CHAPTER 12HOW MARKETS DETERMINE INCOMES

I. CHAPTER OVERVIEW

Now that you have studied how pricing and production decisions are made in output markets, it is time toconsider how pricing and employment decisions are made in input markets. You will recall that relativescarcity and need were seen to determine why it costs more to buy some goods than it does to buy others; butwhat accounts for the large differences in the wages and salaries offered to people engaged in variousoccupations? Scarcity? Need? Or something else?

Even casual consideration of any productive enterprise reveals that all inputs work interdependently toproduce a given product or service. Given this complex interdependence, how can one compute levels ofcompensation that reflect accurately the importance of their respective contributions? How, more specifically,are wage rates determined? And interest rates? And land rents? And so on?

This begins a series of chapters that focus on the distribution of income. Critical in determining the natureof the distribution must be, of course, the ownership of the factors of production and the prices that theycommand. Chapter 12 begins, therefore, with a brief introduction to what economists mean when they speak ofincome and wealth, and where they look to find the sources of income and wealth in a modern economy.

There is, however, more to the distribution of income than simply cataloguing who owns what. There is,more specifically, the question of what determines how much each factor is worth. We can find an answer tothis question using the familiar tools of supply-and-demand analysis. The fundamental differences betweenproduct markets and factor markets lie in the sources of supply and demand components. In a product marketdemand materializes because the good being produced and sold generates some utility for the consumer; theconsumer is willing to pay some positive price for the privilege of owning the good in question. In an inputmarket factors of production are demanded only because they can be employed to produce an item of value.The demand for inputs is therefore a derived demand based not upon the immediate, innate value of the input toa firm, but upon the value of some other good that it can be employed to produce.

Our examination of these issues begins with the demand side of an input market. Because a firm must hirelabor, buy raw materials, and invest in machinery, it is the demander of productive inputs. Its demand is not,however, unlimited. It makes its employment decisions on the basis of least-cost combinations of inputsdefined by its production function and the prices of those inputs. The derived demand for any input willtherefore result from (1) the cost-minimizing behavior of profit-maximizing firms and (2) a marginal-productivity theory of income distribution.

The final section of Chapter 12 will show how this notion of derived demand can be used in a marketcontext. It will, in particular, play derived demand against alternative input supply schedules.

II. LEARNING OBJECTIVES

After you have read Chapter 12 in your text and completed the exercises in this Study Guide chapter, youshould be able to:

1. Compile a list of questions concerning the distribution of income and the factors that help todetermine the shape of this distribution. Differentiate between the terms income and wealth as they areused in economics.2. Recognize the major sources of income and the major reservoirs of wealth in the United States.Describe who owns the factors of production which generate this income and wealth.3. Establish a role for government in redistributing income and wealth using taxation and transferpayments.4. Define the notion of a derived demand for a factor of production, and explain why the demands forfactors are interdependent. That is, explain why the demand for any single factor depends on the level ofuse of other inputs in the production process.5. Show how the demand curve for an input is represented by its marginal revenue product schedule,i.e., explain why the derived demand for any input can be found by multiplying the marginal product ofthat input by the marginal revenue of output.6. Show precisely why, in cases of perfect competition, the marginal revenue product of any input isequal to the competitive price of output multiplied by its marginal product. Then show how theimperfectly competitive case differs from this.

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7. Demonstrate why the least-cost rule describes an optimal combination of factors for firms to use.Further demonstrate that the firm that hires all inputs up to the point at which their prices equal theirmarginal revenue products will guarantee that (1) it is producing the profit-maximizing output and (2) it isincurring the least cost; i.e., (1) the marginal revenue of its sales will equal the marginal cost of itsproduction, and (2) the least-cost rule will be satisfied.8. Show how the market derived-demand curve for any input is equal to the horizontal sum of themarginal revenue product curves of all the firms which employ that input. Recall that a market supplycurve for any good, and so for any factor, is equal to the horizontal sum of the individual factor owner’ssupply curves.9. Illustrate how interaction between the supply and the demand for factors of production determines theirmarket prices. Explain why the distribution of income is the result of the workings of supply and demandin an economy’s input markets.

