## 9/17/14

### managerial economics & business strategy by michael baye 8th edition solutions manual and test bank

managerial economics & business strategy (mcgraw-hill economics) by michael baye and jeff prince 8th edition solutions manual and test bank 0073523224

Chapter 2: Answers to Questions and Problems

1.

a. Since X is a normal good, a decrease in income will lead to a decrease in the demand for X (the demand curve for X will shift to the left).

b. Since Y is an inferior good, an increase in income will lead to a decrease in the demand for good Y (the demand curve for Y will shift to the left).

c. Since goods X and Y are substitutes, an increase in the price of good Y will lead to an increase in the demand for good X (the demand curve for X will shift to the right).

d. No. The term “inferior good” does not mean “inferior quality,” it simply means that income and consumption are inversely related.

2.

a. The supply of good X will increase (shift to the right).

b. The supply of good X will decrease. More specifically, the supply curve will shift vertically up by exactly \$3 at each level of output.

c. The supply of good X will decrease. More specifically, the supply curve will rotate counter-clockwise.

d. The supply curve for good X will increase (shift to the right).

3.

a. units.

b. Notice that although , negative output is impossible. Thus, quantity supplied is zero.

c. To find the supply function, insert Pz = 60 into the supply equation to obtain . Thus, the supply equation is . To obtain the inverse supply equation, simply solve this equation for Px to obtain . The inverse supply function is graphed in Figure 2-1.

Figure 2‑1

4.

a. Good Y is a complement for X, while good Z is a substitute for X.

b. X is a normal good.

c.

d. For the given income and prices of other goods, the demand function for good X is which simplifies to . To find the inverse demand equation, solve for price to obtain . The demand function is graphed in Figure 2-2.

5.

a. Solve the demand function for Px to obtain the following inverse demand function: .

b. Notice that when Px = \$45, units. Also, from part a, we know the vertical intercept of the inverse demand equation is 150. Thus, consumer surplus is \$11,025 (computed as (0.5)(\$150-\$45)210 = \$11,025).

c. When price decreases to \$30, quantity demanded increases to 240 units, so consumer surplus increases to \$14,400 (computed as (0.5)(\$150-\$30)240 = \$14,400).

d. So long as the law of demand holds, a decrease in price leads to an increase in consumer surplus, and vice versa. In general, there is an inverse relationship between the price of a product and consumer surplus.

6.

a. Equating quantity supplied and quantity demanded yields the equation . Solving for P yields the equilibrium price of \$40 per unit. Plugging this into the demand equation yields the equilibrium quanity of 20 units (since quantity demanded at the equilibrium price is ).

b. A price floor of \$50 is effective since it is above the equilibrium price of \$40. As a result, quantity demanded will fall to 10 units (), while quantity supplied will increase to 30 units (). That is, firms produce 30 units but consumers are willing and able to purchase only 10 units. Therefore, at a price floor of \$50, 10 units will be exchanged. Since Qd < Qs there is a surplus amounting to 30-10 = 20 units.

c. A price ceiling of \$32 per unit is effective since it is below the equilibrium price of \$40 per unit. As a result, quantity demanded will increase to 28 units (), while quantity supplied will decrease to 12 units (). That is, while firms are willing to produce only 12 units consumers want to buy 28 units at the ceiling price. Therefore, at the price ceiling of \$32, only 12 units will be available to purchase. Since Qd > Qs, there is a shortage amounting to 28-12 = 16 units. Since only 12 units are available at a price of \$32, the full economic price is the price such that quantity demanded equals the 12 available units: 12 = 60 – PF. Solving yields the full economic price of \$48.

7.

a. Equate quantity demanded and quantity supplied to obtain . Solve this equation for Px to obtain the equilibrium price of Px = 20. The equilibrium quantity is 4 units (since at the equilibrium price quantity demanded is ). The equilibrium is shown in Figure 2-3.

b. A \$12 excise tax shifts the supply curve up by the amount of the tax. Mathematically, this means that the intercept of the inverse supply function increases by \$12. Before the tax, the inverse supply function is . After the tax the inverse supply function is , and the after tax supply function (obtained by solving for Qs in terms of P) is given by . Equating quantity demanded to after-tax quantity supplied yields . Solving for P yields the new equilibrium price of \$24. Plugging this into the demand equation yields the new equilibrium quantity, which is 2 units.

c. Since two units are sold after the tax and the tax rate is \$12 per unit, total tax revenue is \$24.

8.

a. The shortage is 3 units (since at a price of \$6, units). The full economic price is \$12.

b. The surplus is 1.5 units (since at a price of \$12, units. The cost to the government is \$18 (computed as (\$12)(1.5) = \$18).

c. The excise tax shifts supply vertically by \$6. Thus, the new supply curve is and the equilibrium price increases to \$12. The price paid by consumers is \$12 per unit, while the amount received by producers is this \$12 minus the per unit tax. Thus, producers receive \$6 per unit. After the tax, the equilibrium quantity sold is 1 unit.

d. At the equilibrium price of \$10, consumer surplus is . Producer surplus is .

e. No. At a price of \$2 no output is produced.

9.

a. The inverse supply curve is .

b. When Qx = 400, producer surplus is (46-26)*400/2 = \$4,000. When Qx = 1200, producer surplus is (86-26)*1200/2 = \$36,000.

10.

a. The cost of purchasing the surplus is \$40*(24-12) = \$480.

b. The deadweight loss resulting from a \$40 price floor is .

11. Rising input prices that increase production costs will lead to a leftward shift in the supply curve for RAM chips, resulting in a higher equilibrium price of RAM chips. If in addition, income falls, the demand for RAM chips will decrease since they are a normal good. This decrease in demand would tend to decrease the price of RAM chips. The ultimate effect of both of these changes in supply and demand on the equilibrium price of RAM chips is indeterminate. Depending on the relative magnitude of the decreases in supply and demand, the price you will pay for chips may rise or fall.

12. The tariff reduces the supply of raw sugar, resulting in a higher equilibrium price of sugar. Since sugar is an input in making generic soft drinks, this increase in input prices will decrease the supply of generic soft drinks (putting upward pressure on the price of generic soft drinks and tend to reduce quantity). Coke and Pepsi’s advertising campaign will decrease the demand for generic soft drinks (putting downward pressure on the price of generic soft drinks and further reducing the quantity). For these reasons, the equilibrium quantity of generic soft drinks sold will decrease. However, the equilibrium price may rise or fall, depending on the relative magnitude of the shifts in demand and supply.

13. No. this confuses a change in demand with a change in quantity demanded. Higher cigarette prices will not reduce (shift to the left) the demand for cigarettes.

14. To find the equilibrium price and quantity, equate quantity demanded and quantity supplied to obtain 210 – 1.5P = 2.5P – 150. Solving yields the new equilibrium price of \$90 per pint. The equilibrium quantity is 75 units (since Qd = 210 – 1.5*90 = 75

units at that price). Consumer surplus is . Producer surplus is . See Figure 2-4.

 Consumer Surplus
 Producer Surplus
 Supply
 Demand

15. This decline represents a leftward shift in the supply curve for oil, and will result in an increase in the equilibrium price of crude oil. Since oil is an input in producing gasoline, this will decrease the supply of gasoline, resulting in a higher equilibrium price of gasoline and a lower equilibrium quantity. Furthermore, the higher price of gasoline will increase the demand for substitutes, such as small cars. The equilibrium price of small cars is likely to increase, as is the equilibrium quantity of small cars.

16. Equating the initial quantity demanded and quantity supplied gives the equation: 300 – 4P = 3P – 120. Solving for price, we see that the initial equilibrium price is \$60 per month. When the tax rate is reduced, equilibrium is determined by the following equation: 300 – 4P = 3.2P - 120. Solving, we see that the new equilibrium price is about \$58.33 per month. In other words, a typical subscriber would save about \$1.67 (the difference between \$60.00 and \$58.33).

17. Dry beans and rice are probably inferior goods. If so, an increase in income shifts demand for these goods to the left, resulting in a lower equilibrium price. Therefore, G.R. Dry Foods will likely have to sell its products at a lower price.

18. Figure 2-5 illustrates the relevant situation. The equilibrium price is \$3.00, but the ceiling price is \$1.25. Notice that, given the shortage of 14 million transactions caused by the ceiling price of \$1.25, the average consumer spends an extra 14 minutes traveling to another ATM machine. Since the opportunity cost of time is \$24 per hour, the non-pecuniary price of an ATM transaction is \$5.60 (the \$24 per hour

wage times the fractional hour, 14/60, spent searching for another machine). Thus, the full economic price under the price ceiling is \$6.85 per transaction.

Figure 2-5

19. The unusually cold temperatures have caused a decrease in the supply of grapes used to produce Chilean wine, resulting in higher prices. These grapes are an input in making wine, so the supply of Chilean wine decreases and its price increases. Since California and Chilean wines are substitutes, an increase in the price of Chilean wine will increase the demand for Californian wines causing an increase in both the price and quantity of Californian wines.

20. Substituting Pdesktop = 980 into the demand equation yields . Similarly, substituting N = 100 into the supply equation yields . The competitive equilibrium level of industry output and price occurs where , which occurs when industry output (in thousands) and the market price is per unit. Since 100 competitors are assumed to equally share the market, Viking should produce 27.28 thousand units. If Pdesktop = \$1,080, . Under this condition, the new competitive equilibrium occurs when industry output is 2688 thousand units and the per-unit market price is \$63.52. Therefore, Viking should produce 26.88 thousand units. Since demand decreased (shifted left) when the price of desktops increased, memory modules and desktops are complements.

