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

The organization is divided into two profit centres: the division of assembly and the division of distribution.
The demand curve = 3500 - 10Q
The marginal cost = $450.
The distribution division's marginal distribution costs = $50 per unit.

A.
MR= MC, if a firms maximize it's price.

Total MC = 450 + 50 = $500

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

Now, MR = MC

3500 - 20Q = 500

3000 = 20Q

Q = 3000/20 = 150

Now, P = 3500 - 10Q = 3500 - 10 x 150 = 2000

Market price = $2000

B.

Optimum transfer price = 450 + [ 2000 - 450]/2
= 450 + 1550/2 = 450 + 775 = $1225

So, Optimum transfer price = $1225

Profit for each division = 775 x 150 = 116250

Please don't forget to like the solution if it is helpful. Thank you.