Question

Economics - PERFORMANCE EVALUATION

Computer Company assembles personal computers and sells them in the retail marketplace. The company is organized into two profit centers: the assembly division and the distribution division. The demand curve facing the company (and the distribution division) is P = 3,500 – 10Q. The marginal cost for assembly (which includes purchasing the parts) is constant at $450. The distribution division faces constant marginal distribution costs of $50 per unit.

A. What is the profit-maximizing retail price and output for the firm as a whole?

B. If the assembly division has monopoly power to set the transfer price, what transfer price will it select (assuming it knows all the information above)? Calculate the profits for the two-divisions in this case.

Answer 1

Answer :-

Given :-

The company is organized into two profit centers: the assembly division and the distribution division.

The demand curve facing the company is P = 3500 – 10Q.

The marginal cost for assembly is constant at =$450.

The distribution division faces constant marginal distribution costs of = $50 per unit.

(A) :-

When MR= MC , then a firms maximize it's price.

MC = 450 + 50

[ MC = 500 ]

MC = $500

MR = (d/dQ) Q x ( 3500 - 10Q)

[ MR = 3500 - 20Q ]

Now ,

MR = MC

3500 - 20Q = 500

3500 - 500 = 20Q

3000 = 20Q

Q = 3000/20

[ Q = 150 ]

Now,

P = 3500 - 10Q

= 3500 - 10 x 150

= 3500 - 1500

= 2000

[ P = $2000 ]

(B) :-

The Marginal cost for assembly = $450

Market price = $2000

Therefore optimum transfer price should be

= 450 + [ 2000 - 450]/2

= 450 + 1550/2

= 450 + 775

= $1225

Optimum transfer price = $1225

Profit for each division will be = 775 x 150

= 116250