Firm Choices in Input Markets

© 2002 Prentice Hall Business Publishing© 2002 Prentice Hall Business Publishing Principles of Economics, 6/ePrinciples of Economics, 6/e Karl Case, Ray FairKarl Case, Ray Fair

Firm Choices in Input MarketsFirm Choices in Input Markets


Demand for Inputs: A Derived DemandDemand for Inputs: A Derived Demand

• Derived demandDerived demand is demand for resources is demand for resources (inputs) that is dependent on the demand (inputs) that is dependent on the demand for the outputs those resources can be for the outputs those resources can be used to produce.used to produce.

• Inputs are demanded by a firm if, and only Inputs are demanded by a firm if, and only if, households demand the good or service if, households demand the good or service produced by that firm.produced by that firm.


Inputs: Complementary and SubstitutableInputs: Complementary and Substitutable

• The The productivity of an inputproductivity of an input is the is the amount of output produced per unit of that amount of output produced per unit of that input.input.

• Inputs can be Inputs can be complementarycomplementary or or substitutable.substitutable. This means that a firm’s This means that a firm’s input demands are tightly linked together.input demands are tightly linked together.


Diminishing ReturnsDiminishing Returns

• Faced with a capacity constraint in the Faced with a capacity constraint in the short-run, a firm that decides to increase short-run, a firm that decides to increase output will eventually encounter output will eventually encounter diminishing returns.diminishing returns.

• Marginal product of labor (MPMarginal product of labor (MPLL)) is the is the

additional output produced by one additional output produced by one additional unit of labor.additional unit of labor.


Marginal Revenue ProductMarginal Revenue Product

• The marginal revenue product (MRP)The marginal revenue product (MRP) of of a variable input is the additional revenue a a variable input is the additional revenue a firm earns by employing one additional unit firm earns by employing one additional unit of input, of input, ceteris paribusceteris paribus..

• MRPMRPLL equals the price of output, equals the price of output, PPXX, times , times

the marginal product of labor, the marginal product of labor, MPMPLL..


Marginal Revenue Product Per Hour of Marginal Revenue Product Per Hour of Labor in Sandwich Production (One Grill)Labor in Sandwich Production (One Grill)

(1)(1)TOTAL TOTAL

LABOR UNITS LABOR UNITS (EMPLOYEES)(EMPLOYEES)

(2)(2)TOTALTOTAL

PRODUCT PRODUCT (SANDWICHES (SANDWICHES

PER HOUR)PER HOUR)

(3)(3)MARGINAL MARGINAL

PRODUCT OF PRODUCT OF LABOR (LABOR (MPMPLL) )

(SANDWICHES (SANDWICHES PER HOUR)PER HOUR)

(4)(4)PRICE (PRICE (PPXX) )

(VALUE (VALUE ADDED PER ADDED PER SANDWICH)SANDWICH)aa

(5)(5)MARGINAL MARGINAL REVENUEREVENUE

PRODUCT (PRODUCT (MPMPLL X X PPXX))

(PER HOUR)(PER HOUR)

00 00

11 1010 1010 $$.50.50 $$ 5.005.00

22 2525 1515 .50.50 7.507.50

33 3535 1010 .50.50 5.005.00

44 4040 55 .50.50 2.502.50

55 4242 22 .50.50 1.001.00

66 4242 00 .50.50 00

aaThe “price” is essentially profit per sandwich; see discussion in text.The “price” is essentially profit per sandwich; see discussion in text.


Marginal Revenue Product Per Hour of Marginal Revenue Product Per Hour of Labor in Sandwich Production (One Grill)Labor in Sandwich Production (One Grill)

• When output price is When output price is constant, the behavior constant, the behavior of of MRPMRPLL depends only depends only

on the behavior of on the behavior of MPMPLL..

• Under diminishing Under diminishing returns, both returns, both MPMPLL and and

MRPMRPLL eventually eventually

decline.decline.

MRPL = PX MPL


A Firm Using One Variable Factor of A Firm Using One Variable Factor of Production: LaborProduction: Labor

• A competitive firm using only one variable A competitive firm using only one variable factor of production will use that factor as factor of production will use that factor as long as its marginal revenue product long as its marginal revenue product exceeds its unit cost.exceeds its unit cost.

• If the firm uses only labor, then it will hire If the firm uses only labor, then it will hire labor as long as labor as long as MRPMRPLL is greater than the is greater than the

going wage, going wage, W*.W*.