III. REVIEW OF KEY CONCEPTS

Match the following terms from column A with their definition in column B.A B

__ Income 1. Means that the demand for a factor of production depends upon the demand fordistribution the final product.

__ Income 2. The firm will choose an optimal combination of inputs such that the ratios ofthe marginal products to the prices of the inputs are equal for all inputs.

__ Wealth 3. Direct payments from government to individuals that are not in return forcurrent goods and services.

__ Dividend derived 4. Refers to the flow of wages or things of value earned by a person or householdduring a given time period.

__ Transfer 5. Consists of the net dollar value of assets owned at a point in time.payments

__ Personal income 6. Equal to market income plus transfer payments.__ Marginal 7. The addition to total output when the firm hires an additional unit of a single

product factor of production.__ Law of 8. Examines the determination of income in a society.

diminishingreturns

__ Marginal 9. States that as the firm hires additional units of an input, eventually the marginalrevenue product product of that input will fall.

__ Derived demand 10. The product of marginal revenue and marginal product.__ Least-cost rule 11. A firm's demand for inputs that is derived indirectly from the consumer demand

for its final product.

IV. SUMMARY AND CHAPTER OUTLINE

This section summarizes the key concepts from the chapter.

A. Income and Wealth1. The theory of the distribution of income is concerned with (1) the determination of income, and (2) theallocation of total product among factors of production. Both of these questions are important; we need tounderstand how income is generated in an economy, and then how these wages, rent, interest, and profits aredistributed across the owners of labor, land, capital, and entrepreneurial ability.2. Income is a flow of money; wealth is a stock of accumulated economic assets. Remember that a stockmeasure of any economic variable describes the total quantity of the variable at a particular point in time; aflow measure describes the accumulation of an economic variable over a period of time. Both of thesemeasures are important in describing how the returns to factors are distributed across a society.3. Sometimes, governments take actions to redistribute income and wealth in a society. This decision is anormative one and usually occurs when policymakers have determined that there is significant inequity in thedistribution of income and wealth, or when some market failure has occurred. The two most popular tools used

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to achieve this redistribution are taxes and transfer payments. Governments collect money as taxes and returnit to people in the form of direct payments that are not in return for current goods and services.

B. Input Pricing by Marginal Productivity1. The demand for any factor of production is a derived demand, which means that the demand for the factordepends upon, or is derived from, the demand for the final product that it helps to produce. For example, thedemand for coal miners depends upon the demand for coal. Increased concern over acid rain and otherecological problems has decreased the demand for coal, and hence decreased the demand for coal miners. Thedemand for computer chips depends upon the demand for computers. The explosion in the popularity and useof personal computers in the past decades has increased the demand for computers, and hence increased thedemand for computer chips.2. The demand for any input depends directly, and most importantly, upon the productivity of that factor.Take a moment to review some of the production theory from Chapter 6: A production function describes howinputs are transformed into output. Production can be measured in several ways, but the key to our analysis ismarginal product, which is defined as the addition to total output that occurs when a firm hires an additionalunit of an input. Remember that the law of diminishing returns states that as additional units of an input areadded to a production process in the short run, eventually marginal product will fall. This means that themarginal product schedule is downward-sloping, at least over some levels of output.

Given this description of the production process, the demand for an input will be defined by its marginalrevenue product (MRP). Marginal revenue product measures the addition to total revenue that occurs when afirm hires an additional unit of an input. MRP translates marginal product, which is measured in output units,to a meaningful dollar figure. To calculate MRP, multiply the marginal product of the input by the marginalrevenue.3. The derived demand for any factor in a perfectly competitive industry is the (multiplicative) product of theprice of output and the marginal product at each level of factor employment; this is simply a consequence of thehorizontal demand curve faced by perfect competitors, which guarantees that price equals marginal revenue.However, in an imperfectly competitive industry, P > MR because the firm must lower the price of all unitssold in order to sell additional units of output. (Remember that the imperfect competitor is able to charge themaximum price that the market will bear at the optimal level of output.)4. The least-cost rule states that a firm will hire its optimal combination of inputs when each input’smarginal revenue product is equal to its price. This means that the last dollar spent on each input will yield thesame marginal productivity. Suppose input A is used to produce output X. Then,

