Question

A firm sells to consumers who each have a demand demand function given by QD = 80 - P. It has constant marginal cost C = 20 with no fixed cost. Compared to the optimal two-part tariff, a policy of "buy the first 20 units for $60 each and get the next 20 for $40 each" would yield:

A. $600 less in profits

B.$400 less in profits

C.$200 less in profits

D. The same profits because the average price is the same in both cases.

Answer 1

The correct answer is (a) $600 less in profits

Suppose he sells first 20 units for $60 each and next $20 for $40 each. In such case Profit is given by:

Profit = Total Revenue - Total Cost

Total Cost = MC*40 = 40*20 = 800

Total Revenue = Price *Quantity

=> Total Revenue = 20*60 + 20*40 = 2000

Hence Profit is this case = 2000 - 800 = $1200

TWO PART TARIFF
In order to maximize profit under two part tariff a firm charges that price at which Price = Marginal Cost and Charges Entry fee or fixed fee = consumer surplus.

Here MC = 20. Hence P = MC = 20 and Q = 80 - 20 = 60. Hence Quantity sold = 60 and cost of $20 per unit. But we also have to calculate entry or fixed fee.

Consumer surplus is the area above price line and below demand curve.

When Q = 0 , P = 80(Vertical intercept)

Hence Consumer surplus = (1/2)(80 - 20)*60 = 1800

Hence consumer surplus = 1800 and Fixed Fee = 1800

Total Revenue = Fixed fee + amount received from sale of good = 1800 + 20*60

Total Cost = 20*60 = 1200

Hence Profit under optimal 2 part tariff = 1800 + 20*60 - 20*60 = 1800

Hence Profit under two part tariff will be greater by 1800 - 1200 = $600.

Hence the correct answer is (a) $600 less in profits