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

ID: 1115175 • Letter: S

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 and a per unit fee equal to marginal cost.

a. What is the marginal cost and therefore the price charged per unit based on this strategy?

b. At the price found in part a, what quantity will each customer purchase?

c. Determine the firm’s revenue per customer from the per unit charge, using the answers to parts a and b.

d. Determine the consumer surplus that the firm can charge each customer as an entrance fee.

e. Determine the total revenue from each customer using the answers to parts c and d.

f. Determine the total cost at the quantity found in part b.

g. Determine the profit that the firm will make from each customer.

1- marginal cost is the additional cost of producing an additional unit of a commodity, it is calculated here as

D(tc)/dq = 8

now if we keep this price the quantity purchased is 6

now thus entrance fee is equal to the consumer surplus at this price and quantity and here it is

0.5(20-8)(6) = 36

b- quantity purchased is here equal to 6 as calculated above,

c- total revenue is , fixed fee+ variable fee

36+6*8 = 84

d- consumer surplus is calculated above as will be charged and is equal to 36.

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