MRPA = PA ==> MRX x MPA = PA ==> MPA / PA = 1 / MRX

The same expression can be written for each of the other inputs used to produce X; thus the ratio of themarginal product of each input to its price must be equal to the inverse of the marginal revenue of good X.Under these conditions the firm will (a) be producing the profit-maximizing output and (b) be operating at leastcost.

Suppose that you are producing widgets using labor and capital. Suppose further that the marginal productof the last worker was 100 widgets, and you pay workers $50 per day. The marginal product of capital was 300widgets, and you pay $100 per day for each unit of capital. Finally, suppose at this point you have exhaustedyour budget on these two inputs.

Note the problem here: Capital is three times as productive as labor but only costs twice as much! Theleast-cost rule is violated; you could have produced the same output with lower costs by using less labor andmore capital. Or, you could have produced more output with the same total expenditure by using less laborand more capital. When the least-cost rule does not hold, any firm can reallocate its resources to lower costsand increase profits.5. The market demand curve for any input is the horizontal sum of the derived demand curves of all firmsemploying that input. Likewise, the market supply curve for any input is the horizontal sum of the supplycurves of all factor owners selling that input.6. As in any other market we have discussed, given demand and supply curves, we can describe anequilibrium price and quantity exchanged in the market for a factor of production. Thus, the distribution ofincome in an economy is at least in part determined by market forces. Individuals and households sell thefactors that they own in input markets; relative scarcity in these input markets combines with need to determinethe returns to resource owners.

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7. In spite of the importance of this analysis, other questions surrounding the distribution of income andwealth remain unanswered. For instance, how is the initial distribution of factors determined? How doesgovernment policy interact with market forces? These issues will be discussed in greater detail in the next twochapters.

V. HELPFUL HINTS

1. Income and wealth are both important concepts in economics. They both measure the value of resourcesavailable to individuals and households in an economy. However, income is a flow concept. It measures theamount of money that accrues to a resource over a period of time. Wealth is a stock concept. It measures thevalue of resources at a particular point in time. It is critical that you see the difference between these measuresand use each when appropriate.2. Your text authors point out the importance of the interdependence that exists among factors of production,but it bears repeating here. This interdependence occurs because most inputs in a production process arecomplements, at least to some extent. This means that the inputs are used together to produce output.Although there is often some substitutability across factors, it is rare that inputs are perfect substitutes. Thatis, it is rare that a firm could use all land and no labor, or all labor and no land, for example, to produce aproduct. Farmers are able to marginally reduce acreage and increase the number of farmhands hired, or viceversa, and hold output fixed. However, all land and no labor, or all labor and no land, will yield zero output.

This is an important concept to consider, because it affects the way we think about a factor’s productivityand value to the firm. When the North American Free Trade Agreement (NAFTA) was being debated in theUnited States, many opponents lamented the fact that workers in Mexico and the Caribbean earn much lowerwages than workers in the United States and predicted the wholesale movement of many industries uponpassage of the agreement. What they failed to realize was that workers in these regions are paid less becausethey are much less productive than their U.S. counterparts. An important reason for this lower productivityinvolves the notion of factor interdependence. Workers in other countries have much less capital equipment andtechnology to work with; their productivity will tend to remain lower as long as this is the case.3. The decision rule for input employment is parallel to the firm’s profit-maximizing output rule. If we thinkabout marginal revenue as the amount of money that flows into the firm when it sells an additional unit ofoutput and marginal cost as the amount of money that flows out of the firm when it sells an additional unit ofoutput, then the general decision rule says produce until the amount coming in is equal to the amount goingout on the margin. Likewise, if we think about marginal revenue product as the amount of money that flowsinto the firm when it hires an additional unit of input and factor price as the amount of money that flows out ofthe firm when it hires an additional unit of input, then this decision rule also says to hire inputs until theamount coming in is equal to the amount going out on the margin. This very general rule can be applied tomany economic decisions.4. For a more extensive discussion of the alternative shapes of supply curves in factor markets, return toChapter 8 in your textbook, which describes perfectly elastic, perfectly inelastic, and backward-bending supplycurves.

