Question

A monopoly sells its good in the United​ States, where the elasticity of demand is negative 1.6 ​, and in​ Japan, where the elasticity of demand is negative 5.6 . Its marginal cost is ​$7 . At what price does the monopoly sell its good in each country if resales are​ impossible?

Answer 1

a. The monopoly will sell its good in the United​ States at $18.67.

b. The monopoly will sell its good in Japan at $8.52.

Step-by-step explanation:

For any firm, profit is maximized where marginal revenue (MR) is equal to marginal cost (MC), i.e. where;

MR = MC ................................. (1)

For a monopolist, relationship between MR, the price elasticity of demand, and the price that gives maximum profits is given as follows:

MR = P(1 + 1/E) .................... (2)

Where P denotes price and E denotes elasticity of demand.

Since from equation (1) we have MR = MC, it also implies that from equation (2):

MC = P(1 + 1/E) .................... (3)

Equation (3) will now be used to solve this question when it can price discriminate and also impossible to resell as follows:

a. Calculation of monopoly price in the United​ States

Given;

MC = $7

E = -1.6

Substituting the values into equation (3) and solve for P, we have:

$7 = P(1 + 1/(-1.6))

P = $7 / (1 - 0.625)

P = $7 / 0.375

P = $18.67

Therefore, the monopoly will sell its good in the United​ States at $18.67.

b. Calculation of monopoly price in the Japan

Given;

MC = $7

E = -5.6

Substituting the values into equation (3) and solve for P, we have:

$7 = P(1 + 1/(-5.6))

P = $7 / (1 - 0.178571428571429)

P = $7 / 0.821428571428571

P = $8.52

Therefore, the monopoly will sell its good in Japan at $8.52.