Question

A firm's total cost of producing Q units of output is C (Q) = 79 + 20Q. The inverse demand curve for the firm's product is P(Q) = 100-Q, where P denotes the price of the product. 

a) If the price of the product is set equal to the firm's marginal cost, what profit will the firm earn? 

b) If the firm charges a two-part tariff (a fixed fee plus a per unit price), how large is the fixed fee? How large is the deadweight loss?

Answer 1

From the information provided the marginal cost is $20.

a) when the price is equal to the marginal cost of production it means that the price will be $20. At this price there will be 100-20= 80 units sold by the firm. Cost of producing these units will be C = 79+20*80 = 1679 and total revenue will be 80*20 = 1600. This indicates that there will be a loss of $79

b) in case of two part tariff that per unit price will still be equal to the marginal cost which is $20. The fixed fee will be equal to the consumer surplus at this level. This is computed as 0.5*(100-20)*80 = $800. There will be no deadweight loss because price is set equal to the marginal cost.