21. Mid Towne IGA aimed to educate consumers that its contract with Local 655 union members was different than its rivals, so it engaged in informative advertising. Mid Towne IGA’s informative advertising increases demand (demand shifts rightward) resulting from (1) Local 655 union members locked out of rival supermarkets (2) consumers who are sympathetic to the Local 655 union, and (3) consumers who do not like the aggravation of picketing employees and other disruptions at the supermarket. This shift is depicted in Figure 2-6, where the equilibrium price and quantity both increase. It is unlikely that demand will remain high for Mid Towne IGA. As contracts are renegotiated and Local 655 union members are back to work, demand will likely settle back around its original level.

Figure 2-6

22. The price gouging statute imposes an effective price ceiling on necessary commodities during times of emergencies; legally retailers cannot raise prices by a significant amount. When a natural disaster occurs, the demand for necessary commodities such as food and water can dramatically increase, as people want to be stocked-up on emergency items. In addition, since it can be difficult for retailers to receive shipments during emergency periods, the supply of these items is often reduced. Given the simultaneous reduction in supply and increase in demand, one would expect the price to increase during times of emergencies. However, since the price gouging statute acts as a price ceiling, the price will probably remain at its normal level, and a shortage will result.

23. While there is undoubtedly a link between unemployment and crime, the governor’s plan is likely flawed since it only examines one side of the market. Raising the minimum wage will make the prospect of working more appealing for teenagers, but it will also have an effect on business owners and managers in the state. The

minimum wage is a price floor. Raising the minimum wage will reduce the quantity demand for labor within the state, and result in a labor surplus. More teenagers will seek jobs, but fewer businesses will hire teenagers. It is very likely that the governor’s plan will result in greater juvenile delinquency.

### Managerial Economics, 7/E solutions manual and test bank by Paul Keat Philip K Young

Managerial Economics, 7/E solutions manual and test bank by Paul Keat Philip K Young

CHAPTER 2

THE FIRM AND ITS GOALS

Questions

1. Yes. The company can profit from this action in several ways. Graduate students, impressed with the computers, may become recruits for the computer firm. This increases the employment market for the firm, and it may become able to hire some superior graduates. Or, these students, after graduation, will work for other firms and recommend the computer made by this manufacturer for use in their work place. In short, if the additional profits from future sales exceed the cost of the donation, then such a policy is quite consistent with profit maximization.

2. This is an incomplete objective, and may not be consistent with the objective of profit maximization. Setting a profit margin too high may result in smaller profits than could possibly be achieved with a lower profit margin. In other words, setting a profit margin may not result in profit maximization. The profit maximization goal should be stated in absolute values, since a high ratio applied to a small base could yield a lower absolute profit, while a low ratio applied to a high base could yield a high amount. For example, a 10% profit margin on revenue of \$10 million results in \$1 million in profits, while a 5% margin on revenue of \$30 million yields \$1.5 million in profits.

3. This comment is incorrect. It is quite true that the existence of consumer organizations, legal requirements and warranty requirements may raise a company’s costs above what they would have been in their absence. But such costs will now be included in a company’s cost calculations. Given these costs, a company can still attempt to maximize its profits under the new circumstances. The total profit level will be lower than if these costs did not exist, but the process of profit maximization will still be in place.

4. Shareholder wealth maximization is the more comprehensive of the two. Profit maximization is a period of value that may be obtained by short-term management action which could be detrimental to profits in future periods.

But a company with longer range horizons will want to consider a stream of earnings (or cash flows) over time. This stream is then discounted at the company’s cost of capital to the present to obtain the present value of this stream. This present value is the value of the firm or that of the stockholders. When such an objective is used, the company is considering the shape and duration of the cash flow stream and the return required by stockholders (i.e. the equity cost of capital). The required rate of return is affected by risk, and, thus, risk enters into the valuation. Obviously, this measure is much more inclusive than the maximization of profit for any one period.

5. Stockholders generally may not know what maximum profits their firm could generate. Thus, they will look for a satisfactory return (both dividend and price appreciation). Company management will not be held to maximization but will manage the corporation in a way as to satisfy the shareholders. The term often used to describe this is “satisficing.”

6. The “principal-agent problem” refers to the possible divergence of objectives between the owners and managers of an enterprise. While the owners of a firm (stockholders, when the firm is a corporation) are interested mainly in the increase in the firm’s value, managers may have other interests. Managers may be more interested in their own incomes and perquisites. They may also strive for revenue growth rather than profits. They may, in the interest of their own security, be more conservative in running the business, and may forgo investments with high potential that may entail some risk.

7. Since the ownership in a corporation is widely dispersed, and thus individual stockholders have little power, it may be believed by managers that it is not necessary to endeavor to maximize company profits. Since the managers usually own only a small fraction of the corporation’s stock, their interest may not be served best by maximizing the value of the corporation. Thus they may be more interested in maximizing their own incomes and perquisites. They may also not take prudent risks to maximize returns, since a severe reversal in business fortunes could cause them to lose their positions. Not taking the appropriate risks may result in rather mediocre but still satisfactory shareholder returns.

8. There are several forces which will tend to create a convergence between the interests of stockholders and managers, and thus cause managers to be interested in maximizing a corporation’s profits or value:

a. Corporate shares are not only owned by widely dispersed stockholders but by large institutional holders (banks, insurance companies, mutual funds, pension funds). These organizations employ analysts who continually study stock performance. Non-performing companies would be sold from these institutions’ portfolios, and lead to decreased prices of these stocks. This could then result in takeovers by other companies, proxy fights, etc. which could lead to the dismissal of present management.

b. Competitive pressures could lead to stock price declines for a non-performing company, and again result in takeovers, proxy contests, etc.

c. In many corporations, management remuneration is tied to performance and managers frequently are awarded stock options which gain value as the price of shares rises. Thus, managers will have an interest in maximizing stockholder welfare.

9. It probably does. Other types of objectives may be partial; but profit and wealth maximization still appear to be the most inclusive objectives. Further, it is much more possible to test this hypothesis than some of the others.

10. No. Accounting depreciation is calculated on historical costs. Thus, depreciating a machine which cost \$10,000 when originally purchased can result only in a maximum of \$10,000 of depreciation charges set aside toward the purchase of a replacement machine. If this machine (due to inflation) now costs \$20,000, then the funds earmarked for the new machine will be insufficient to purchase it. For economists, replacement costs are the relevant quantities.

11. Implicit costs can include in them costs not considered by accountants, such as the owners’ opportunity costs. Thus, accounting profit would generally be higher than economic profit. Economists would include opportunity costs in their calculation of costs; economists’ costs include what is usually referred to as normal profit.

12. You would compare the amount of time spent on each employment, projected business profits versus salaries that could be earned from working for others, the interest that you could earn on your investment in your business against keeping your funds invested elsewhere (i.e. savings account or other), and the risk involved in the two alternatives. You may even include some estimate (hard to quantify) of any psychic value you derive from being your own boss.

13. Depreciation should reflect the actual change in the value of the equipment and the change in the equipment’s replacement cost.

14. A multinational corporation is usually faced with different legal, economic, cultural and tax conditions in the many countries in which it operates. Such considerations will complicate greatly the tasks of a corporation’s managers and create constraints on their actions. However, if management learns to live with such additional risk and restrictions, corporations can still pursue the goal of profit maximization.

15. Transaction costs are costs which a company incurs in dealing with other entities. Among the

costs incurred are those of investigation, contract negotiation, contract enforcement, and transaction coordination. Opportunistic behavior occurs when one of the parties to the transaction takes advantage of the other. This may happen when the transactions involve specialized products or specialized equipment, that may be affected by changes in future market conditions or technology. The possibility of opportunistic behavior thus makes the transaction more risky and will tend to increase transaction costs.

16. As markets expand, companies specializing in particular products will grow and become efficient, and will tend to be able to produce these products at costs that are lower than if produced by an integrated company. This has become true for highly technical products and services. The existence of the Internet has brought about significant decreases in transaction costs, such as the costs of search, investigation, contracting and coordination.

17. High transaction costs will cause a firm to internalize some of its costs. Some of the reasons for high transaction costs are:

a. The negotiation and enforcement of contracts.

b. Uncertainty and frequency of transactions.

c. Assets-specificity which may lead to opportunistic behavior.

18. Using the constant dividend growth formula P = D1/(k - g), and noting that the \$2 dividend was paid last year, so this year’s dividend would be expected to be 6% higher:

2*(1.06) /(0.13 - 0.06) = 2*(1.06)/0.07 = \$30.29 per share

30.29 x 2,000,000 = \$60,571,428

19. Shareholder wealth is calculated by multiplying the number of shares outstanding by the price of the stock. MVA is the difference between the market value of the company (including both stocks and bonds) and the capital contributed by the investors. The latter concept is more meaningful since it measures the increase in wealth of the investors above what they have contributed. A company could have a very high market value, but investors may have actually contributed more than the company is worth. In such a case, there has been a destruction of investors’ value. General Motors appears to be an example of such a situation.

Managerial Economics, 7e (Keat)

Chapter 2 The Firm and Its Goals

Multiple-Choice Questions

1) Transaction costs include

A) costs of negotiating contracts with other firms.

B) cost of enforcing contracts.

C) the existence of asset-specificity.

D) All of the above

Diff: 1

2) A company will strive to minimize

A) transaction costs.

B) costs of internal operations.

C) total costs of transactions and internal operations combined.

D) variable costs.

Diff: 1

3) The best example of an economic goal of a firm is

A) providing good products/services to its customers.

B) improving its public image.

C) increasing employee morale.

D) increasing shareholder wealth.

Diff: 1

4) A large corporation's profit objective may not be profit or wealth maximization, because

A) stockholders have little power in corporate decision making.

B) management is more interested in maximizing its own income.

C) managers are overly concerned with their own survival and may not take all prudent risks.

D) All of the above

Diff: 2

5) One of the weaknesses in pursuing the objective of profit maximization is that it ignores

A) the timing of cash flows.

