Suppose that each of a firm’s customers has the following demand curve: P = 20 –

Question

Suppose that each of a firm’s customers has the following demand curve: P = 20 – 2Q. Suppose also that the firm’s total cost function is TC = 8Q.

Strategy: An entrance fee with no per unit charge.

a. Use the demand curve equation to determine how much each customer will purchase if there is no per unit charge (that is, P = 0).

b. Determine the consumer surplus that the firm can charge each customer as an entrance fee when price is zero.

c. What is the total cost per customer at the quantity consumed by each customer in part a?

d. Determine the profit that the firm will make from each customer. (Remember that the total revenue per customer will be the entrance fee since there is no per unit charge.)

Explanation / Answer

Answer
a)
The firm produces at MC=P
MC=dTC/dQ=8
equating
20-2Q=8
Q=6
Each customer will purchase 6 units of goods

b)
CS=0.5*(20-8)*6
=$36
the firm charge the bunch of goods is $36
c)
Cost=8*6=48
the cost per customer is $48
d)
profit=P-TC=36-48=-12
The firm makes loss of $12 from each customer

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