VI. MULTIPLE CHOICE QUESTIONS

These questions are organized by topic from the chapter outline. Choose the best answer from the optionsavailable.

A. Income and Wealth1. Income refers to:

a. total cash expenditures made by households over the course of a year.b. the net dollar value of assets owned at a point in time.c. payments from households to governments.d. the total value of a stock portfolio owned by an investor.e. total flow of wages or other things of value earned by a person or household over the course of a year.

2. Wealth refers to:a. total cash expenditures made by households over the course of a year.b. the net dollar value of assets owned at a point in time.c. payments from households to governments.

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d. the total value of a stock portfolio owned by an investor.e. total receipts or cash earned by a person or household over the course of a year.

3. The single most important asset of most households in the U.S. is:a. a home.b. a stock portfolio.c. a car.d. savings account balances.e. expected social security payments.

4. Severe recession in the northeast coupled with a decline in the defense-oriented manufacturing base led to asevere decrease in the demand for housing in Connecticut in the early 1990s. This meant that homeowners’:

a. wealth declined due to the decreased price of housing.b. income declined due to the decreased price of housing.c. wealth increased as the price of housing returned to a more normal level.d. transfer payments from the state increased.e. income declined due to the decreased supply of housing available.

5. The theory of income and wealth distribution analyzes:a. the problem.b. the how problem.c. the for whom problem.d. none of the above.

B. Input Pricing by Marginal Productivity6. During the 1960s and 1970s, as the baby boom generation flowed through grade school, high school, andcollege, the demand for teachers increased. This describes:

a. a derived supply of teachers.b. a derived demand for teachers.c. an increase in the supply curve of teachers.d. a decrease in the demand curve for teachers.e. none of the above.

7. Which of the following examples illustrates the law of diminishing returns at a fish packing plant?a. The firm expands its plant facility in order to take advantage of economies of scale.b. The firm hires additional workers for the third shift but finds that marginal product falls with eachadditional worker.c. An increase in interest rates increases the fixed costs of the firm’s operations.d. The firm starts using cod instead of halibut for its frozen fish filets.e. All the above describe diminishing returns.

8. If inputs A, B, and C are used together to produce product X, then the marginal product of input A is the:a. extra output of X resulting from the employment of 1 extra unit of A, inputs B and C being increasedproportionately.b. amount of input A required to produce 1 extra unit of X, the amounts of inputs B and C being heldconstant.c. extra output of X resulting from the employment of 1 extra unit of A, the amounts of inputs B and Cbeing held constant.d. amount of input A required to produce 1 extra unit of X, the amounts of inputs B and C beingincreased proportionately.e. none of the above.

9. The marginal revenue product of input A used to produce output X is the:a. marginal product of A multiplied by the price of A.b. average product of A multiplied by the price of X.c. marginal product of A multiplied by the quantity of X produced.d. average product of A multiplied by the marginal revenue of X.e. none of the above.

The production function in Table 12-1 describes the relationship between the number of workers employed in awidget factory per day and total product. Widgets are sold in a perfectly competitive market. Use Table 12-1to answer questions 9 through 11.

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TABLE 12-1Quantityof Labor Total Product

0 03 604 755 806 807 768 70

10. Diminishing returns set in after the:a. second worker.b. third worker.c. fourth worker.d. fifth worker.e. sixth worker.

11. If the price of labor is $150 per day and the price of widgets is $10, how many workers should this firmhire?

a. 0.b. 2.c. 3.d. 4.e. 5.