B) the time-value of money concept.

C) the riskiness of cash flows.

D) All of the above

Diff: 1

6) Goals which are concerned with creating and maintaining employee and customer satisfaction and social responsibility are referred to as ________ objectives.

A) social

B) noneconomic

C) welfare

D) public relations

Diff: 1

7) Financial risk occurs due to variations in returns which

A) is induced by leverage.

B) is due to the ups and downs of the economy.

C) is due to changes in government regulations.

D) is a result of changes in exchange rates.

Diff: 2

8) Financial risk is associated with changes in

A) the demand for a firm's products.

B) a firm's debt.

C) a firm's labor costs.

D) government regulations of a firm's activities.

Diff: 2

9) ________ risk involves variation in returns due to the ups and downs of the economy, the industry and the firm.

A) Structural

B) Fluctuational

D) Financial

Diff: 1

10) Unlike an accountant, an economist measures costs on a(n) ________ basis.

A) explicit

B) replacement

C) historical

D) conservative

Diff: 1

11) ________ maximization is achieved when a company manages its business in such a way that its cash flows over time, discounted at the appropriate discount rate, will cause the value of the company's common stock to be at a maximum.

A) Profit

B) Stockholder wealth

C) Asset

D) None of the above

Diff: 1

12) The calculation of stockholder wealth involves

A) the time-value of money concept.

B) the cash flow stream.

D) All of the above

Diff: 1

13) Another name for stockholder wealth maximization is

A) profit maximization.

B) maximization of earnings per share.

C) maximization of the value of the common stock.

D) maximization of cash flows.

Diff: 1

14) Accounting costs

A) are historical costs.

B) are replacements costs.

C) usually include implicit costs.

D) usually include normal profits.

Diff: 1

15) A firm earns a normal profit when its total revenues just offset both the ________ cost and ________ cost.

A) accounting; opportunity

B) accounting; replacement

C) historical; replacement

D) explicit; accounting

Diff: 2

16) A firm's "normal profit" is best characterized by the

A) average of a firm's profits over the past five years.

B) amount of profit necessary to keep the price of a firm's stock from changing.

C) amount of profit a firm could earn in its next best alternative activity.

D) the average amount of profit earned in the firm's industry.

Diff: 3

A) will always be a positive number.

B) may be a negative number.

C) measures the market value of the firm.

D) None of the above

Diff: 2

18) Opportunistic behavior is best described as a firm

A) gathering as much information as possible before dealing with another entity.

B) attempting to make a profit from its dealings with another entity.

C) firm trying to take advantage of another entity in its dealings with it.

D) selecting another entity to deal with.

Diff: 2

19) Firms are organized to keep their costs as low as possible by

A) comparing external transactions costs with internal operating cost.

B) analyzing supply and demand conditions.

C) minimizing their use of borrowed funds.

D) utilizing the latest technology.

Diff: 2

Analytical Questions

1) a. If a stock is expected to pay an annual dividend of \$20 forever, what is the approximate present value of the stock, given that the discount rate is 5%?

b. If a stock is expected to pay an annual dividend of \$20 forever, what is the approximate present value of the stock, given that the discount rate is 8%?

c. If a stock is expected to pay an annual dividend of \$20 this year, what is the approximate present value of the stock, given that the discount rate is 8% and dividends are expected to grow at a rate of 2% per year?

a. P = D/k = 20/.05 = \$400

b. P = 20/.08 = \$250

c. P = D1/(k - g) = 20/(.08 - .02) = \$333.33

2) If a stock is expected to pay a dividend of \$40 for the current year, what is the approximate present value of this stock, given at discount rate of 5% and a dividend growth rate of 3%?

Answer: P = \$40/(0.05 - 0.03) = \$40/0.02 = \$2,000

3) Describe the difference between the Economic Value Added (EVA) and the Market Value Added (MVA) approach to determining stockholder wealth.

Answer: EVA is the difference between a firm's return on total capital and its cost of capital, while MVA is the difference between the market value (equity plus debt) of a firm and the amount of capital investors have paid into the company.

### Managerial Economics 7th edition by William F. Samuelson, Stephen G. Marks solutions manual and test bank

Managerial Economics  7th edition by William F. Samuelson, Stephen G. Marks solutions manual and test bank

CHAPTER TWO

OPTIMAL DECISIONS USING MARGINAL ANALYSIS

OBJECTIVES

1. To introduce the basic economic model of the firm

- The main focus is on determining the firm’s profit-maximizing level of output.

- The main assumption is that there is a single product (or multiple, independent products) with deterministic demand and cost.

2. To depict the behavior of price, revenue, cost, and profit as output varies.

3. To explain the notion of marginal profit (including its relationship to calculus) and show that maximum profit occurs at an output such that marginal profit equal zero

4. To reinterpret the optimality condition in terms of the basic components, marginal revenue and marginal cost.

5. To illustrate the uses of sensitivity analysis

TEACHING SUGGESTIONS

I. Introduction and Motivation

A. This is a “nuts and bolts” chapter. Because it appears up front in the text, it’s important to explain the motivation and assumptions. It is a good idea to remind students of the following points.

1) The model of the firm is deliberately simplified so that its logic is laid bare. Many additional complications will be supplied in later chapters. The key simplifications for now are:

• The model is of a generic firm. Although microchips are chosen to make the discussion concrete, there is no description of the kind of market or the nature of competition within it. The description and analysis of different market structures comes in Chapters 7 through 10.

• Profit is the sole goal of the firm; price and output are the sole decision variables.

• The description of demand and cost is as “bare bones” as it gets. The demand curve and cost function are taken as given. (How the firm might estimate these are studied in Chapters 4 through 6.)

B. In general, our policy is to use extended decision examples, different than the ones in the text, to illustrate the most important concepts. (Going over the same examples pushes the boredom envelope.) In the present chapter, we make an exception to this rule. It is important to make sure that students with different economic and quantitative backgrounds all get off roughly on the same foot. Reviewing a familiar example (microchips) makes this much easier.

II. Teaching the “Nuts and Bolts”

A. Graphic Overview. The text presents the revenue, cost, and profit functions in three equivalent forms: in tables, in graphs, and in equations. In our view, the best way to convey the logic of the relationships is via graphs. (The student who craves actual numbers can get plenty of them in the text tables.) Here is one strategy for teaching the nuts and bolts:

1. Using the microchip example, depict the demand curve, briefly note its properties and demand equation (in both forms).

2. Next focus on revenue, noting the tradeoff between price and quantity. Present and justify the revenue equation. Graph it and note its properties.

3. Repeat the same process with the cost function (reminding students about fixed versus variable cost). At this point, your blackboard graph should be a copy of Figure 2.8 (p. 46). Steps 1-3 should take no more than 20 minutes.

4. Since the gap between the revenue and cost curves measures profit, one could find the optimal output by carefully measuring the maximum gap (perhaps using calipers). Emphasize that marginal analysis provides a much easier and more insightful approach. Point out the economic meaning of marginal cost and marginal revenue. Note that they are the slopes of the respective curves.

5. Next argue (as on p. 47) that the profit gap increases (with additional output) when MR > MC but narrows when MR < MC. (On the graph, select quantities that are too great or too small to make the point.) Identify Q* where the tangent to the revenue curve is parallel to the slope of the cost function. In short, optimal output occurs where MR = MC.

B. Other Topics. The approach in part A provides a simple way of conveying the basic logic of marginal analysis using the components of MR and MC. Once this ground is covered, the instructor should emphasize other basic points:

1. The equivalence between MÏ€ = 0 and MR = MC.

2. Calculus derivations of MÏ€, MR, and MC.

3. The exact numerical solution for the microchip example.

4. The graphs of MR and MC and an exploration of comparative statics effects (shifts in the curves) and the effects on Q*.

C. Applications. Besides the applications in the text (pp. 45-49), the following problems are recommended: Problem 1 (a quick but important check), Problems 6, 7 and 9 (numerical applications), Problem 13 (the general solution), and Problem 14. (If the class has a good grasp of this last problem, nothing else will seem difficult.) The following question gets students thinking:

1. a. For five years, an oil drilling company has profitably operated in the state of Alaska (the only place it operates). Last year, the state legislature instituted a flat annual tax of \$100,000 on any company extracting oil (or natural gas) in Alaska. How would this tax affect the amount of oil the company extracts? Explain.

b. Suppose instead that the state imposes a well-head tax, let’s say a tax of \$10.00 on each barrel of oil extracted. Answer the questions of part a.

c. Finally, suppose that the state levies a proportional income tax (say 10% of net income). Answer the questions of part a. What would be the effect of a progressive tax?

d. Now suppose that the company has a limited number of drilling rigs extracting oil at Alaskan sites and at other sites in the United States. What would be the effect on the company’s oil output in Alaska if the state levied a proportional income tax as in part c?

a. This tax acts as a fixed cost. As long as it remains profitable to produce in Alaska, the tax has no effect on the firm’s optimal output.

b. The well-head tax increases the marginal cost of extraction by \$10.00 per barrel. The upward shift in MC means the new intersection of MR and MC occurs at a lower optimal level of output.

c. The income tax (either proportional or progressive) has no effect on the company’s optimal output. For instance, suppose that the company’s after-tax income is p = .9(R-C) under a 10% proportional tax. To maximize its after-tax income, the best the company can do is to continue to maximize its before-tax income. Another way of seeing this is to note that the tax causes a 10% downward shift in the firm’s MR and MC curves. With the matching shift, the new intersection of MR and MC is at the same optimal quantity as the old intersection.

d. When the firm operates in multiple states with limited drilling rigs, using a rig in Alaska means less oil is pumped (and lower profit is earned) somewhere else. There is an opportunity cost to Alaskan drilling. Thus, one can argue that before the tax, the company should have allocated rigs so as to equate marginal profits in the different states. With the tax, the marginal profit in Alaska is reduced, prompting the possible switch of rigs from Alaska to other (higher marginal profit) locations.

