Question

Suppose a manufacturer is a monopoly. This manufacturer produces a good at MC = 20 and sells it to a retailer. The retailer is also a monopoly, and it sells the good bought from the manufacturer to consumers. The retailer has no additional costs other than the price they pay to the manufacturer. The retailer faces a demand curve P = 180 –2Q, where Q is the number of units sold.

a) What price will the manufacturer charge to the retailer?

b) What price will the retailer charge to the consumers?

c) If the two firms merged, what would be the price charged?

d) If the two firms merged into a single firm, how much profit would the firm make?

e) How much profit would the two firms make if they do not merge?

ΠM =

ΠR =

Total Π =

Answer 1

a). Price charged by manufacturer to retailer = $ 20.

Explanation :- Monopolist will choose to produce the quantity level where marginal cost (MC) equals to marginal revenue (MR). Accordingly, Manufacturer, being monopolist, will charge the price of $ 20 (equal to MC) to retailer while selling him goods.

b). Price charged by retailer to consumers = $ 100.

Explanation :- P = 180 -2Q

Total revenue (TR) = P * Q

TR = (180 -2Q) * Q

TR = 180Q - 2Q²

Marginal revenue (MR) is the first derivative of total revenue (TR) function.

MR = 180 - 2 * 2Q

MR = 180 - 4Q

For monopolist, MR = MC

180 - 4Q = 20

180 - 20 = 4Q

160 = 4Q

Q = 160 / 4

Q = 40 units.

P = 180 - 2 * 40

P = 180 - 80

P = $ 100.