Question

Problem X A,B: The market demand for a product is given by P = 30 ? 3Q. Assume the marginal cost of production is constant, MC = 6.

a) What is the optimal two-part tariff for a producer on this market? What is the resulting profit?

b) Assume now that there are two groups of consumers, one with the demand given above, and another group with a higher demand given by P = 30 ? 2Q. Also, assume marginal cost is zero. What is the optimal two-part tariff and the resulting profit under this scenario?

Please answer this question in complete detail as I don't understand this subject too well. Thank you

Answer 1

The market demand for a product is given by P = 30 - 3Q. Assume the marginal cost of production is constant, MC = 6.

a) What is the optimal two-part tariff for a producer on this market? What is the resulting profit?

In a two part tariff scheme, price is generally set equal to marginal cost and at that quantity, the entire consumer surplus is considered as the second part of price which is the fixed fee. In this case P = MC results in 30 - 3Q = 6 or Q = 24/3 = 8. Hence CS = 0.5*(Max price - MC)*qty = 0.5*(30 - 6)*8 = $96. Profit = CS = $96 per consumer. Pricing scheme: $6 per unit and $96 as fixed fee.

b) Assume now that there are two groups of consumers, one with the demand given above, and another group with a higher demand given by P = 30 - 2Q. Also, assume marginal cost is zero.

In this case P = MC results in 30 - 2Q = 0 or Q = 30/2 = 15. Hence CS = 0.5*(Max price - MC)*qty = 0.5*(30 - 0)*15 = $225. Pricing scheme: $0 per unit and $225 as fixed fee.