12. If the price of labor falls to $50 per day while the price of a widget remains fixed, how many workersshould this firm hire?

a. 0.b. 2.c. 3.d. 4.e. 5.

13. A firm operates in conditions of imperfect competition. The price of one of the factors of production,input A, is $10; its marginal product is 5. If this firm were operating at its profit-maximizing output, then themarginal revenue from the sale of X must be equal to:

a. $1.00.b. $1.50.c. $2.00.d. $5.00.e. $10.00.

14. Given the information provided in question 12, the marginal revenue product of input A must have been:a. $1.00.b. $1.50.c. $2.00.d. $5.00.e. $10.00.

15. The firm from question 12 also uses input B, whose marginal product is 100 at the current usage level.The price of input B must be equal to:

a. $1.b. $2.c. $5.d. $100.e. $200.

16. Consider a monopoly. The price of one of its inputs, input A, is $10, and the marginal product of A is 5.The price of its output is $2. The firm has satisfied the least-cost rule for input employment. This firm is:

a. not producing its maximum-profit output and should contract production.b. not producing its maximum-profit output and should expand production.c. producing its maximum-profit output at least cost.

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d. producing its maximum-profit output but could reduce its costs by employing less of input A andmore of its other inputs.e. producing its maximum-profit output but could reduce its costs by employing more of input A andless of its other inputs.

17. Return to the data provided in question 15. If you were told that marginal revenue must be one of the fivefollowing dollar amounts, then you would know that marginal revenue must be equal to:

a. $1.b. $2.c. $3.d. $4.e. $5.

18. Now alter the information provided in question 15 in one respect only: assume that the firm operates in aperfectly competitive industry. Which alternative in question 16 would now be correct:

a. $1.b. $2.c. $3.d. $4.e. $5.

19. The least-cost rule for a firm making an optimal input employment decision using inputs A and B states:a. MPA / PA = MPB / PB.b. MPA ¥ PA = MPB ¥ PB.c. MUA / PA = MUB / PB.d. MRPA = MRPB.e. none of the above.

20. The market demand curve for labor in an economy is the:a. vertical summation of the individual firms’ marginal product curves.b. horizontal summation of the individual firms’ marginal revenue product curves.c. horizontal summation of the individual firms’ marginal cost curves.d. inverse of the marginal revenue curve.e. perfectly elastic demand curve at the market price.

21. Consider a simple, one-good economy with two factors of production—one of fixed supply and one ofvariable supply. If production in this economy were to display constant returns to scale, then:

a. each factor should earn a return based on average productivity.b. the returns to both factors sum to a total which exceeds total output.c. the sum of the factor shares equals total product.d. the area under the total product curve is total output.e. both factors should receive the same return.

22. According to John B. Clark’s theory of income distribution, if 10 units of a particular input wereemployed, then the price paid to each of those units should be equal to the value of:

a. the average of the marginal products of each of the 10 units.b. its own marginal product.c. the marginal product of the tenth unit.d. the average product of the 10 units.e. none of the above.

23. The marginal revenue product of an input is:a. the selling price of the last unit of output.b. the increment of total revenue resulting from the use of an additional unit of input.c. used in determining marginal product.d. none of the above.

24. If a unit of land costs $1 and a unit of labor costs $2 in the production of wheat, then the wheat producer isat a least cost position when the:a. marginal product of land is 2 times the marginal product of labor.b. quantity of land is 1/2 the quantity of labor.c. marginal product of labor is 2 times the product of land.d. impossible to tell unless the price of wheat is known.

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VII. PROBLEM SOLVING

The following problems are designed to help you apply the concepts that you learned in this chapter.

A. Income and Wealth1. a. Income is defined as the amount of money received from all sources during a given period of time (a

year, a month, etc.). In the spaces provided below, list the major sources of income in the United States(labor income, rent, dividends, interest, and transfer payments) in the order of their importance.

