The inverse market demand curve facing a monopoly retailer of gold jewelry is described by P=3000-0.5Q. The retailer buys jewelry at a wholesale price, r, set by the monopolist manufacturer. Marginal cost for the manufacturer is 500. The retailer has additional marginal costs=100.
What is the profit-maximizing wholesale price for the manufacturer?
What is the profit-maximizing retail price for the retailer?
What is the profit-maximizing quantity?
If the two firms merged, what would be the profit-maximizing retail price and quantity?
DR = P = 3000-0.5Q is the demand faced by the retailer
Dw = MRR = 3000-Q is the marginal revenue of the retailer and the demand curve faced by the wholesaler
Hence, MRW = 3000-2Q is the marginal revenue faced by the wholesaler; MCW = 500
Maximising condition for wholesaler's profit
MRW = MCW
or, Qw = 1250 Pw = 3000-1250 = 1750 this is the price paid by the retailer to the wholesaler per unit of jewellery
Therefore, MCR = 1750+100 = 1850
Maximising condition for the retailer's profit MCR = MRR
or, QR =1150 PR = 3000- 0.5*1150= 2425 (maximising output and prices for the retailer)
If the two firms merge they will face the demand curve P = 3000-0.5Q and marginal revenue curve would be MR = 3000-Q and MC = 500
Profit maximising condition for the merged firm is MC= MR
500 = 3000-Q
or, Q =2500
P = 3000- 0.5* 2500
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