D. Mini-case: Apple Computer in the Mid-1990s

The mini-case reproduced on the next page provides a hands-on application of profit maximization and marginal analysis.

a. Clearly, the period 1994-1995 was marked by a significant adverse shift in demand against Apple due to major enhancements of competing computers: lower prices, better interfaces (Windows), sales to order (Dell), and more abundant software.

b. Setting MR = MC implies 4,500 - .3Q = 1,500, so Q* = 10,000 units and P = \$3,000. Given 1994’s state of demand, Apple’s 1994 production strategy was indeed optimal.

c. In 1995, demand and MR have declined significantly. Now, setting MR = MC implies 3,900 - .3Q = 1,350, so Q* = 8,500 units and P = \$2,625. Apple should cut its price and its planned output.

Apple Computer in the Mid 90s

Between 1991 and 1994, Apple Computer engaged in a holding action in the desktop market dominated by PCs using Intel chips and running Microsoft’s operating system.1

In 1994, Apple’s flagship model, the Power Mac, sold roughly 10,000 units per month at an average price of \$3,000 per unit. At the time, Apple claimed about a 9% market share of the desktop market (down from greater than 15% in the 1980s).

By the end of 1995, Apple had witnessed a dramatic shift in the competitive environment. In the preceding 18 months, Intel had cut the prices of its top-performing Pentium chip by some 40%. Consequently, Apple’s two largest competitors, Compaq and IBM, reduced average PC prices by 15%. Mail-order retailer Dell continued to gain market share via aggressive pricing. At the same time, Microsoft introduced Windows 95, finally offering the PC world the look and feel of the Mac interface. Many software developers began producing applications only for the Windows operating system or delaying development of Macintosh applications until months after Windows versions had been shipped. Overall, fewer users were switching from PCs to Macs.

Apple’s top managers grappled with the appropriate pricing response to these competitive events. Driven by the speedy new PowerPC chip, the Power Mac offered capabilities and a user-interface that compared favorably to those of PCs. Analysts expected that Apple could stay competitive by matching its rivals’ price cuts. However, John Sculley, Apple’s CEO, was adamant about retaining a 50% gross profit margin and maintaining premium prices. He was confident that Apple would remain strong in key market segments – the home PC market, the education market, and desktop publishing.

Questions.

1. What effect (if any) did the events of 1995 have on the demand curve for Power Macs?

Should Apple preserve its profit margins or instead cut prices?

2. a) In 1994, the marginal cost of producing the Power Mac was about \$1,500 per unit, and a rough estimate of the monthly demand curve was: P = 4,500 - .15Q. At the time, what was Apple’s optimal output and pricing policy?

b) By the end of 1995, some analysts estimated that the Power Mac’s user value (relative to rival PCs) had fallen by as much as \$600 per unit. What does this mean for Apple’s new demand curve at end-of-year 1995? How much would sales fall if Apple held to its 1994 price? Assuming a marginal cost reduction to \$1,350 per unit, what output and price policy should Apple now adopt?

1 This account is based on J. Carlton, “Apple’s Choice: Preserve Profits or Cut Prices,” The Wall Street Journal, February 22, 1996, p. B1.

R. Gibson, “Franchisee v. Franchiser,” The Wall Street Journal, February 14, 2011, p. R3.

R. Gibson, “Burger King Franchisees Can’t Have it Their Way,” The Wall Street Journal, January 21, 2010, p. B1.

M. Cieply, “For Movie Stars, the Big Money is now Deferred,” The New York Times, March 4, 2010, pp. A1, A3.

N. S. Riley, “Other People’s Money,” The Wall Street Journal, October 3, 2008, p. W11.

R. Chittum, “Price Points,” The Wall Street Journal, October 30, 2006, p. R7. (How providers of consumer services compare extra revenues and extra costs.)

T. H. Davenport, “Competing on Analytics,” Harvard Business Review, January 2006.

C. Oggier and E, Fragniere, and J. Stuby, “Nestle Improves its Financial Reporting with Management Science,” Interfaces, July-August, 2005, pp. 271-280.

J. Thomas, W. Reinartz, and V. Kumar, “Getting the Most out of your Customers,” Harvard Business Review, July-August, 2004, pp. 117-123.

A. M. Geoffrion and R. Krishnan, “Prospects for Operations Research in the E-Business Era,” Interfaces, March-April, 2001, pp. 6-36.

D. Ekwurzel and J. McMillan, “Economics Online,” Journal of Economic Literature, March 2001, pp. 7-10.

“Economics on the Net,” The Economist, March 13, 1999, p. 7.

W. Biddle, “Skeleton Alleged in the Stealth Bomber’s Closet,” Science, May 12, 1989.

II. Case

Colgate-Palmolive Co.: The Precision Toothbrush (9-593-064), Harvard Business School, 1993. Teaching Note (5-595-025). (Explores profit analyses of alternative launch strategies.)

III. Quips and Quotes

Small mistakes are the stepping stones to large failures.

There was an old saying about our small town. Our town’s population never changed. Every time a baby was born a man left town. (Does this say something about the balance of marginal changes at an optimum?)

The head of a small commuter plane service reported that as costs rose, the company’s breakeven point rose from 6 to 8 to 11 passengers. “I finally figured we were in trouble since our planes only have 9 seats.”

If you laid all of the economists in the world end to end, they still wouldn’t reach a conclusion. (George Bernard Shaw)

An economist is a person who is very good with numbers but who lacks the personality to be an accountant.

The age of chivalry is gone; that of sophisters, economists, and calculators has succeeded. (Edmund Burke)

Please find me a one-armed economist so we will not always hear, “On the other hand . . .” (Herbert Hoover)

1. This statement confuses the use of average values and marginal values. The proper statement is that output should be expanded so long as marginal revenue exceeds marginal cost. Clearly, average revenue is not the same as marginal revenue, nor is average cost identical to marginal cost. Indeed, if management followed the average-revenue/average-cost rule, it would expand output to the point where AR = AC, in which case it is making zero profit per unit and, therefore, zero total profit!

2. The revenue function is R = 170Q - 20Q2. Maximizing revenue means setting marginal revenue equal to zero. Marginal revenue is: MR = dR/dQ = 170 - 40Q. Setting 170 - 40Q = 0 implies Q = 4.25 lots. By contrast, profit is maximized by expanding output only to Q = 3.3 lots. Although the firm can increase its revenue by expanding output from 3.3 to 4.5 lots, it sacrifices profit by doing so (since the extra revenue gained falls short of the extra cost incurred.)

3. In planning for a smaller enrollment, the college would look to answer many of the following questions: How large is the expected decline in enrollment? (Can marketing measures be taken to counteract the drop?) How does this decline translate into lower tuition revenue (and perhaps lower alumni donations)? How should the university plan its downsizing? Via cuts in faculty and administration? Reduced spending on buildings, labs, and books? Less scholarship aid? How great would be the resulting cost savings? Can the university become smaller (as it must) without compromising academic excellence?

4. a. p = PQ – C = (120 - .5Q)Q - (420 + 60Q + Q2) = -420 + 60Q - 1.5Q2. Therefore, Mp = dp /dQ = 60 - 3Q = 0. Solving yields Q* = 20.

Alternatively, R = PQ = (120 - .5Q)Q = 120Q - .5Q2. Therefore, MR = 120 – Q. In turn, C = -420 + 60Q + Q2, implying: MC = 60 + 2Q. Equating marginal revenue and marginal cost yields: 120 - Q = 60 + 2Q, or Q* = 20.

b. Here, R = 120Q; it follows that MR = 120. Equating MR and MC yields: 120 = 60 + 2Q, or Q* = 30.

5. a. The firm exactly breaks even at the quantity Q such that p = 120Q - [420 + 60Q] = 0. Solving for Q, we find 60Q = 420 or Q = 7 units.

b. In the general case, we set: p = PQ - [F + cQ] = 0. Solving for Q, we have: (P - c)Q = F or Q = F/(P - c). This formula makes intuitive sense. The firm earns a margin (or contribution) of (P - c) on each unit sold. Dividing this margin into the fixed cost reveals the number of units needed to exactly cover the firm’s total fixed costs.

c. Here, MR = 120 and MC = dC/dQ = 60. Because MR and MC are both constant and distinct, it is impossible to equate them. The modified rule is to expand output as far as possible (up to capacity), because MR > MC.

6. a. If DVDs are given away (P = \$0), demand is predicted to be: Q = 1600 - (200)(0) = 1,600 units. At this output, firm A’s cost is: 1,200 + (2)(1,600) =\$4,400, and firm B’s cost is: (4)(1,600) = \$6,400. Firm A is the cheaper option and should be chosen. (In fact, firm A is cheaper as long as Q > 600.)

b. To maximize profit, we simply set MR = MC for each supplier and compare the maximum profit attainable from each. We know that MR = 8 - Q/100 and the marginal costs are MCA = 2 and MCB = 4. Thus, for firm A, we find: 8 - QA/100 = 2, and so QA = 600 and PA = \$5 (from the price equation). For firm B, we find QB = 400 and PB = \$6. With Firm A, the station’s profit is: 3,000 - [1,200 + (2)(600)] = \$600. With Firm B, its profit is 2,400 - 1,600 = \$800. Thus, an order of 400 DVDs from firm B (priced at \$6 each) is optimal.

