# The opportunity cost of a decision

1. (4 pts.) Joe faced the following options: (a) pay $10,000 tuition to attend classes at Econ Tech; (b) work as a fry cook for $10,000; or (c) work as a waiter at an elite restaurant and earn $20,000. What is Joe's opportunity cost of attending classes at Econ Tech?

2. (8 pts.) Sun City, Arizona, a retirement community that features full-service living arrangements, is considering proposals to provide lawn-care to elderly residents. The city has conducted a survey of Sun City residents to estimate the amount they would be willing to pay for various amounts of lawn service. The city has also estimated the total cost of service per resident. Data appear below. Use the indicated demand and cost data to complete the following table and answer the questions below.

Hours of

Lawn Care

per Month Price

per

Hour

Total Revenue

Marginal

Revenue

Total

Cost

Marginal

Cost

Profit

0 $7.50 $ 0.00

1 7.25 7.00

2 7.00 13.50

3 6.75 19.50

4 6.50 25.25

5 6.25 30.75

6 6.00 35.75

7 5.75 40.25

8 5.50 44.00

9 5.25 50.00

10 5.00 60.00

A. Explain briefly how you calculated the values in the 4 empty columns above.

B. How many hours of lawn care per month will maximize total profit?

C. What is the value of total profits at the profit-maximizing level of lawn care hours?

D. What is the relationship between marginal revenue and marginal cost at the profit-maximizing level of lawn care hours? Explain the significance of this relationship for profit maximization.

3. (4 pts.) You own and manage a small espresso café and are contemplating a purchase of a new machine that costs $5,000 to enhance the quality of your products and efficiency of your operation. You estimate that by purchasing the machine, total revenues will rise by $2,000 and that total explicit costs will fall by $1000. Further, with the new machine, you expect you will spend less time on equipment maintenance, allowing more time to spend with employees, customers and on strategic planning.

A. What is the net benefit of this purchase?

B. Should you purchase the new machine? Why or why not? Explain your criteria and assumptions carefully.

4. (4 pts.) Use the following equations for Revenue (R) and Cost (C) to answer the following questions:

R(Q) = $1000Q - $1Q2

C(Q) = $500 + $100Q

A. What level of production, Q, will yield maximum profit?

B. Calculate the maximum level of profit.

5. (4 pts.) State the Law of Demand. Then, write down a product or service you pay for regularly and indicate two reasons your demand for this product or service would fall (shift) and explain why these two factors would cause your demand to fall.

6. (14 pts.) Suppose demand and supply for a product are given by:

QS = 0.25P - 0.5

QD = 7 - 0.5P

A. Graph the supply and demand curves on the same graph, labeling everything carefully.

B. Determine the equilibrium price/output combination both graphically and algebraically.

C. Calculate the value of consumer surplus in this market and show it on your graph.

D. Will a price of $12 result in a shortage or a surplus in this market? Calculate the size (in units of Q) of the shortage or surplus, and show this on the graph.

E. If a $6.00 excise tax is imposed on the product what will be the new supply function? Show the effect of this tax on the graph, then determine the new equilibrium values of price and quantity both graphically and algebraically. (Hint: use inverse supply functions.)

F. How much tax revenue will the government earn with the $6.00 tax?

7. (4 pts.) Rapel Valley in Chile is renowned for producing high quality wine at a fraction of the cost of many other vineyards around the world. Rapel Valley produces over 20 million bottles of wine annually and exports 5 million of those bottles to the U.S. Strong La Nina weather patterns can cause unusually cold temperatures, sharply reducing wine production in that region of Chile. Assuming La Nina does not affect the California wine-producing region and that California wines are substitutes for Chilean wines, how will La Nina impact prices and quantity sold of California wines? Why?

8. (5 pts.) Last year's gas price increases in the U.S. were caused by two factors: 1) increased demand for gas in China, the U.S., and other countries, and 2) because most U.S. oil refineries were producing at or near their capacity limits, even before the hurricanes. Sketch a supply & demand graph for gasoline and show on the graph how the capacity limits (i.e. fixed capacity) at oil refineries combined with rising demand for gasoline have combined to cause gas prices to rise. Label all parts of the graph carefully.

9. (3 pts.) If quantity demanded for athletic shoes falls by 3% when the price increases by 5%, what is the value of the own-price elasticity of the athletic shoes? Is the demand at this point is elastic or inelastic? How do you know?

10. (3 pts.) Would the absolute value of the own-price elasticity of demand for fruit be greater than or less than that of bananas? Why?

11. (3 pts.) You manage a supermarket and know the income elasticity of peanut butter is -0.75. If government reports are estimating 2% growth in personal incomes this year, how should you adjust your purchase of peanut butter in percentage terms? Why?

12. (6 pts.) You monitor cash flow at Kodak and received a report that the cross-price elasticity of demand between digital and disposable cameras is 0.25 and that the own-price elasticity of demand for disposable cameras is -0.8. If Kodak earns about $600 million from sales of digital cameras and about $400 million from sales of disposable cameras, how will a 1 percent decrease in the price of disposable cameras affect Kodak's overall revenues from both disposable and digital camera sales? Indicate whether total revenues would rise, fall, or remain unchanged. If they would rise or fall, indicate the dollar amount of the change. Whatever your answer, EXPLAIN it in words.

13. (4 pts.) Suppose the demand for good X is: Qdx = 100 - 2PX + 4PY - 2M + 4A

where PX is the price of good X, PY is the price of good Y, M is income, and A is the amount of advertising on good X.

