Merriwell Corporation has a virtual monopoly in the ultra high speed computer market. Merriwell has recently introduced a new computer that will be used by installations around the world. The installations have identical demands for the computers. Merriwell's managers have decided to lease rather than sell the computers, but they have not yet decided whether to use a single hourly rental charge or a two-part tariff. Under the two-part tariff, users would be charged a monthly "access charge" plus an hourly rental rate. Merriwell's staff has estimated the following demand and marginal revenue curves for each user:

Demand: P = 45 - .025Q

Marginal Revenue: MR = 45 - .05Q

Where P = price per hour of computer time, and Q = the number of hours of computer time leased per month. Merriwell offers their users extensive maintenance assistance and technical support. The firm's engineers estimate that marginal cost is $30 per computer hour.

A. Assuming that Merriwell decides to set a single price, what will the firm's price and output be?

B. Assuming that Merriwell uses a two-part tariff, what "access charge" and hourly rental fee should the firm set?

C. Which strategy would you advise for Merriwell, the single price, or the two-part tariff? Explain.

Part I - Question 2

A firm sells a single product through its sales division and produces the product in its manufacturing division. The demand for the product is:

P_F = 250 - 2.5Q (firm demand)

The total cost of manufacturing is:

TC_M = 25 + 30Q + Q²

and the total cost of sales (excluding cost of transfer):

TC_S = 20 + 20Q + .5Q²

a.  Given the above demand and cost data, calculate the company's profit-maximizing price and output levels as well as the optimum profit. Assume that there is no external market for the intermediate product.

b.  Calculate and interpret the optimal transfer price that will result in maximum profit for the company. What problem would occur if the transfer price was set above this level?

c.  Suppose you represent corporate headquarters. What instructions would you give to the managers of the sales division to ensure that overall profits for the firm are maximized?

PART II: ANSWER TWO OF THE THREE QUESTIONS

Part II - Question 1

The Do-Drop-Inn, Inc., provides vacation lodging services to both family and senior citizen customers. Yearly demand and marginal revenue relations for overnight lodging services, Q, are as follows:

Family

P_F = $40 - $0.0004Q_F                                          Hint:  MR_F = ∂TR_F/ ∂Q_F                                          

Senior Citizens

P_S

= $30 - $0.00025Q_S                                                                    Hint:  MR_S = ∂TR_S/ ∂Q_S                                          

Marginal costs are constant at $20 per unit.

A. Assuming the company can discriminate in price between family and senior citizen customers, calculate the profit-maximizing price, output, and total profit contribution levels.

B. Which market segment has more elastic demand? Explain.

Part II - Question 2

TLC Tree Service, Inc., provides tree spraying services to residential customers in the Detroit area. The company recently raised its service price from $50 to $60 per tree. As a result, sales fell to 3,900 from 4,900 units in the prior year.

A. Calculate and interpret the arc price elasticity of demand for TLC service.

B. What is the profit-maximizing markup on tree spraying service? What price should the firm charge?