7. a. The marginal cost per book is MC = 40 + 10 = \$50. (The marketing costs are fixed, so the \$10 figure mentioned is an average fixed cost per book.) Setting MR = MC, we find MR = 150 – 2Q = 50, implying Q* = 50 thousand books. In turn, P* = 150 –50 = \$100 per book.

b. When the rival publisher raises its price dramatically, the firm’s demand curve shifts upward and to the right. The new intersection of MR and MC now occurs at a greater output. Thus, it is incorrect to try to maintain sales via a full \$15 price hike. For instance, in the case of a parallel upward shift, P = 165 – Q. Setting MR = MC, we find: MR = 165 – 2Q = 50, implying Q* = 57.5 thousand books, and in turn, P* = 165 – 57.5 = \$107.50 per book. Here, OS should increase its price by only \$7.50 (not \$15).

c. By using an outside printer, OS is saving on fixed costs but is incurring a higher marginal cost (i.e., printing cost) per book. With a higher marginal cost, the intersection of MR and MC occurs at a lower optimal quantity. OS should reduce its targeted sales quantity of the text and raise the price it charges per book. Presumably, the fixed cost savings outweighs the variable cost increase.

8. The fall in revenue from waiting each additional month is: MR = dR/dt = -8. The reduction in cost of a month’s delay is: MC = dC/dt = -20 + .5t. The optimal introduction date is found by equating MR and MC: -8 = -20 + .5t, which implies: .5t = 12 or t* = 24 months. The marketing manager’s 12-month target is too early. Delaying 12 more months sacrifices revenue but more than compensates in reduced costs.

9. a. The MC per passenger is \$20. Setting MR = MC, we find 120 - .2Q = 20, so Q = 500 passengers (carried by 5 planes). The fare is \$70 and the airline’s weekly profit is: \$35,000 - 10,000 = \$25,000.

b. If it carries the freight, the airline can fly only 4 passenger flights, or 400 passengers. At this lower volume of traffic, it can raise its ticket price to P = \$80. Its total revenue is (80)(400) + 4,000 = \$36,000. Since this is greater than its previous revenue (\$35,000) and its costs are the same, the airline should sign the freight agreement.

10. The latter view is correct. The additional post-sale revenues increase MR, effectively shifting the MR curve up and to the right. The new intersection of MR and MC occurs at a higher output, which, in turn, implies a cut in price. (Of course, one must discount the additional profit from service and supplies to take into account the time value of money.)

11. p = -423 + 10.4P - .05P2 implies Mp = 10.4 - .1P. Setting Mp = 0, we obtain: 10.4 - .1P = 0, or P = \$104 thousand. This is exactly the optimal price found earlier.

12. a. First note that if marginal cost and marginal benefit to consumers both increased by \$25, the optimal output would not change since MR(Q*) = MC(Q*) implies that MR(Q*) + 25 = MC(Q*) + 25. The price would rise by \$25 but, since marginal costs rise by \$25, the firm’s total profits would remain the same. If marginal costs increased by more than \$25, profits would fall. Thus the firm should not redesign when the increase in MC is \$30.

b. If MC increases by \$15 and MR increases by \$25, the new intersection of the MR and MC occurs at a greater output. Output, price, and profit would all rise. Price, however, would rise by less than \$25.

13. Setting MR = MC, one has: a – 2bQ = c, so that Q = (a - c)/2b. We substitute this expression into the price equation to obtain:

P = a - b[(a - c)/2b] = a - (a - c)/2 = a/2 + c/2 = (a + c)/2.

The firm’s optimal quantity increases after a favorable shift in demand - either an increase in the intercept (a) or a fall in the slope (b). But quantity decreases if it becomes more costly to produce extra units, that is., if the marginal cost (c) increases. Price is raised after a favorable demand shift (an increase in a) or after an increase in marginal cost (c). Note that only \$.50 of each dollar of cost increase is passed on to the consumer in the form of a higher price.

*14. The Burger Queen (BQ) facts are P = 3 - Q/800 and MC = \$.80.

a. Set MR = 0 to find BQ’s revenue-maximizing Q and P. Thus, we have 3 - Q/400 = 0, so Q = 1,200 and P = \$1.50. Total revenue is \$1,800 and BQ’s share is 20% or \$360. The franchise owner’s revenue is \$1,440, its costs are (.8)(1,200) = \$960, so its profit is \$480.

b. The franchise owner maximizes its profit by setting MR = MC. Note that the relevant MR is (.8)(3 - Q/400) = 2.4 - Q/500. After setting MR = .80, we find Q = 800. In turn, P = \$2.00 and the parties’ total profit is (2.00 - .80)(800) = \$960, which is considerably larger than \$840, the total profit in part (a).

c. Regardless of the exact split, both parties have an interest in maximizing total profit, and this is done by setting (full) MR equal to MC. Thus, we have 3 - Q/400 = .80, so that Q = 880. In turn, P = \$1.90, and total profit is: (1.90 - .80)(880) = \$968.

d. The chief disadvantage of profit sharing is that it is difficult, time-consuming, and expensive for the parent company to monitor the reported profits of the numerous franchises. Revenue is relatively easy to check (from the cash register receipts) but costs are another matter. Individual franchisees have an incentive to exaggerate the costs they report in order to lower the measured profits from which the parent’s split is determined. The difficulty in monitoring cost and profit is the main strike against profit sharing.

15. a. The profit function is p = -10 - 48Q + 15Q2 - Q3. At outputs of 0, 2, 8, and 14, the respective profits are -10, -54, 54, and -486.

b. Marginal profit is Mp = dp/dQ = -48 + 30Q - 3Q2 = -3(Q - 2)(Q - 8), after factoring. Thus, marginal profit is zero at Q = 2 and Q = 8. From part a, we see that profit achieves a local minimum at Q = 2 and a maximum at Q = 8.

Discussion Question

Suppose the firm considers expanding its direct sales force from 20 to, say 23 sales people. Clearly, the firm should be able to estimate the marginal cost of the typical additional sales person (wages plus fringe benefits plus support costs including company vehicle). The additional net profit generated by an additional sales person is a little more difficult to predict. An estimate might be based on the average profitability of its current sales force. A more detailed estimate might judge how many new client contacts a salesperson makes, historically what fraction of these contacts result in new business, what is the average profit of these new accounts, and so on. If the marginal profit of a sales person is estimated to be between \$100,000 and \$120,000 while the marginal cost is \$85,000, then the firm has a clear-cut course of action, namely hire the additional 1, 2, or 3 employees.

S1. a and b. Setting MR = MC implies: 800 – 4Q = 200 + Q. Therefore, Q* = 120 parts and P* = \$560.

c. To confirm these values on a spreadsheet, we maximize cell F7 by changing cell B7. Maximum profit in cell F7 is \$16,000.

S2. a. Given p = 20[A/(A+8)] –A, it follows that Mp = 20[8/(A+8)2] – 1. Setting Mp = 0 implies (A+8)2 = 160, or A* = \$4.649 million.

b. Confirm this value on your spreadsheet by maximizing cell F7 by changing cell C7. Maximum profit in F7 is \$2.702 million.

S3. a. To confirm these values on our spreadsheet, we maximize cell F7 by changing cell B7. The optimal sales volume is: Q* = 2.4 million units and the optimal price is P* = \$210. Amazon’s margin on each reader is: 210 – 126 = \$84, and its maximum profit (or, more precisely contribution) is \$201.6 million.

b. We extend the spreadsheet by including contribution from sales of e-books (\$100 per kindle sold) in cell G7 and add this to Kindle profit to compute total profit in cell H7. Maximizing total profit, we find the new optimal solution to be: Q* = 3.829 million units and P* = \$160. (This price is close to current price levels for the Kindle.)

By lowering price, Amazon increases its Kindle sales. The increased profit from e-books more than makes up for reduced Kindle profit. Note that e-book profit is almost three times Kindle profit. Amazon’s total profit comes to some \$513.0 million.

Appendix Problems

1. When tax rates become very high, individuals will make great efforts to shield their income from taxes. Furthermore, higher taxes will discourage the taxed activities altogether. (In the extreme case of a 100% tax, there is no point in undertaking income-generating activities.) Thus, a higher tax rate means a smaller tax base. Increasing the tax rate from zero, the revenue curve first increases, eventually peaks, and then falls to zero (at a 100% tax). Thus, the curve is shaped like an upside-down U.

2. a. B(t) = 80 - 100t. Therefore, R = 80t - 100t2. Setting MR = dR/dt = 0, we find: 80 - 200t = 0, or t = .4.

b. B(t) = 80 - 240t2. Therefore, R = 80t - 240t3. Setting MR = dR/dt = 0, we find: 80 - 720t2 = 0. Therefore, t2 = 1/9, or t = 1/3.

c. B(t) = 80 - 80t.5. Therefore, R = 80t - 80t1.5. Setting MR = dR/dt = 0, we find: 80 - 120t.5 = 0. Thus, t.5 = 2/3, or t = 4/9.

3. a. p = 20x - x2 + 16y - 2y2. Setting dp/dx = 0 and dp/dy = 0 implies x = 10 and y = 4.

b. The Lagrangian is L = p + z(8 - x - y). Therefore, the optimality conditions are: 20 - 2x - z = 0, 16 - 4y - z = 0, and x + y = 8. The solution is x = 6, y = 2, and z = 8.

c. The Lagrangian is L = p + z(7.5 - x - .5y). Therefore, the optimality conditions are: 20 - 2x - z = 0, 16 - 4y - .5z = 0, and x + .5y = 7.5. The solution is x = 6, y = 3, and z = 8.

File: Ch02; CHAPTER 2: Optimal Decisions Using Marginal Analysis

MULTIPLE CHOICE

1. According to the model of the firm, the management’s main goal is to:

a) increase revenue from sales.

b) maximize profit.

c) maximize its market share.

d) minimize its variable cost per unit.

e) maintain a steady and predictable growth in earnings.

