The average consumer at a firm with market power has an inverse demand function of P = 10 − Q.The firm's cost function is C = 2Q.If the firm engages in two-part pricing,what is the optimal fixed fee to charge each consumer?
A) $2
B) $32
C) $64
D) None of the answers are correct.

Question

Quizplus · Accepted Answer

In two-part pricing, the firm charges a fixed fee (F) to each consumer in addition to a per-unit price (P). To determine the optimal fixed fee, we need to find the profit-maximizing values of F and P.

First, we can use the inverse demand function to find the profit-maximizing per-unit price:

TR = P(Q)Q = (10 − Q)Q 
MR = 10 − 2Q

Setting MR = MC:

10 − 2Q = 2 
Q = 4

P = 10 − Q = 6

So the profit-maximizing per-unit price is $6.

Next, we can use this per-unit price to find the optimal fixed fee:

TC = 2Q + F 
FC = 2(4) + F = 8 + F

To maximize profit, we need to set the fixed fee such that the marginal consumer is just willing to pay the full price (P + F) but no more. In other words, we need to set the fixed fee equal to the difference between the consumer's willingness to pay (P) and the marginal cost (MC) of providing the service:

F = P − MC = 6 − 2 = 4

Therefore, the optimal fixed fee to charge each consumer is $4.

The total price that each consumer would pay is: 
Total Price = Fixed Fee + (Per Unit Price x Quantity) 
Total Price = 4 + (6 x Q) = 4 + (6 x 4) = $28

Thus, the best choice is B.

The Average Consumer at a Firm with Market Power Has