesclerk. Suppose the only buyers who present the ad are those who would not have been willing to buy the product at P_H.

a. If Crazy Harry’s demand curve is given by P = 16 - 4Q, what are the profit-maximizing values of P_H and P_L? (Enter your answers as whole numbers.)

P_H:

P_L:

b. How much economic profit does Harry make? (Enter your answer as a whole number.)



c. How much profit would he have made if he had been forced to charge the same price to all buyers? (Round your answer to 2 decimal places (e.g., 32.16). For any negative answer, be sure to include a negative sign (-) in front of the answer.)



d. Are buyers better or worse off as a result of Harry’s being able to charge two prices?

Answer 1

(a). TC = 4Q + 12
MC = 4

P = 16-4Q
Total Revenue is PQ = 16Q - 4Q²
Marginal Revenue, MR = 16 - 8Q

The regular price, PH is given at monopoly's profit maximization condition, which is MC=MR
Therefore, 16-8Q = 4
Q_PH = 12/8

Now, PH = 16 - 4Q = 16 - 4(12/8)
PH = 10

For PL, the profit maximization condition is P = MC
Therefore, 16 - 4Q = 4
Q_PL = 3
PL = 4 (i.e. the marginal cost)

(b) The economic profit, = TR - TC

= 10*12/8 + 4*3 - [4*3 +12]

= 3

(c) If he was to charge same price to all customers, then he would not be able to sell upto 3 units of his product.

His profit would have been, = 10*12/8 - [4*12/8 + 12] = -3

(d) Buyers are better off as a result of Harry's price discrimination because now every customer can buy their product at their maximum willingness to pay (MWTP), while some customers have a consumer surplus as well.