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Easy

PAGE: 30

2. According to the law of demand, if a firm reduces the price of its good:

a) consumers in the market will demand more units of the good.

b) some consumers will exit the market.

c) consumers will demand fewer units than before the price cut.

d) the quantity of goods produced and sold by the firm will decline.

e) competing firms will increase prices.

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Easy

PAGE: 31

3. Which of the following is true of a firm that faces a downward sloping demand curve?

a) In order to sell more units, the firm needs to lower its price.

b) The total cost curve for the firm is also downward sloping.

c) The firm's total revenue and price are directly correlated.

d) The marginal revenue from each unit sold is constant.

e) The firm faces a constant marginal cost curve.

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Easy

PAGE: 31-32

4. The demand for a product is given by Q = 600 – 30P, where P = price and Q = quantity. At P = \$15, the firm sells _____ units.

a) 100

b) 150

c) 300

d) 450

e) 600

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 33

5. The demand for a product is given by P = 1,750 – 25Q, where P = price and Q = quantity. If the firm wishes to sell 50 units, each unit should be priced at _____.

a) \$500

b) \$400

c) \$300

d) \$200

e) \$100

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 33

6. A firm’s demand curve is given by Q = 800 – 2P, where P = price and Q = quantity. Therefore, its inverse demand equation is _____.

a) MR = 800 – 4P

b) P = 800 – 2Q

c) P = 400 – 0.5Q

d) P = 800 – 0.5Q

e) 800 = Q + 2P

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 33-34

7. Suppose a firm's inverse demand function is P = 40 – 8Q. What is the firm's revenue function?

a) R = 40Q – 8Q2

b) R = 40 – 16Q

c) R = –8Q

d) R = 40/Q – Q

e) R = 5 – Q

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 35

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product.

Table 2-1

8. Refer to Table 2-1. What is the firm’s profit from the sale of the 3rd unit of the good?

a) \$13

b) \$11

c) \$12

d) \$39

e) \$27

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 37-38

9. Refer to Table 2-1. What is the marginal profit of the firm from the sale of the 2nd unit of the good?

a) \$9

b) \$3

c) \$1

d) \$5

e) \$21

SECTION REFERENCE: Marginal Analysis

DIFFICULTY LEVEL: Medium

PAGE: 39

10. Suppose, at its current output level, a firm’s marginal profit is positive. Therefore, to maximize profit, it should:

a) decrease output until marginal profit is zero.

b) increase output because marginal revenue [MR] is less than marginal cost [MC].

c) increase both its output and its price.

d) increase output because MR is greater than MC.

e) increase output until it is producing at full capacity.

SECTION REFERENCE: Marginal Analysis

DIFFICULTY LEVEL: Medium

PAGE: 40

11. Suppose a firm’s profit is given by the equation p = –200 + 80Q – 0.2Q2, where p = profit and Q = quantity. Which of the following is true?

a) The firm’s marginal profit [Mp] is given by the equation: Mp = 80 – 0.2Q.

b) The firm’s profit-maximizing output is Q = 400.

c) The firm’s profit-maximizing output is Q = 200.

d) The firm’s marginal profit [Mp] is given by the equation: Mp = 80 – 2Q.

e) The firm’s profit-maximizing output is Q = 800.

SECTION REFERENCE: Marginal Analysis

DIFFICULTY LEVEL: Medium

PAGE: 41-42

12. If a firm’s profit is given by p = 36Q2 – 360Q – 150, where p = profit and Q = quantity produced, then its optimal output is _____ units.

a) 12

b) 5

c) 2

d) 20

e) 36

SECTION REFERENCE: Marginal Analysis

DIFFICULTY LEVEL: Hard

PAGE: 41-42

13. What is the marginal revenue [MR] equation for a firm with the demand function P = a – bQ, where P = price and Q = quantity?

a) MR = b – Q

b) MR = a – 2bQ

c) MR = a + 2Q

d) MR = 2Q

e) MR = 2a + Q

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 44

14. A firm’s total revenue function is given by R = 100 + 10Q + 2Q2, where R = revenue and Q = quantity. Which of the following is true if Q = 10?

a) The firm’s total revenue is \$400 and the marginal revenue is \$10.

b) The firm’s marginal revenue is constant at \$40.

c) The average revenue of the firm is \$50.

d) The total revenue of the firm is \$500.

e) The marginal revenue of the firm is \$50.

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 44

15. Which of the following correctly defines marginal revenue?

a) Marginal revenue is the price at which the firm sells the last unit of the good.

b) Marginal revenue is the change in revenue from a unit increase in the price of the good.

c) Marginal revenue is the additional revenue from a unit increase in output and sales.

d) Marginal revenue is the additional revenue earned from an increase in demand for the good.

e) Marginal revenue is the difference between price and marginal cost for the last unit sold.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Easy

PAGE: 44

16. For a downward-sloping demand curve, the associated marginal revenue curve:

a) coincides with the demand curve.

b) lies below and is parallel to the demand curve.

c) has twice the slope as the demand curve.

d) is positive for all levels of sales.

e) is parallel to the quantity axis.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Easy

PAGE: 44

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product.

Table 2-1

17. Refer to Table 2-1. What is the marginal revenue of the firm associated with the sale of the 5th unit of the good?

a) \$55

b) \$8

c) \$7

d) \$48

e) \$4

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 44

18. Refer to Table 2-1. What is the profit-maximizing level of output for the firm?

a) 3 units

b) 2 units

c) 1 unit

d) 5 units

e) 4 units

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 45

19. Given that a firm's inverse demand function is P = 100 – 5Q and total cost is given by C = 550 + 10Q, what is the firm's profit-maximizing level of output?

a) 10 units

b) 15 units

c) 9 units

d) 8 units

e) 5 units

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 45

20. Which of the following correctly defines marginal cost?

a) Marginal cost is the addition made to fixed cost when an extra unit is produced.

b) Marginal cost is the additional cost of producing an extra unit of output.

c) Marginal cost is the additional cost of increasing the scale of production in the long run.

d) Marginal cost is the difference between price and marginal revenue for the last unit sold.

e) Marginal cost is the same as the firm’s variable cost at all levels of output.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Easy

PAGE: 45

21. Given the total cost equation for a firm, the marginal cost equation can be derived by:

a) dividing total cost by total output.

b) taking the first derivative of the cost function with respect to quantity.

c) dividing total variable cost by total output.

d) subtracting variable cost from the fixed cost at all levels of output.

e) multiplying the total cost equation by price.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Easy

PAGE: 45

22. To maximize profit, the firm should set output at the level where:

a) the average cost per unit is minimized.

b) average revenue just equals average cost.

c) marginal cost equals zero.

d) marginal revenue is equal to marginal cost.

e) marginal revenue equals zero.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Easy

PAGE: 45

23. Assume that a firm is producing at its profit-maximizing level of output. A decrease in the price of raw materials used in production is most likely to lead to:

a) an increase in quantity produced at an unchanged price.

b) a fall in the price of the good and an increase in the quantity produced.

c) a fall in both the price of the good and the quantity produced.

d) an increase in both the price of the good and the quantity produced.

e) a fall in the quantity produced of the good at an unchanged price.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50

24. A firm negotiates a new labor contract with a higher average hourly wage. What is the most likely effect of the higher wage on the firm's price and output?

a) Both price and output will not be affected.

b) Price will increase but output will not change.

c) Both price and output will increase.

d) Price will not change but output will decrease.

e) Price will increase but output will decrease.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50

25. Assume that a firm is producing at its profit-maximizing level of output. A decrease in fixed cost implies that:

a) marginal revenue will increase but marginal cost will decrease.

b) marginal revenue will not change but marginal cost will decrease.

c) neither average total cost nor marginal cost will change.

d) neither marginal revenue nor marginal cost will change.

e) both marginal revenue and marginal cost will decrease.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50

26. Due to an increase in the price of a competitor’s product, the demand for a firm’s product increases sharply. How is this most likely to affect the firm’s marginal revenue and marginal cost?

a) Marginal revenue will increase but marginal cost will decrease.

b) Both marginal revenue and marginal cost will not be affected.

c) Both marginal revenue and marginal cost will increase.

d) Marginal revenue will not change but marginal cost will increase.

e) Marginal revenue will increase but marginal cost will not change.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50-51

27. Assume that Burger King, a fast food chain, enters into a franchise agreement. The royalty paid to Burger King by the franchisee is calculated as a percentage of the franchisee’s revenue. Given that the franchisee faces a downward-sloping demand curve, which of the following is likely to be true?

a) The franchisee’s revenue-maximizing output will be greater than its profit-maximizing output.

b) To maximize revenue, Burger King will want the franchisee to produce at the level where total revenue is positive but falling.

c) The franchisee will produce at the level where the slope of the total revenue curve is zero in order to maximize profits.

d) The profit-maximizing level of output for the franchisee will be at the level where marginal revenue is lesser than marginal cost.

e) To maximize revenue, Burger King will want the franchisee to produce at the level where marginal revenue equals marginal cost.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 53

28. Are there any types of goods or situations where the law of demand does not hold? Explain.

ANSWER: The law of demand states that all other factors held constant, the higher the unit price of a good, the fewer the number of units demanded by consumers and, consequently, sold by firms. For certain goods, a high price is associated with a higher status or luxury, for example, a fancy wine or a designer bag. For such goods, a high price is seen as a sign of exclusivity, which means that the demand for these goods increases as price increases. These are called Veblen goods.

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Medium

PAGE: 31

29. What is the law of demand? How do managers use it in decision-making?

ANSWER: The law of demand states that all other factors held constant, the higher the unit price of a good, the fewer the number of units demanded by consumers and, consequently, sold by the firm. Managers use the demand curve as the basis for predicting the revenue consequences of alternative output and pricing policies.

