Exam 11: Topics in Pricing and Profit Analysis

Alpha Electronics produces sophisticated business computers. Its subsidiary, HRD Drives, produces hard disks which Alpha uses in each computer. HRD operates in a competitive market; each disk sells for $120.00 on the open market. Management has determined that the demand curve for quantity sold per month of the computers is: Q_c = 8,000 - .4P_c while Alpha's marginal cost for the computers, excluding the cost of the disks is: MC_c = 5Q_c In addition, management has determined that the total cost function for the disks is: TC_d = 18Q_d + .0075Q_d² a. At what final product price and rate of output will the firm maximize profit? b. How much of the transfer product should be produced? c. Should the final product division obtain all of its disks for the computers from HRD Drives? Why or why not?

In the case of joint products produced in fixed proportions, each increment of output, Q, consists of a different ratio of the jointly produced products.

Price discrimination is permitted when it can be justified under each of the following basis EXCEPT:

Bundling is a pricing strategy:

Where there is a perfectly competitive external market for a transfer product, the final product division should not pay the transfer product division a price in excess of that at which the transfer product can be obtained from outside suppliers.

A firm produces two products, "r" and "s", and the production process is such that one unit of "r" is always obtained with one unit of "s". If the demand curves for "r" and "s" are estimated to be: Q_r = 75 - P_r so that MR_r = 75 - 2Q_r) and Q_s = 100 - .5P_s so that MR_s = 200 - 4Q_s) and the marginal cost of production is MC = 75 + 4Q_j, where Q_j consists of one unit of each product, the firm will maximize profits if it sells 20 units of "r" and 20 units if "j".

Where there is a perfectly competitive external market for a transfer product, and the final product division maximizes profit at a lower output level than that of the transfer product division, the transfer products division should sell the quantity Q_T - Q_F of the transfer product in the external market at the prevailing market price.

A firm produces two products, x and y, and the production process is such that one unit of x is always obtained with one unit of y. If the demand for x and y are estimated to be: Q_x = 100 - P_x so that MR_x = 100 - 2Q_x) Q_y = 220 - P_y so that MR_y = 220 - 2Q_y) and the marginal cost of production is MC = 50 + .5Q_j, where Q_j consists of one unit of each product, how much of product x and product y should the firm sell in order to maximize profit?

The decision rule for maximizing profits for joint products is:

When a firm is practicing price discrimination in two markets, the profit maximizing condition is met at MR_A = MR_B = SMC.