A. Is Y a complement or a substitute for X? How do you know? Explain.

B. Is X a normal good or an inferior good? How do you know? Explain.

14. (8 pts.) The demand for coupon books has been estimated as:

Qdx = 5000 - 4000P + 0.02Pop + 0.5M + 1.5A

Where Q is quantity, P is price ($), Pop is population, M is income per household and A is advertising expenditures ($). Suppose the books sell for $10, Pop = 1,000,000 persons, M = $30,000 and A = $10,000.

A. Calculate the own-price elasticity of demand then interpret your result; that is, explain whether demand at this point is elastic or inelastic.

B. Graph this demand curve, labeling it DB. Show at least 2 specific points on the graph.

C. Suppose household income rises to $35,000. Determine the new demand function, then graph the new demand curve for the coupon books on the graph in part B, labeling it DC. Show at least 2 specific points on the graph.

15. (12 pts.) In 1993, a public transportation agency serving commuter rail transportation needs of a large city was considering a fare increase on trains from $1.00 to $1.50. So the board ordered the manager to conduct a study of the likely impact of this proposed fare increase. The manager collected data on important variables thought to have a significant impact on the demand for rides (in 1000s) over 24 years as follows: Price per ride (in cents); Population in the metropolitan area serviced by the agency (in 1000s); Disposable per capita income; and the Parking rate per hour in the downtown area (in cents.) The transit manager then performed a multiple regression on the data to determine the impact of the rate increase. The data and regression results appear below:

Data and Regression results on Transit Ridership

Year Weekly riders (x1000) Price (cents) Population (x1000) Income Parking rate (cents)

1966 1200 15 1800 2900 50

1967 1190 15 1790 3100 50

1968 1195 15 1780 3200 60

1969 1110 25 1778 3250 60

1970 1105 25 1750 3275 60

1971 1115 25 1740 3290 70

1972 1130 25 1725 4100 75

1973 1095 30 1725 4300 75

1974 1090 30 1720 4400 75

1975 1087 30 1705 4600 80

1976 1080 30 1710 4815 80

1977 1020 40 1700 5285 80

1978 1010 40 1695 5665 85

1979 1010 40 1695 5800 100

1980 1005 40 1690 5900 105

1981 995 40 1630 5915 105

1982 930 75 1640 6325 105

1983 915 75 1635 6500 110

1984 920 75 1630 6612 125

1985 940 75 1620 6883 130

1986 950 75 1615 7005 150

1987 910 100 1605 7234 155

1988 930 100 1590 7500 165

1989 933 100 1595 7600 175

1990 940 100 1590 7800 175

1991 948 100 1600 8000 190

1992 955 100 1610 8100 200

Regression Statistics

Multiple R 0.979803684

R Square 0.960015259

Adjusted R Square 0.952745306

Standard Error 20.48984448

Observations 27

ANOVA

df SS MS F Significance F

Regression 4 221760.3247 55440.08117 132.0524714 4.82838E-15

Residual 22 9236.341987 419.8337267

Total 26 230996.6667

Coefficients Standard Error t Stat P-value

Intercept 85.43924099 492.8046279 0.173373455 0.863943188

Price per ride (cents) -1.617484194 0.495975827 -3.261215782 0.00357601

Population (1000s) 0.643769498 0.262358085 2.453781813 0.022522326

Income -0.047474815 0.012311414 -3.856162496 0.000856

Parking rate (cents) 1.943790812 0.349156013 5.567112521 1.35042E-05

Based on the regression output for Transit Ridership, answer the following questions:

A. Write down the resulting demand equation for transit service.

B. Give an economic interpretation for each of the coefficients in the resulting demand equation.

C. Which regression coefficient(s) is (are) statistically significant at the 5% level? Explain how you know in each case.

D. How well does the regression equation fit the data? Explain how you know.

E. If the fare had been increased to $1.50, what would have been the expected change in weekly revenues of the transit system if all other variables remained at their 1992 levels? Explain.

16. (10 pts.) The following table summarizes the short-run production function for a window manufacturer. The product sells for $5 per unit, workers are paid $50 per unit, and the rental price of capital is $10 per unit. Complete the following table, then answer the questions below.

Capital (K) Labor (L) Output (Q) Marginal Product of Labor (MPL) Value of Marginal Product of Labor ($)

5 0 0

5 1 10

5 2 30

5 3 60

5 4 80

5 5 90

5 6 95

5 7 95

5 8 90

5 9 80

5 10 60

5 11 30

A. Briefly explain how you calculated the values in the empty columns above.

B. Which input is fixed and which input is variable?

C. How much are the fixed costs, in dollars?

D. How many units of the variable input should be used to maximize profit? Explain how you know.

E. Calculate the value of maximum profit.

F. Over what range of variable input usage do increasing marginal returns exist?

17. (4 pts.) A local restaurateur whose business had been profitable for many years recently purchased a liquor license, giving her a legal right to sell beer, wine and spirits at the restaurant. The license cost $75,000. While the license is transferable, only $65,000 is refundable if the owner chooses not to use it. After selling alcoholic beverages for about a year, the owner realized she was losing dinner customers and that her formerly profitable restaurant was becoming a noisy, unprofitable bar. Subsequently, she spent $6000 on advertisements in local newspapers and magazines offering to sell the license for $70,000. After a long wait, she received one offer to purchase the license for $66,000. Would you recommend she accept the $66,000 offer? Why or why not? Explain.

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#### Solution Summary

The opportunity cost of a decision is examined.

Analyze Cost and Role in Decision Making

Analyzing Cost and Its Role in Decision Making

The concept of opportunity cost and examination of how to calculate the cost of alternatives over single and multiple time periods. Analyze cost and its role in the decision-making process by answering the following questions:

? Citing examples, differentiate between opportunity cost, marginal cost, and relevant cost.

? Assess the relationship of marginal benefit and marginal costs. How is marginal benefit measured, and how does it relate to marginal costs?

? What other factors must managers address before making decisions? Why?