SECTION REFERENCE: A Simple Model of the Firm

DIFFICULTY LEVEL: Easy

PAGE: 31-33

30. Carefully define marginal analysis, and explain how it is useful in managerial economics.

ANSWER: Marginal analysis is the process of considering small changes in a decision and determining whether such a change will improve the ultimate objective. The manager can follow a clear rule: Make a small move to a nearby alternative if and only if the move will improve one's objective. Keep moving until no further move will help.

SECTION REFERENCE: Marginal Analysis

DIFFICULTY LEVEL: Easy

PAGE: 38-40

31. Suppose that a firm operates in a competitive market where the commodity price is \$15 per unit. The firm’s cost equation is C = 25 + 0.25Q2, where C = total cost and Q = quantity.

(a) Find the profit-maximizing level of output for the firm. Determine its level of profit.

ANSWER: In a competitive market, revenue [R] = price × quantity = 15Q implying marginal revenue [MR] = ∂R/∂Q = \$15. In turn, marginal cost [MC] = ∂C/∂Q = 0.5Q. Setting MR = MC, gives 15 = 0.5Q, or Q = 30 units. At Q = 30 units, R = \$450, C =\$250, and profit = \$200.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 44-45

(b) Suppose that fixed costs increase to \$75. Verify that this change in fixed costs does not affect the firm's optimal output.

ANSWER: The increase in fixed cost has no effect on MR or MC. MC = ∂C/∂Q = 0.5Q and MR = ∂R/∂Q = \$15. Setting MR = MC, yields 15 = 0.5Q, or Q = 30 units. The firm's optimal level of output is unaffected. However, with the \$50 rise in fixed cost, the firm's profit falls to \$150.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50

32. The demand for a firm’s product is given by the equation: P = 36 – 0.2Q. The firm’s cost equation is given by C = 200 + 20Q.

(a) Determine the firm’s optimal quantity and price.

ANSWER: Marginal revenue [MR] = ∂R/∂Q = 36 – 0.4Q and marginal cost [MC] = ∂C/∂Q = \$20. Setting MR = MC implies that the optimal output [Q*] = 40 units. From the price equation, it follows that the optimal price [P*] = 36 – (0.2)(40) = \$28. Finally, profit is given by: p = \$1,120 – 1,000 = \$120.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 44-45

(b) Suppose that the firm’s costs change to C = 100 + 24Q. Determine the new optimal quantity and price. Explain why the results differ from the previous case.

ANSWER: With the new cost function, MC = \$24. Setting MR = MC implies 36 – 0.4Q = 24, or Q* = 30 units. In turn, P* = 36 – (0.2)(30) = \$30. Finally, profit is given by: p = \$900 – \$820 = \$80. Here, the reduction in fixed cost has no impact on output, but the increase in marginal cost induces a smaller output quantity and a greater price.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50

33. A firm faces the demand curve, P = 80 – 3Q, and has the cost equation: C = 200 + 20Q, where P = price, C = total cost, and Q = quantity.

(a) Find the optimal quantity and price for the firm.

ANSWER: Profit is maximized by setting marginal revenue [MR] = marginal cost [MC]. From the price equation, MR = 80 – 6Q. Equating this with MC = \$20 implies 80 – 6Q = 20, or the optimal output [Q*] = 10 units. In turn, the optimal price [P*] = 80 – (3)(10) = \$50.

SECTION REFERENCE: Marginal Revenue and Marginal Cost

DIFFICULTY LEVEL: Medium

PAGE: 44-45

(b) Now suppose that the demand for the firm’s product changes to: P = 110 – 3Q. Find the new optimal quantity and price. Has there been an increase or a decrease in demand? Explain.

ANSWER: According to the new price equation, P = 110 – 3Q, MR = 110 – 6Q. Setting MR = MC implies 110 – 6Q = 20, or Q* = 15 units. In turn, P* = 110 – (3)(15) = \$65. The increase in demand (in this case a parallel outward shift of the demand curve) has induced the firm to increase both its price and quantity.

SECTION REFERENCE: Sensitivity Analysis

DIFFICULTY LEVEL: Medium

PAGE: 50

### Fundamentals of futures and options markets, 8/e john c. Hull solutions manual and test bank

Fundamentals of futures and options markets, 8/e john c. Hull solutions manual and test bank

CHAPTER 2

Mechanics of Futures Markets

Practice Questions

Problem 2.8.

The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on. Do these options increase or decrease the futures price? Explain your reasoning.
These options make the contract less attractive to the party with the long position and more attractive to the party with the short position. They therefore tend to reduce the futures price.

Problem 2.9.

What are the most important aspects of the design of a new futures contract?
The most important aspects of the design of a new futures contract are the specification of the underlying asset, the size of the contract, the delivery arrangements, and the delivery months.

Problem 2.10.

Explain how margin protect investors against the possibility of default.

Margin is money deposited by an investor with his or her broker. It acts as a guarantee that the investor can cover any losses on the futures contract. The balance in the margin account is adjusted daily to reflect gains and losses on the futures contract. If losses are above a certain level, the investor is required to deposit further margin. This system makes it unlikely that the investor will default. A similar system of margin accounts makes it unlikely that the investor’s broker will default on the contract it has with the clearing house member and unlikely that the clearing house member will default with the clearing house.

Problem 2.11.

A trader buys two July futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is \$6,000 per contract, and the maintenance margin is \$4,500 per contract. What price change would lead to a margin call? Under what circumstances could \$2,000 be withdrawn from the margin account?
There is a margin call if more than \$1,500 is lost on one contract. This happens if the futures price of frozen orange juice falls by more than 10 cents to below 150 cents per lb. \$2,000 can be withdrawn from the margin account if there is a gain on one contract of \$1,000. This will happen if the futures price rises by 6.67 cents to 166.67 cents per lb.

Problem 2.12.

Show that, if the futures price of a commodity is greater than the spot price during the delivery period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures price is less than the spot price? Explain your answer.
If the futures price is greater than the spot price during the delivery period, an arbitrageur buys the asset, shorts a futures contract, and makes delivery for an immediate profit. If the futures price is less than the spot price during the delivery period, there is no similar perfect arbitrage strategy. An arbitrageur can take a long futures position but cannot force immediate delivery of the asset. The decision on when delivery will be made is made by the party with the short position. Nevertheless companies interested in acquiring the asset will find it attractive to enter into a long futures contract and wait for delivery to be made.

Problem 2.13.

Explain the difference between a market-if-touched order and a stop order.
A market-if-touched order is executed at the best available price after a trade occurs at a specified price or at a price more favorable than the specified price. A stop order is executed at the best available price after there is a bid or offer at the specified price or at a price less favorable than the specified price.

Problem 2.14.

Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.
A stop-limit order to sell at 20.30 with a limit of 20.10 means that as soon as there is a bid at 20.30 the contract should be sold providing this can be done at 20.10 or a higher price.

Problem 2.15.

At the end of one day a clearing house member is long 100 contracts, and the settlement price is \$50,000 per contract. The original margin is \$2,000 per contract. On the following day the member becomes responsible for clearing an additional 20 long contracts, entered into at a price of \$51,000 per contract. The settlement price at the end of this day is \$50,200. How much does the member have to add to its margin account with the exchange clearing house?
The clearing house member is required to provide 20×\$2,000 = \$40,000 as initial margin for the new contracts. There is a gain of (50,200 50,000) 100 \$20,000 on the existing contracts. There is also a loss of (51,000 – 50,200) × 20 = \$16,000 on the new contracts. The member must therefore add

40,000 – 20,000 + 16,000 = \$36,000

to the margin account.

Problem 2.16.

On July 1, 2013, a Japanese company enters into a forward contract to buy \$1 million with yen on January 1, 2014. On September 1, 2013, it enters into a forward contract to sell \$1 million on January 1, 2014. Describe the profit or loss the company will make in dollars as a function of the forward exchange rates on July 1, 2013 and September 1, 2013.
Suppose and are the forward exchange rates for the contracts entered into July 1, 2013 and September 1, 2013, respectively. Suppose further that is the spot rate on January 1, 2014. (All exchange rates are measured as yen per dollar). The payoff from the first contract is million yen and the payoff from the second contract is million yen. The total payoff is therefore million yen.

Problem 2.17.

The forward price on the Swiss franc for delivery in 45 days is quoted as 1.1000. The futures price for a contract that will be delivered in 45 days is 0.9000. Explain these two quotes. Which is more favorable for an investor wanting to sell Swiss francs?
The 1.1000 forward quote is the number of Swiss francs per dollar. The 0.9000 futures quote is the number of dollars per Swiss franc. When quoted in the same way as the futures price the forward price is. The Swiss franc is therefore more valuable in the forward market than in the futures market. The forward market is therefore more attractive for an investor wanting to sell Swiss francs.

Problem 2.18.

Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
Hog futures are traded by the CME Group. The broker will request some initial margin. The order will be relayed by telephone to your broker’s trading desk on the floor of the exchange (or to the trading desk of another broker). It will be sent by messenger to a commission broker who will execute the trade according to your instructions. Confirmation of the trade eventually reaches you. If there are adverse movements in the futures price your broker may contact you to request additional margin.

Problem 2.19.

“Speculation in futures markets is pure gambling. It is not in the public interest to allow speculators to trade on a futures exchange.” Discuss this viewpoint.
Speculators are important market participants because they add liquidity to the market. However, contracts must be useful for hedging as well as speculation. This is because regulators generally only approve contracts when they are likely to be of interest to hedgers as well as speculators.

Problem 2.20.

Explain the difference between bilateral and central clearing for OTC derivatives.

