Question

6. Consider a market in which there is a monopoly manufacturer and a monopoly retailer. The manufacturer M makes an input for a marginal cost of 20 per unit. This input is sold to the retailer R, who then sells to the final goods market (t o the end user). The retailer has no costs of its own (other than any price charged for the input by M). The final market demand is given by P = 200 – q. Assume that both firms act to maximise their own profit (and price discrimination is not feasible). Th e Manufacturer charges the Retailer t per unit per unit, and the retailer charges the final consumers pR (and sells quantity qR). To maximise its profits, M sets a t of

a. 60

b. 70

c. 80

d. 90 *

e. None of the above

Answer 1

End consumer demand P = 200 - q

Total revenue to the retailer = Pq = (200 - q)*q

Total cost to the retailer = t*q

Retailer will set the price to maximise their profit --> MR = MC

MR for retailer = d (TR)/ Dq = 200-2q

MC for retailer = t

200-2q = t

Hence, for the manufacturer, the demand curve is 200 - 2q = t

Total revenue for manufacturer = (200-2q)*q

Marginal revenue for manufacturer = 200 - 4q

For maximising profit, MR = MC ---> 200-4q = 20

q = 45 units.

t = 200-2q = 110

So, the answer is E (none of the above).