Question

1. Consider a wholesaler and a retailer selling designer handbags. Each has market power. The wholesaler sells designer handbags to the retailer, which then sells the handbags to consumers. The demand for handbags is captured by P = 24-Q. Assume that the marginal cost of producing a handbag is constant (MC=$8). Consider the following scenarios: a. Suppose that the retailer is the only firm and that it can produce the handbags it sells (there is no wholesaler here). How many handbags will be produced and what price will be charged? Draw a graph and show these points on the diagram. b. Now suppose that the retailer cannot produce handbags and must instead buy them from the wholesaler. The wholesaler charges the downstream firm $16 per handbag. How many handbags will the retailer purchase and sell, and what price will the retailer charge? 2. If the wholesaler and retailer in problem 1 merged, what would be the effect on overall social surplus?

Answer 1

1. a)

P = 24 – Q

TR = PQ= 24Q – Q²

MR = 24 – 2Q

And MC = 8

When the retailer is the only producer and seller in the market, retailer has the monopoly power in the market. In equilibrium, MR = MC => 24 – 2Q = 8

=> 2Q= 16 => Q= 8

The retailer can produce 8 units of bags and the price will be P = 24 -8 = $16

In diagram, AR, MR curves of the retailer is negatively sloped and MC curve is horizontal straight line being constant. The profit maximizing output is 8 units and price is $16.

b) As the retailer has to buy each bag from the wholesaler, the marginal cost of the retailer increased from $8 to $16

In equilibrium, MR = MC => 24 – 2Q = 16

=> 2Q= 8 => Q= 4

The retailer can produce 4 units of bags and the price will be P = 24 -4 = $20

2. If the retailer and wholesaler merged, the first equilibrium in question 1 will be restored, i.e, each bag will be sold at $16 and 8 units will be sold in the market. Hence, social surplus is consumer surplus + producer surplus.

CS = area under demand curve and above price line. PS = area under price line and above supply curve (here, MC)

CS = 1/2 * (24- 16) * 8 = 8* 8* 1/2 = $32

PS = (16 - 8) * 8 = $64

Total social surplus = $(32 + 64) = $96

Social surplus will increase as both retailer and consumers are benefited.