In bilateral clearing, two market participants enter into an agreement with each other covering all outstanding derivative transactions between the two parties. Typically the agreement covers collateral arrangements, events of default, the circumstances under which one side can terminate the transactions, etc. In central clearing a CCP (central clearing party) stands between the two sides of an OTC derivative transaction in much the same way that the exchange clearing house does for exchange-traded contracts. It absorbs the credit risk but requires initial and variation margin from each side.

Problem 2.21.

What do you think would happen if an exchange started trading a contract in which the quality of the underlying asset was incompletely specified?
The contract would not be a success. Parties with short positions would hold their contracts until delivery and then deliver the cheapest form of the asset. This might well be viewed by the party with the long position as garbage! Once news of the quality problem became widely known no one would be prepared to buy the contract. This shows that futures contracts are feasible only when there are rigorous standards within an industry for defining the quality of the asset. Many futures contracts have in practice failed because of the problem of defining quality.

Problem 2.22.

“When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one.” Explain this statement.
If both sides of the transaction are entering into a new contract, the open interest increases by one. If both sides of the transaction are closing out existing positions, the open interest decreases by one. If one party is entering into a new contract while the other party is closing out an existing position, the open interest stays the same.

Problem 2.23.

Suppose that on October 24, 2013, a company sells one April 2014 live-cattle futures contract. It closes out its position on January 21, 2014. The futures price (per pound) is 91.20 cents when it enters into the contract, 88.30 cents when it closes out the position and 88.80 cents at the end of December 2013. One contract is for the delivery of 40,000 pounds of cattle. What is the profit? How is it taxed if the company is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.

The total profit is

40,000 × (0.9120 – 0.8830) = \$1,160

If you are a hedger this is all taxed in 2014. If you are a speculator

40,000 × (0.9120 – 0.8880) = \$960

is taxed in 2013 and

40,000 × (0.8880 – 0.8830) = \$200

is taxed in 2014.

Problem 2.24

Explain how CCPs work. What are the advantages to the financial system of requiring all

standardized derivatives transactions to be cleared through CCPs?

A CCP stands between the two parties in an OTC derivative transaction in much the same way that a clearing house does for exchange-traded contracts. It absorbs the credit risk but requires initial and variation margin from each side. In addition, CCP members are required to contribute to a default fund. The advantage to the financial system is that there is a lot more collateral (i.e., margin) available and it is therefore much less likely that a default by one major participant in the derivatives market will lead to losses by other market participants. There is also more transparency in that the trades of different financial institutions are more readily known. The disadvantage is that CCPs are replacing banks as the too-big-to-fail entities in the financial system. There clearly needs to be careful oversight of the management of CCPs.

Further Questions

Problem 2.25
Trader A enters into futures contracts to buy 1 million euros for 1.4 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange (dollars per euro) declines sharply during the first two months and then increases for the third month to close at 1.4300. Ignoring daily settlement, what is the total profit of each trader? When the impact of daily settlement is taken into account, which trader does better?

The total profit of each trader in dollars is 0.03×1,000,000 = 30,000. Trader B’s profit is realized at the end of the three months. Trader A’s profit is realized day-by-day during the three months. Substantial losses are made during the first two months and profits are made during the final month. It is likely that Trader B has done better because Trader A had to finance its losses during the first two months.

Problem 2.26

Explain what is meant by open interest. Why does the open interest usually decline during

the month preceding the delivery month? On a particular day, there were 2,000 trades in a

particular futures contract. This means that there were 2,000 buyers (going long) and

2,000 sellers (going short). Of the 2,000 buyers, 1,400 were closing out positions and 600

were entering into new positions. Of the 2,000 sellers, 1,200 were closing out positions and

800 were entering into new positions. What is the impact of the day’s trading on open

interest?

Open interest is the number of contract outstanding. Many traders close out their positions just before the delivery month is reached. This is why the open interest declines during the month preceding the delivery month. The open interest went down by 600. We can see this in two ways. First, 1,400 shorts closed out and there were 800 new shorts. Second, 1,200 longs closed out and there were 600 new longs.

Problem 2.27

One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2013 a company sells a March 2015 orange juice futures contract for 120 cents per pound. In December 2013, the futures price is 140 cents. In December 2014, the futures price is 110 cents. In February 2015, the futures price is 125 cents. The company has a December year end. What is the company's profit or loss on the contract? How is it realized? What is the accounting and tax treatment of the transaction is the company is classified as a) a hedger and b) a speculator?

The price goes up during the time the company holds the contract from 120 to 125 cents per pound. Overall the company therefore takes a loss of 15,000×0.05 = \$750. If the company is classified as a hedger this loss is realized in 2015, If it is classified as a speculator it realizes a loss of 15,000×0.20 = \$3000 in 2013, a gain of 15,000×0.30 = \$4,500 in 20104 and a loss of 15,000×0.15 = \$2,250 in 2015.

Problem 2.28.

A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is \$3,000 and the maintenance margin is \$2,000. What price change would lead to a margin call? Under what circumstances could \$1,500 be withdrawn from the margin account?
There is a margin call if \$1000 is lost on the contract. This will happen if the price of wheat futures rises by 20 cents from 250 cents to 270 cents per bushel. \$1500 can be withdrawn if the futures price falls by 30 cents to 220 cents per bushel.

Problem 2.29.

Suppose that there are no storage costs for crude oil and the interest rate for borrowing or

lending is 5% per annum. How could you make money if the June and December futures

contracts for a particular year trade at \$80 and \$86, respectively.

You could go long one June oil contract and short one December contract. In June you take delivery of the oil borrowing \$80 per barrel at 5% to meet cash outflows. The interest accumulated in six months is about 80×0.05×0.5 or \$2. In December the oil is sold for \$86 per barrel and \$82 is repaid on the loan. The strategy therefore leads to a profit of \$4. Note that this profit is independent of the actual price of oil in June 2010 or December 2009. It will be slightly affected by the daily settlement procedures.

Problem 2.30.

What position is equivalent to a long forward contract to buy an asset at on a certain date and a put option to sell it foron that date?

The equivalent position is a long position in a call with strike price.

Problem 2.31

A company has derivatives transactions with Banks A, B, and C which are worth +\$20 million, −\$15 million, and −\$25 million, respectively to the company. How much margin or collateral does the company have to provide in each of the following two situations?

a) The transactions are cleared bilaterally and are subject to one-way collateral agreements where the company posts variation margin, but no initial margin. The banks do not have to post collateral.

b) The transactions are cleared centrally through the same CCP and the CCP requires a total initial margin of \$10 million.

If the transactions are cleared bilaterally, the company has to provide collateral to Banks A, B, and C of (in millions of dollars) 0, 15, and 25, respectively. The total collateral required is \$40 million. If the transactions are cleared centrally they are netted against each other and the company’s total variation margin (in millions of dollars) is –20 + 15 + 25 or \$20 million in total. The total margin required (including the initial margin) is therefore \$30 million.

Problem 2.32

A bank’s derivatives transactions with a counterparty are worth +\$10 million to the bank

and are cleared bilaterally. The counterparty has posted \$10 million of cash collateral.

What credit exposure does the bank have?

The counterparty may stop posting collateral and some time will then elapse before the bank is able to close out the transactions. During that time the transactions may move in the bank’s favor, increasing its exposure. Note that the bank is likely to have hedged the transactions and will incur a loss on the hedge if the transactions move in the bank’s favor. For example, if the transactions change in value from \$10 to \$13 million after the counterparty stops posting collateral, the bank loses \$3 million on the hedge and will not necessarily realize an offsetting gain on the transactions.

Problem 2.33. (Excel file)

The author’s Web page (www.rotman.utoronto.ca/~hull/data) contains daily closing prices for crude oil futures contract and gold futures contract. You are required to download the data and answer the following:

a) How high do the maintenance margin levels for oil and gold have to be set so that there is a 1% chance that an investor with a balance slightly above the maintenance margin level on a particular day has a negative balance two days later (i.e. one day after a margin call). How high do they have to be for a 0.1% chance. Assume daily price changes are normally distributed with mean zero. Explain why the exchange might be interested in this calculation.

b) Imagine an investor who starts with a long position in the oil contract at the beginning of the period covered by the data and keeps the contract for the whole of the period of time covered by the data. Margin balances in excess of the initial margin are withdrawn. Use the maintenance margin you calculated in part (a) for a 1% risk level and assume that the maintenance margin is 75% of the initial margin. Calculate the number of margin calls and the number of times the investor has a negative margin balance and therefore an incentive to walk away. Assume that all margin calls are met in your calculations. Repeat the calculations for an investor who starts with a short position in the gold contract.
The data for this problem in the 7th edition is different from that in the 6th edition.

a) For gold the standard deviation of daily changes is \$15.184 per ounce or \$1518.4 per contract. For a 1% risk this means that the maintenance margin should be set at or 4996 when rounded. For a 0.1% risk the maintenance margin should be set at or 6636 when rounded.

For crude oil the standard deviation of daily changes is \$1.5777 per barrel or \$1577.7 per contract. For a 1% risk, this means that the maintenance margin should be set at or 5191 when rounded. For a 0.1% chance the maintenance margin should be set at or 6895 when rounded. NYMEX might be interested in these calculations because they indicate the chance of a trader who is just above the maintenance margin level at the beginning of the period having a negative margin level before funds have to be submitted to the broker.

b) For a 1% risk the initial margin is set at 6,921 for on crude oil. (This is the maintenance margin of 5,191 divided by 0.75.) As the spreadsheet shows, for a long investor in oil there are 157 margin calls and 9 times (out of 1039 days) where the investor is tempted to walk away. For a 1% risk the initial margin is set at 6,661 for gold. (This is 4,996 divided by 0.75.) As the spreadsheet shows, for a short investor in gold there are 81 margin calls and 4 times (out of 459 days) when the investor is tempted to walk away. When the 0.1% risk level is used there is 1 time when the oil investor might walk away and 2 times when the gold investor might do so.