(1)(2)(3)(4)(5)

b. Wealth consists of the net dollar value of assets owned at any particular time. In the spaces providedbelow, list three major tangible assets and three major financial assets that comprise wealth in the UnitedStates in the order of their importance.Tangible assets:

(1)(2)(3)

Financial assets:(1)(2)(3)

B. Input Pricing by Marginal Productivity2. Suppose that good X is produced from three inputs, A, B, and C; a very small portion of the productionfunction is recorded in Table 12-2.

TABLE 12-2Employment Levels

Output A B C200 10 30 20203 10 31 20

a. We can infer from Table 12-2 that (the MP of X is 3 / the MP of A is 3 / the MP of B is 3 / the MPof C is 3).b. If the employment of some input such as B were gradually to increase, then we should expect that themarginal product of B would gradually (increase / decline) because of the (law of diminishing returns /relative scarcity of B that would result in the production process). Similarly, if the quantity of Bemployed were to decline, then we should expect that the marginal product of B would (increase / decline)because of the (law of diminishing returns / relative scarcity of B that would result in the productionprocess).c. If the employment of some input such as B were gradually to increase, with the employment of inputsA and C held constant, then we should expect to see the marginal products of A and C (increase /decrease) because of the (law of diminishing returns / relative scarcity of A and C that would resultin the production process). This exercise helps to illustrate the (independence / interdependence) ofinput productivities.

3. Suppose that a firm is satisfying the least-cost rule with respect to inputs A, B, and C and that it wants tofind out if it is at its maximum-profit output level. To do this, it can look at any one of its inputs—say, inputA. A’s price might be $4 per unit, for example, and its MP might be 3. Assume that the firm knows that themarginal revenue from the sale of X is $1.

a. Under these conditions, A’s MRP is ($1 / $2 / $3 / $4 / $7 / $12). Since it costs ($1 / $2 / $3 / $4 /$7 / $12) to buy that last unit of A, its employment (added $1 to / subtracted $1 from / did notchange) total profit. The firm, remember, is satisfying the least-cost rule in making its employmentdecisions. It follows, therefore, that the same conclusion would have been reached had we looked at inputB or input C. Hence, in the given circumstances, the firm (definitely is / definitely is not / may or may

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not be) earning maximum possible profit. In order for it to move toward higher profit, in fact, it should(reduce / increase) its output by (reducing / increasing) its employment of all inputs.b. Now try a different example to illustrate the point more fully. Suppose that the MPs of A, B, and Care, respectively 12, 8, and 2. Let their prices be, respectively, $6, $4, and $1. The firm (is / is not),therefore, producing its current output at minimum cost.c. Continue this second illustration by assuming that the marginal revenue from the sale of X is equal to$1. Input A’s MRP would therefore equal ($12 / $10 / $8 / $6 / $4 / $2). Input B’s MRP wouldmeanwhile equal ($12 / $10 / $8 / $6 / $4 / $2). The MRP for input C would be ($12 / $10 / $8 / $6 / $4/ $2). This firm (is / is not) producing the profit-maximizing output. To achieve this maximum, itshould (increase / decrease) its output by (increasing / decreasing) its employment of (input A only /input B only / input C only / all inputs simultaneously).d. As the firm makes these adjustments in employment, the marginal revenue products of all inputs (fall/ rise). The increase in the employment of each input should be halted when each MRP has (fallen below /reached equality with / risen above) the price of the (input / finished product).

4. Consult Table 12-3. The outputs of identical fields of corn are recorded there for a variety of levels ofemployment of labor. Let there be 10 workers in an economy defined by the two cornfields, and let the worlddetermine the price of corn at $2.

