Question

PERFORMANCE EVALUATION – Economics for Business Decisions

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

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?

A firms maximize its profit when MR =MC

MC = 450 + 50 = $500

MR = (d/dQ)(Q)(3500 - 10Q) = 3500 - 20Q

we have

3500 - 20Q = 500

=> Q = 3000/20

= 150

and P = 3500 - 10*150

= $ 2000

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

Market price is 2000 and Assemly cost is 450

hence optimum transfer price should be

450 + (2000 - 450)/2

= 550 + 1550/2

= 450 + 775

= $1225

Profit for each division will be 775*150

= 116250