Suppose that the demand for a monopolist's product is estimated to be Q^d = 100 - 2P and its total costs are C(Q) = 10Q. Under first-degree price discrimination, the optimal price(s), number of total units exchanged, profit, and consumer surplus are: A) P = $30; Q = 40, Π = $800; CS = $400. B) 10 ≤ P ≤ 100; Q = 80; Π = $1,600; CS = $1,600. C) 10 ≤ P ≤ 50; Q = 80, Π = $1,600; CS = $0. D) P = $30; Q = 40, Π = $600; CS = $0.

Question

Quizplus · Accepted Answer

Under first-degree price discrimination, the monopolist charges each consumer their maximum willingness to pay, which varies across consumers. This means that the monopolist will sell the same quantity of units as in a competitive market (Q = 80), but at different prices. The monopolist will set the price for the first unit at $50 (the highest price any consumer is willing to pay) and gradually decrease the price until the 80th unit is sold at a price of $10 (the lowest price any consumer is willing to pay). 
Total revenue will be the sum of the prices charged for each of the 80 units sold: 
total revenue = $50 + $48 + $46 + ... + $12 + $10 = $2,480 
Total cost will be: 
total cost = 10*80 = $800 
Profit will be: 
profit = total revenue - total cost = $1,680 
Consumer surplus will be zero under first-degree price discrimination since each consumer pays their maximum willingness to pay.
Thus, the optimal price range is 10 ≤ P ≤ 50, the number of total units exchanged is 80, the profit is $1,600, and consumer surplus is $0. Choice C is the only option that matches all these criteria.

Suppose That the Demand for a Monopolist's Product Is Estimated