Question

# The inverse market demand curve facing a monopoly retailer of gold jewelry is described by P=3000-0.5Q....

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

3000-2Q=500

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

1850= 3000-Q

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

= 1750

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