Question

A monopolist has two specific demanders with demand equations: A = 10-p and B = 10 -2p. This monopolist implements an optimal two-part tariff pricing scheme, under which demanders pay a fixed fee a for the right to consume the good and a uniform price p for each unit consumed. The monopolist chooses a and p to maximize profits. This monopolist produces at constant average and marginal costs of AC = MC = 2. The monopolist's profits are and the average price paid by demander B (NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed. Use a period for the deammal separator and a comma to separate groups of thousands. HINT: See Example 14.6.)

Answer 1

Part 1) We have the following information

Average Cost (AC) = Marginal Cost (MC) = 2

Fixed fees = a

Uniform price for each unit consumed = p

Ideally we want to capture the entire consumer surplus. Consumers have the most surplus when Price = MC (the lowest price at which producer will still offer the good). In this case, if one charges 2 per unit, Consumer A would purchase

q_A = 10 – p

q_A = 10 – 2

q_A = 8

and Consumer B would purchase

q_B = 10 – 2p

q_B = 10 – (2 × 2)

q_B = 10 – 4

q_B = 6

Price A Consumes A Consumer B 1o * Consumer Surplus umer Surplus > 10 Quantity She

The consumer surpluses (CS) would be

CS of A = ½ × 8 × 8

CS of A = 32

If the monopolist charges the Consumer A 32 for the right to consume the good, then the monopolist will "break even" when Consumer A purchases the good at 2 for each unit. So, the consumer A will purchase the product and at the same time the monopolist would get the entire consumer surplus.

CS of B = ½ × 3 × 6

CS of B = 9

If the monopolist charges the Consumer B 9 for the right to consume the good, then the monopolist will "break even" when Consumer B purchases the good at 2 for each unit. So, the consumer B will purchase the product and at the same time the monopolist would get the entire consumer surplus.

Profit from Consumer A = Total Revenue (TR) – Total Cost (TC)

TR from A = Fees for the right + (Price × Quantity)

TR from A = 32 + (2 × 8)

TR from A = 32 + 16

TR from A = 48

TC = 2q_A = 2 × 8 = 16

Profit from Consumer A = 48 – 16

Profit from Consumer A = 32

Profit from Consumer B = Total Revenue (TR) – Total Cost (TC)

TR from B = Fees for the right + (Price × Quantity)

TR from B = 9 + (2 × 6)

TR from B = 9 + 12

TR from B = 21

TC = 2q_A = 2 × 6 = 12

Profit from Consumer B = 21 – 12

Profit from Consumer B = 9

Total Profit = 32 + 9 = 41

Part 2) Diagram B represents the situation where the monopolist can operate only at a long-term loss and will decline to serve the market. This is because in diagram b the price of the monopolist is lower than the average cost.