Question

In: Economics

10. Consider a market in which there is a monopoly manufacturer and a mo nopoly retailer....

10. Consider a market in which there is a monopoly manufacturer and a mo nopoly 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 (to 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). The Manufacturer charges the Retailer t per unit per unit, and the retailer charges the fi nal consumers pR (and sells quantity qR). What is the loss from the two firms acting like separate profit maximisers (compared with the profit maximising outcome)?

a. 75

b. 125

c. 250

d. 375

*e. None of the above

Expert Solution

There is a monopoly manufacturer and a monopoly retailer.

M has a marginal cost of 20 per unit which is purchased as an input by retailer R at a price 't' that greater than the marginal cost of $20.

M charges the Retailer t per unit per unit, and the retailer charges the final consumers pR and sells quantity qR). This implies for retailer, the marginal cost is t.

Market demand faced by retailer is given by pR = 200 – qR.

Marginal revenue is MR = 200 - 2qR.

This gives MR = MC or 200 - 2qR = t

This is the demand function faced by manufacturer and so its marginal revenue is

MR(M) = 200 - 4qR. Its MC is 20 so we have

200 - 4qR = 20

qR = 180/4 = 45 units and we then have

t = 200 - 2*45 = $110 and pR = 200 - 45 = $155

Profit for both of them = profit for retailer + profit for manufacturer

= (155 - 110)*45 + (110 - 20)*45

= 6075

Now if they maximize profit jointly, M will sell the input to R at its marginal cost of 20. This will then imply that R has a marginal cost of 20

Marginal revenue is MR = 200 - 2qR.

This gives MR = MC or 200 - 2qR = 20

qR = 180/2 = 90 units and we then have

pR = 200 - 90 = $110

Profit for both of them = profit for retailer + profit for manufacturer

= 0 + (110 - 20)*90

= 8100

Hence the loss from the two firms acting like separate profit maximisers (compared with the profit maximising outcome) = 6075 - 8100 = -2025

Rahul Sunny answered 6 hours ago

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