TABLE 12-3Marginal

Marginal RevenueLabor Corn Output Product Product

Employed (bu) of Labor of Labor0 0 n/a n/a1 10 ___ $___2 19 ___ ___3 27 ___ ___4 34 ___ ___5 40 ___ ___6 45 ___ ___7 49 ___ ___8 52 ___ ___9 54 ___ ___

10 55 ___ ___

a. Fill in the “Marginal Product” and “Marginal Revenue Product” columns of the table. The numbersthat you record there will be used to demonstrate that paying labor (the only input here) its marginalrevenue product will result in a level of output that maximizes the value of the corn crop in terms of theworld price.b. Suppose, initially, that seven workers toil in one field (field A) and three toil in the other (field B) .The output of field A would be ___ bushels worth $___; each worker, if paid his or her marginal revenueproduct, would receive $___. The output of field B would meanwhile be ___ bushels worth $___; eachworker there would receive $___ . In response to the wages that you computed, you should expect thatworkers would want to move (from A to B / from B to A).c. Suppose that the workers do indeed move so that four workers remain to work field A while six workfield B. Output of field A would fall to ___ bushels with a value of $___, and output of field B wouldclimb to ___ units worth $___ on the world market. The total value of output would climb from $___ to$___.d. To equalize the wages paid to workers in both fields so that there will be no incentive for workers towant to switch from one to the other, ___ workers would have to work each field. Were that the case, totaloutput would climb to ___ bushels worth $___ and each worker would earn $___. There (exists another /does not exist any other) distribution of workers that would increase the output of corn and thus increasethe value of the economy’s production on the world market.

5. You are once again a consultant on profit maximization. What would you recommend in each of the fivecases listed in Table 12-4?

In each case, the production of some good X depends only upon the employment of inputs A and B.Assume for each case that the marginal product of input A is constant and equal to 3 and that the marginalproduct of B is constant and equal to 9. The heading “MR from Sale of X” in Table 12-4 refers to marginal

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revenue at the current level of output and sales. Similarly, the headings “Price of A” and “Price of B” denotethe prices which the firm must pay for inputs A and B.

Indicate, for each case, whether or not the firm has achieved a position of maximum profit. Write “yes” or“no” in the column provided. Use the following numerical codes to indicate, in the last column, what is wrongwith the firm’s present position.

1 = Present position is the correct one.2 = For present output, employment of A is too high, employment of B too low.3 = For present output, employment of A is too low, employment of B too high.4 = Reduce output by employing less of both A and B.5 = Increase output by employing more of both A and B.

TABLE 12-4MR from At

Sale Price Price MaximumCase of X of A of B Profit? AnswerA $1 $2 $10 ___ ___B 2 6 18 ___ ___C 3 12 18 ___ ___D 4 9 18 ___ ___E 5 21 54 ___ ___

6. The market demand for any input is the (vertical / geometric / horizontal) sum of the individual demandschedules of all the firms interested in employing that input; i.e., the sum of their (marginal product /marginal revenue product / marginal utility) schedules.

More specifically, suppose that there are only three firms interested in employing input A, and that thesefirms sell their output, X, in a perfectly competitive market. (There should be more firms in a perfectlycompetitive market, but for the sake of illustration here we will keep things simple.) The firms’ productionfunctions are given in Table 12-5.

TABLE 12-5Total Total Total

Quantity of Product Product ProductInput A Firm 1 Firm 2 Firm 3

1 15 5 22 29 15 73 42 30 174 54 50 255 65 65 306 75 75 30

a. If the price of input A is $10, and the price of X is $1, what is the optimal quantity of input A foreach firm to hire?

Firm 1 = ___; Firm 2 = ___; Firm 3 = ___.b. If the price of input A rises to $15, and the price of X remains at $1, what is the optimal quantity ofinput A for each firm to hire?

Firm 1 = ___; Firm 2 = ___; Firm 3 = ___.c. Using this information, draw a market demand curve for input A in Figure 12-1.d. Suppose that the market supply of input A is fixed at 15 units. Draw the market supply curve inFigure 12-1. The equilibrium price in the market for input A is $___ and the quantity exchanged will be___.e. The market supply curve for input A is (perfectly elastic / perfectly inelastic). This means that

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Figure 12-1

VIII. DISCUSSION QUESTIONS

Answer the following questions, making sure that you can explain the work you did to arrive at the answers.

