Question

1. (20 points) Assume you are an altruistic monopolist, meaning that you want to both maximize profits AND social welfare. You have many customers, and your inverse market demand curve is P = 100 - Q. Marginal cost is 20. HINT: To start this problem, draw a graph similar to Fig. 6.2 (noting that it is missing its marginal revenue curve), and keep in mind that you can draw both the demand and MR curves without any calculations. If you get stuck with the math in a. below, you may earn partial credit by clearly labeling the diagram in support of your answers to question a. a. Is it possible for you to increase both profits and total surplus by undertaking a two-part tariff scheme, compared to a single-price strategy? To answer this question, calculate profits and total surplus for both scenarios (single monopoly price and single two-part tariff). b. Instead of pursuing a two-part tariff, and assuming you know that men value your product differently than women, what would you need to know about the two types of consumers in order to optimally price to each? No calculations are required to answer this question And if this approach were successful, where would you expect prices, total profits, and total surplus to fall relative to the single-price and two-part tariff scenarios in a. above? Again, no calculations are necessary to answer the question.

Answer 1

a)

P = 100 - Q

TR= 100Q - Q^2

MR = 100 - 2Q

MR = MC

100 - 2Q = 20

2Q = 80

Q = 40

P = 100-40

= 60

Profit = 60*40 - 20*40

= 2400 - 800

= 1600

Surplus : CS + PS

= 0.5( 100-60)(40) +40*40

= 2400

Two part tariffs

P = MC

100-Q = 20

Q = 80

P= 20

Profit = CS

= 0.5 (100 - 20)(80)

= 0.5*80*80

= 0.5*6400

= 3200

Surplus is larger under the two part tariff.

b)

This is called the thrid degree price discrimination.

the third degree price discrimination , there would be a larger profits compared to the single price system. While profit of third degree price discrimination is less than the two part tariffs.

Maximum profits can be gained from the two-part tariffs.

Surplus is maximum under the two part tariffs. total Surplus is minimum under the single price strategy