Economics 5415 Fall 1995
Managerial Economics Professor Henderson
Test No. 1
1. a. Fill in the missing data for price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), profit (), and marginal profit (M) in the following table:
Q P TR MR TC MC M
0 $160 $ 0 $ -- $ 0 $ -- $ 0 $ --
1 150 150 150 25 25 125 125
2 140 55 30 100
3 390 35 300 75
4 90 130 350
5 110 550 175
6 600 50 55 370
7 630 290 60 -30
8 80 640 355 285
9 75 -85
10 600 525
b. At what output (Q) level is profit maximized? Explain.
c. At what output level is total revenue maximized? Explain.
d. Discuss the reasons for the differences in your answers to parts b and c.
2. Characterize each of the following statements as true or false, and explain your answers.
a. Given a downward-sloping demand curve and positive marginal costs, profit-maximizing firms will always sell less output and at higher prices than will revenue-maximizing firms.
b. To maximize the value of the firm, management should always produce the level of output that maximizes short-run profit.
c. Total profit is the difference between total revenue and total cost and will always exceed zero at the profit-maximizing output level.
d. Marginal cost must be less than average cost at the average-cost minimizing output level.
e. The demand curve will be downward-sloping if marginal revenue is less than price.
3. The Indigent Care Center, Inc. is a private, not-for-profit medical treatment center located in Denver, Colorado. An important issue facing Jessica Nicholson, ICC's administrative director, is the determination of an appropriate patient load (level of output). To efficiently employ scarce ICC resources, the board of trustees has instructed Nicholson to maximize ICC operating surplus, defined as revenues minus operating costs. They have also asked Nicholson to determine the effects of two proposals for meeting new state health care regulations. Plan A involves an increase in costs of $100 per patient, whereas Plan B involves a $20,000 increase in fixed expenses. In her calculations, Nicholson has been asked to assume that a $3,000 fee will be received from the state for each patient treated. The fee is assumed fixed regardless of the patient load and does not depend on whether Plan A or Plan B is adopted. ICC has the following cost functions where Q is the number of ICC patients.
TC = 75,000 + 2,000Q + 2.5Q2
MC = 2,000 + 5Q
a. Before considering the effects of the proposed regulations, calculate ICC's optimal patient load and operating surplus level.
b. Calculate these levels under Plan A.
c. Calculate these levels under Plan B.
4. The demand for Penn's Oil motor oil can be characterized by the following point elasticities:
Indicate whether each of the following statements is true or false, and explain your answer.
a. A price increase for Penn's Oil will decrease both the number of units demanded and the total revenue of sellers.
b. The cross-price elasticity indicates that a 2% increase in the price of Value Lean will cause a 3% increase in Penn's Oil demand.
c. Demand for Penn's Oil is price elastic and the motor oil is a cyclical, normal good.
d. Falling Value Lean's prices will definitely increase revenues received by manufacturers of both brands of oil.
e. A 0.9% price reduction for Penn's Oil would be necessary to overcome the effects of a 3% decline in income.
5. KRDY-FM is contemplating a T-shirt advertising promotion. Monthly sales data from T-shirt shops marketing the "Listen to KRDY-FM" design indicate that Q = 3,000 - 500P, where Q is T-shirt sales and P is price.
a. How many T-shirts could KRDY sell at $4 each?
b. What price would KRDY have to charge to sell 2,000 T-shirts?
c. At what price would T-shirt sales equal zero?
d. How many T-shirts could be given away?
e. Calculate the point price elasticity of demand at a price of $4.
6. Hydraulics Ltd. has designed a pipeline that provides a throughput of 70,000 gallons of water per 24-hour period. If the diameter of the pipeline were increased by 1 inch, throughput would increase by 4,000 gallons per day. Alternatively, throughput could be increased by 6,000 gallons per day using the original pipe diameter with pumps that had 100 more horsepower.
a. Estimate the marginal rate of technical substitution between pump horsepower and pipe diameter.
b. Assuming the cost of additional pump size is $600 per horsepower and the cost of larger diameter pipe is $200,000 per inch, does the original design exhibit the property required for optimal input combinations? If so, why? If not, why not?
7. Fisherman's Wharf Cotton, Inc., (FWC) sells souvenir T-shirts on San Francisco's Pier 9 at a price of $10. Of this amount, $6 is profit contribution. FWC is considering an attempt to differentiate its product from several other competitors by using higher quality T-shirts. Doing so would increase FWC's unit cost by $1 per T-shirt. Current monthly profits are $5,000 on 2,500 unit sales.
a. Assuming average variable costs are constant at all output levels, what is FWC's total cost function before the proposed change?
b. What will the total cost function be if higher quality T-shirts are used?
c. Assume T-shirt prices remain stable at $10. What percentage increase in sales would be necessary to maintain current profits levels?
8. Malibu Motor Company is trying to decide the optimal number of two automobile models to maintain in inventory. The Alpha is a mid-sized car, and the Omega is a luxury sports car. Malibu has a showroom and lot space constraint of 60,000 square feet. It has a line-of-credit at the bank of $400,000 and because of nationwide demand the manufacturer will only allow 40 Omegas in inventory at any one time. One Alpha takes up 600 square feet of space and one Omega 450 square feet. Malibu needs $3,200 to finance each Alpha and $6,400 to finance each Omega. Profit contribution is $1,000 per Alpha and $3,000 per Omega.
a. Set up the primal and solve for the optimal combination of Alpha and Omega inventory.
b. Show your solution graphically.
c. What is the optimal profit?
d. Set up the dual. What is the marginal value of one more square foot of showroom or lot space? What is the marginal value of one more dollar in the line-of-credit?
If you have the time and energy, try this one for extra credit.
9. Skidmore and Associates is a small architectural firm located in Los Angeles, California, specializing in the preparation of architectural designs for multi-family residential housing complexes and commercial retail centers. Prevailing prices in the market are $10,000 for residential housing designs and $25,000 for commercial retail designs.
Six architects run the firm, and work a 50-hour workweek, 50 weeks per year. They are assisted by six drafting personnel and two secretaries, all of whom work a typical 40-hour workweek, 50 weeks per year. The firm must decide how to target its promotional efforts so as to best use its resources during the coming year. Based on previous experience, the firm expects that an average of 150 hours of architect and 100 hours of drafting time will by required for each residential housing complex design, whereas commercial retail design will require an average of 250 architect hours and 200 drafting hours. Fifty hours of secretarial time will also be required for each architectural design, housing and commercial. In addition, variable computer and other processing costs are expected to average $1,000 per residential design and $1,500 per commercial retail design.
a. Set up the linear programming problem the firm would use to determine the profit-maximizing output levels for residential and commercial designs.
b. Carefully sketch the objective function and constraints.
c. Completely solve and interpret the solution values.
d. Calculate maximum possible net profits per year for the firm assuming that architects draw a salary of $100,000 per year, drafting personnel earn $35,000 per year, secretaries are paid $10 per hour, and fixed overhead (including promotion and other expenses) averages $250,000.
e. Set up and solve the dual. How much money could be saved by eliminating one position in the drafting category?