Marginal Revenue Product and Factor Demand for Marginal Revenue Product and Factor Demand for a Firm Using One Variable Input (Labor)a Firm Using One Variable Input (Labor)

• The hypothetical firm will demand 210 units of labor.The hypothetical firm will demand 210 units of labor.

W* =MRPL = 10


Short-Run Demand Curve for a Factor Short-Run Demand Curve for a Factor of Productionof Production

• When a firm uses only When a firm uses only one variable factor of one variable factor of production, that factor’s production, that factor’s marginal revenue product marginal revenue product curve is the firm’s curve is the firm’s demand curve for that demand curve for that factor in the short run.factor in the short run.


Comparing Marginal Revenue and Comparing Marginal Revenue and Marginal Cost to Maximize ProfitsMarginal Cost to Maximize Profits

• Assuming that labor is the only variable Assuming that labor is the only variable input, if society values a good more than it input, if society values a good more than it costs firms to hire the workers to produce costs firms to hire the workers to produce that good, the good will be produced.that good, the good will be produced.

• Firms weigh the value of outputs as Firms weigh the value of outputs as reflected in output price against the value reflected in output price against the value of inputs as reflected in marginal costs.of inputs as reflected in marginal costs.


The Two Profit-Maximizing ConditionsThe Two Profit-Maximizing Conditions

• The two profit-maximizing conditions are simply two The two profit-maximizing conditions are simply two views of the same choice process.views of the same choice process.


The Trade-Off Facing FirmsThe Trade-Off Facing Firms


A Firm Employing Two Variable A Firm Employing Two Variable Factors of ProductionFactors of Production

• Land, labor, and capital are used together Land, labor, and capital are used together to produce outputs.to produce outputs.

• When an expanding firm adds to its stock When an expanding firm adds to its stock of capital, it raises the productivity of its of capital, it raises the productivity of its labor, and vice versa. Each factor labor, and vice versa. Each factor complements the other.complements the other.


Substitution and Output Effects of a Substitution and Output Effects of a Change in Factor PriceChange in Factor Price

• Two effects occur when the price of an Two effects occur when the price of an input changes:input changes:

• Factor substitution effectFactor substitution effect: The tendency of firms to substitute away from a factor whose price has risen and toward a factor whose price has fallen.



• Two effects occur when the price of an Two effects occur when the price of an input changes:input changes:

• Output effect of a factor price effect of a factor price increase (decrease)increase (decrease): When a firm decreases (increases) its output in response to a factor price increase (decrease), this decreases (increases) its demand for all factors.



• When When PPLL = = PPKK = $1, the labor-intensive method of = $1, the labor-intensive method of

producing output is less costly.producing output is less costly.

TECHNOLOGYTECHNOLOGY

INPUT REQUIREMENTSINPUT REQUIREMENTSPER UNIT OF OUTPUTPER UNIT OF OUTPUT

UNIT COST IFUNIT COST IFPPLL = $1 = $1

PPKK = $1 = $1

((PPLL x x LL) + () + (PPKK x x KK))

UNIT COST IFUNIT COST IFPPLL = $2 = $2

PPKK = $1 = $1

((PPLL x x LL) + () + (PPKK x x KK))KK LL

AA (capital intensive) (capital intensive) 1010 55 $15$15 $20$20

BB (labor intensive) (labor intensive) 33 1010 $13$13 $23$23

Response of a Firm to an Increasing Wage RateResponse of a Firm to an Increasing Wage Rate



• When the price of labor rises, labor becomes more When the price of labor rises, labor becomes more expensive relative to capital. The firm substitutes capital expensive relative to capital. The firm substitutes capital for labor and switches from technique for labor and switches from technique BB to technique to technique AA..

TO PRODUCE 100 UNITS OF OUTPUTTO PRODUCE 100 UNITS OF OUTPUT

TOTALTOTALCAPITALCAPITAL

DEMANDEDDEMANDED

TOTALTOTALLABORLABOR

DEMANDEDDEMANDED

TOTALTOTALVARIABLEVARIABLE

COSTCOST

When When PPLL = $1, = $1, PPKK = $1, = $1,

firm uses technology firm uses technology BB300300 1,0001,000 $1,300$1,300

When When PPLL = $2, = $2, PPKK = $1, = $1,

firm uses technology firm uses technology AA1,0001,000 500500 $2,000$2,000

The Substitution Effect of an Increase in Wages on a Firm The Substitution Effect of an Increase in Wages on a Firm Producing 100 Units of OutputProducing 100 Units of Output


Many Labor MarketsMany Labor Markets

• If labor markets are competitive, the wages If labor markets are competitive, the wages in those markets are determined by the in those markets are determined by the interaction of supply and demand.interaction of supply and demand.

