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

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