Question

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?

Answer 1

D_R = P = 3000-0.5Q is the demand faced by the retailer

D_w = MR_R = 3000-Q is the marginal revenue of the retailer and the demand curve faced by the wholesaler

Hence, MR_W = 3000-2Q is the marginal revenue faced by the wholesaler; MC_W = 500

Maximising condition for wholesaler's profit

MR_W = MC_W

3000-2Q=500

or, Q_w = 1250 P_w = 3000-1250 = 1750 this is the price paid by the retailer to the wholesaler per unit of jewellery

Therefore, MC_R = 1750+100 = 1850

Maximising condition for the retailer's profit MC_R = MR_R

1850= 3000-Q

or, Q_R =1150 P_R = 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