• Firms will hire workers only as long as the Firms will hire workers only as long as the value of their product exceeds the relevant value of their product exceeds the relevant market wage. This is true in all competitive market wage. This is true in all competitive labor markets.labor markets.


Land MarketsLand Markets

• Unlike labor and Unlike labor and capital, the total capital, the total supply of land is supply of land is strictly fixed (perfectly strictly fixed (perfectly inelastic.inelastic.


Demand Determined PriceDemand Determined Price

• The price of a good that is The price of a good that is in fixed supply is in fixed supply is demand demand determineddetermined..

• Because land is fixed in Because land is fixed in supply, its price is supply, its price is determined exclusively by determined exclusively by what households and firms what households and firms are willing to pay for it.are willing to pay for it.

• The return to any factor of production in fixed The return to any factor of production in fixed supply is called supply is called pure rentpure rent..


Land in a Given Use Versus Land of a Land in a Given Use Versus Land of a Given QualityGiven Quality

• The supply of land in a The supply of land in a given usegiven use may not be may not be perfectly inelastic or perfectly inelastic or fixed.fixed.

• The supply of land of a The supply of land of a given qualitygiven quality at a given at a given location is truly fixed in location is truly fixed in supply.supply.


Rent and the Value of OutputRent and the Value of OutputProduced on LandProduced on Land

• A firm will pay for and use land as long as A firm will pay for and use land as long as the revenue earned from selling the output the revenue earned from selling the output produced on that land is sufficient to cover produced on that land is sufficient to cover the price of the land.the price of the land.

• The firm will use land (The firm will use land (AA) up to the point at ) up to the point at which:which:

MRPA = PA


The Firm’s Profit-Maximization The Firm’s Profit-Maximization Condition in Input MarketsCondition in Input Markets

• Profit-maximizing condition for the Profit-maximizing condition for the perfectly competitive firm is:perfectly competitive firm is:

PPLL = MRP = MRPLL = ( = (MPMPLL X X PPXX))

PPKK = = MRPMRPKK = ( = (MPMPKK X X PPXX))

PPAA = = MRPMRPAA = ( = (MPMPAA X X PPXX))

where where LL is labor, is labor, KK is capital, is capital, AA is land (acres), is land (acres), XX is output, and is output, and PPXX is the price of that output. is the price of that output.


The Firm’s Profit-Maximization The Firm’s Profit-Maximization Condition in Input MarketsCondition in Input Markets

• Profit-maximizing condition for the perfectly Profit-maximizing condition for the perfectly competitive firm, written another way is:competitive firm, written another way is:

M P

P

M P

P

M P

P PL

L

K

K

A

A X

1

• In words, the marginal product of the last dollar spent on labor must be equal to the marginal product of the last dollar spent on capital, which must be equal to the marginal product of the last dollar spent on land, and so forth.


Input Demand CurvesInput Demand Curves

• If product demand increases, product price will If product demand increases, product price will rise and marginal revenue product will increase.rise and marginal revenue product will increase.


Input Demand CurvesInput Demand Curves

• If the productivity of labor increases, both If the productivity of labor increases, both marginal product and marginal revenue product marginal product and marginal revenue product will increase.will increase.


Impact of Capital Accumulation on Impact of Capital Accumulation on Factor DemandFactor Demand

• The production and use of capital enhances the The production and use of capital enhances the productivity of labor, and normally increases the productivity of labor, and normally increases the demand for labor and drives up wages.demand for labor and drives up wages.


Impact of Technological ChangeImpact of Technological Change

• Technological changeTechnological change refers to the refers to the introduction of new methods of production introduction of new methods of production or new products intended to increase the or new products intended to increase the productivity of existing inputs or to raise productivity of existing inputs or to raise marginal products.marginal products.

• Technological change can, and does, have Technological change can, and does, have a powerful influence on factor demands.a powerful influence on factor demands.

Firm Choices in Input Markets

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