Question

Monoetronic is a monopolist selling wireless glucose monitors for patients with diabetes. Suppose its marginal cost is $200. Suppose its inverse demand curve in the U.S. is

p_a = 1,500 – 2q_a

and the inverse demand curve in Canada is

p_c = 1,000 – q_c

Assume that Canadian customers cannot buy Monoetronic’s wireless glucose monitors from the American market (i.e., resale is impossible).

(a) What are the company’s profit-maximizing quantity and price in the U.S.? What are the profit-maximizing quantity and price in Canada?

(b) With profit-maximizing quantity and price you identify in (a), what is the elasticity of demand for wireless glucose monitors in each country? Which country has more elastic demand?Is price higher or lower in the country with more elastic demand?

Answer 1

Marginal cost is $200

Inverse demand functions are Pa = 1500 – 2qa and Pc = 1000 – qc

Marginal revenue functions are MRa = 1500 – 4qa and MRc = 1000 – 2qc

Use MR = MC in respective markets when there is a price discrimination

1500 – 4qa = 200 and 1000 – 2qc = 200

a) This gives qa = 1300/4 = 325 units and qc = 800/2 = 400 units

This also gives Pa = 1500 – 2*325 = $850 per unit and Pc = 1000 – 400 = $600 per unit

These are the prices and quantities in these two markets

b) Use ed = P/(P – MC)

In the US, ed = -850/(850 – 200) = -1.308 and in Canada, ed = -600/(600 – 200) = -1.50

Here, market in Canada is more elastic. This is also the market where price is lower, because price discrimination allows the price to be lower relatively, in the market with elastic demand to maximize profits.