1. List and explain two factors that help to determine the distribution of income in an economy.2. Which factor of production receives the greatest portion of national income in the United States? Given thesmall number of people who control land, capital, and entrepreneurship, why might the government step in toredistribute this income? What methods might the government use?3. Explain in your own words how declining interest rates affect the incomes and wealth of (1) many older,retired people and (2) younger families with children. Who benefits from lower interest rates and who loses?4. Why do we say that there is a derived demand for factors of production?5. Consider the Happy Firm, which produces baseball caps using labor and capital. Presently, MPL / PL >MPC / PC. Carefully explain why this is not optimal for the firm. That is, why should the firm change itsmix of labor and capital?6. Reconsider Figure 12-7 from your textbook. Your authors explain that “it is the amount of wealth ratherthan the rate of return that makes the rectangle of the top wealthholders so large.” Use this idea to explain theadage, “Shirt sleeves to shirt sleeves in three generations.”

IX. ANSWERS TO STUDY GUIDEQUESTIONS

III. Review of Key Concepts8 Income distribution4 Income5 Wealth

11 Derived demand3 Transfer payments6 Personal income7 Marginal product9 Law of diminishing returns

10 Marginal revenue product1 Derived demand2 Least-cost rule

VI. Multiple Choice Questions1. E 2. B 3. A 4. A 5. C 6. B7. B 8. C 9. E 10. A 11. D 12. E

13. C 14. E 15. E 16. A 17. A 18. C

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19. A 20. B 21. C 22. C 23. B 24. C

VII. Problem Solvingl. a. (1) Labor income

(2) Transfer payments(3) Interest(4) Dividends(5) Rent

b. (1) Own home(2) Rental property(3) Motor vehicle(1) Interest-earning accounts(2) Equity in business(3) Stocks and mutual funds

2. a. the MP of B is 3b. decline, law of diminishing returns, increase, law of diminishing returnsc. increase, relative scarcity of A and C that would result in the production process, interdependence

3. a. $3, $4, subtracted $1 from, definitely is not, reduce, reducingb. isc. $12, $8, $2, is not, increase, increasing, all inputs simultaneouslyd. fall, reached equality with, input

4. a. See Table 12-3.

TABLE 12-3Labor Corn Mrp

Employed Output of Labor(bu)

0 0 n/a1 10 $202 19 183 27 164 34 145 40 126 45 107 49 88 52 69 54 4

10 55 2

b. 49, $98, $8, 27, $54, $16, from A to Bc. 34, $68, 45, $90, $152, $158d. 5, 80, $160, $12, does not exist any other

5. a. no, 3b. yes, 1c. no, 2d. no, 5e. no, 4

6. horizontal, marginal revenue producta. 6, 6, 3b. 1, 5, 0c. See Figure 12-1.d. See Figure 12- 1. $10, 15 workerse. perfectly inelastic. This means that workers still supply the same quantity of labor at any wage;workers will not respond to changes in the wage rate.

VIII. Discussion Questions1. Market supply and demand and government redistribution policies.

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2. Labor receives the greatest portion of national income. To redistribute income accruing to land, capital,and entrepreneurship, the government might place higher taxes on this income, to be used for governmentwelfare programs.3. Declining interest rates hurt many people who are elderly or retired by lowering income earned on savings.Declining interest rates help younger families with children by making borrowing (particularly mortgageborrowing for home purchases) less costly. Borrowers benefit from lower interest rates but savers suffer.4. We say there is a derived demand for factors of production because the demand for the factors is dependentupon the demand for the final product. Without a demand for the good that the factor is used to produce, therewould be no demand for the factor.5. This situation is not optimal for the firm because the last dollar spent on labor was more productive thanthe last dollar spent on capital. If the firm shifted some resources from capital to labor, total output wouldincrease without any increase in expenditure.6. This adage implies that it is difficult to move from the middle to the upper class. Because people in theupper class have more capital assets, and because they are willing to undertake more risky investment projects,they are able to build on their wealth much more quickly than someone in the middle class. Because people inthe middle class have a smaller pool of wealth to begin with, and because they invest more conservatively, theymay be unable to hurdle class boundaries.

Figure 12-1

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