Question

Consider a model of an upstream manufacturer producing a good that it sells to a downstream retailer for resale. Both the upstream manufacturer and the downstream retailer are monopolists. Inverse market demand for the final good is given by P = 100 - Q. The marginal cost for the upstream firm is 40 per unit of good produced. The retailer faces no costs other than the cost of purchasing the good from the manufacturer.

b) Now, suppose that the upstream and downstream firms merge. Derive the profit maximizing price and quantity, and the corresponding profits. Are consumers better off or worse off as a result of the merger? Provide a careful economic explanation for your answer.

Answer 1

b) Merger:

TR = PQ = (100 - Q)Q

TR = 100Q - Q²

MR = 100 - 2Q

MC = 40

Equilibrium condition; MR = MC

100 - 2Q = 40

2Q = 60

Q = 30 units

P = 100 - Q = 100 - 30

P = $ 70

Profit = TR - TC = PQ - 40Q = Q(P - 40)

Profit = 30(70 - 40) = 30 x 30

Profit = $ 900