Chapter 11 Input Markets and the Allocation of Resources

© 2005 Pearson Education Canada Inc.11.1

Chapter 11Chapter 11

Input Markets and the Input Markets and the Allocation of ResourcesAllocation of Resources


Perfectly Competitive Input MarketsPerfectly Competitive Input Markets

There are two types of input markets:There are two types of input markets:1.1. Primary inputPrimary input markets include resources markets include resources

that have not been processed by other that have not been processed by other firms, such as land, oil and labour.firms, such as land, oil and labour.

2.2. Intermediate inputIntermediate input markets are the markets are the processed output from other firms, such processed output from other firms, such as iron ingots, hog bellies and rolled as iron ingots, hog bellies and rolled steel.steel.


Assumptions of Perfectly Assumptions of Perfectly Competitive Input MarketsCompetitive Input Markets

1.1. Large NumbersLarge Numbers-There are a large number of input -There are a large number of input demanders/suppliers and no individual buys (sells) a demanders/suppliers and no individual buys (sells) a significant portion of total quantity traded.significant portion of total quantity traded.

2.2. Perfect Information-Perfect Information-Demanders/suppliers have Demanders/suppliers have perfect knowledge of prices and all firms have perfect perfect knowledge of prices and all firms have perfect information of production functions.information of production functions.

3.3. Input HomogeneityInput Homogeneity-In any input market, all units of -In any input market, all units of the input are identical.the input are identical.

4.4. Perfect Mobility of ResourcesPerfect Mobility of Resources-All inputs are -All inputs are perfectly mobile.perfectly mobile.


The Supply of Non-Labour InputsThe Supply of Non-Labour Inputs

Renewable resources, such as land, can Renewable resources, such as land, can be used over and over again.be used over and over again.

Non-Renewable resources, like oil, once Non-Renewable resources, like oil, once used it is gone.used it is gone.

In the analysis that follows, it is assumed In the analysis that follows, it is assumed that the supply of non-labour inputs is that the supply of non-labour inputs is perfectly price-elastic. perfectly price-elastic.


The Supply of LabourThe Supply of Labour An individual faces two constraints:An individual faces two constraints:1.1. The The time constraint saystime constraint says that total time that total time

available (T) equals work time (h) plus available (T) equals work time (h) plus leisure time (xleisure time (x11): h+x): h+x11=T =T

2.2. The The income constraintincome constraint says that a says that a person’s income (xperson’s income (x22) is the sum of work ) is the sum of work income (wage x h) and non-work income income (wage x h) and non-work income (A): X(A): X22=wh+A=wh+A


The Leisure-Income ConstraintThe Leisure-Income Constraint The leisure income constraint: The leisure income constraint:

wxwx11+x+x22=A+wT=A+wT The wage (w) is the price of leisure and The wage (w) is the price of leisure and

the slope of the budget constraint.the slope of the budget constraint. A+wT is full (all work) income. A+wT is full (all work) income. The utility maximizing bundle of The utility maximizing bundle of

leisure/labour is where the indifference leisure/labour is where the indifference curve is tangent to the leisure-income curve is tangent to the leisure-income constraint in Figure 11.1constraint in Figure 11.1


Figure 11.1 The demand for Figure 11.1 The demand for leisure and the supply of labourleisure and the supply of labour


Figure 11.2 Leisure as a normal goodFigure 11.2 Leisure as a normal good


Figure 11.3 Income and substitution Figure 11.3 Income and substitution effects for a wage changeeffects for a wage change


Response to a Change in Wage RateResponse to a Change in Wage Rate

When leisure is a normal good, the hours of When leisure is a normal good, the hours of work may increase or decrease in response to a work may increase or decrease in response to a wage increase depending upon whether the wage increase depending upon whether the income effect is greater than or less than the income effect is greater than or less than the income effect. income effect.

When leisure is an inferior good, an increase in When leisure is an inferior good, an increase in wage rate invariably leads to a decrease in wage rate invariably leads to a decrease in leisure hours and an increase in work hours leisure hours and an increase in work hours


Figure 11.4 (a & b) The demand for Figure 11.4 (a & b) The demand for leisure and the supply of labourleisure and the supply of labour


Firm’s Demand for One variable InputFirm’s Demand for One variable Input

The short-run demand function The short-run demand function relates to a scenario where only one relates to a scenario where only one input is variable.input is variable.


Input Demand in a One-Good EconomyInput Demand in a One-Good Economy

For any wage less than the maximum For any wage less than the maximum value of the average product, the value of the average product, the firm’s demand function is the firm’s demand function is the downward sloping portion of the downward sloping portion of the marginal product curve.marginal product curve.

For any wage rate greater than the For any wage rate greater than the maximum value of the average maximum value of the average product, the firm maximizes profits product, the firm maximizes profits by hiring no labour.by hiring no labour.


Figure 11.5 Input demand in a one-good economyFigure 11.5 Input demand in a one-good economy


Transforming the Product Curves Transforming the Product Curves into Revenue Curvesinto Revenue Curves

Marginal Revenue Product is the marginal Marginal Revenue Product is the marginal product from an addition unit of labour product from an addition unit of labour times the marginal revenue when the times the marginal revenue when the additional output is sold:additional output is sold:

MRP(z)=MR(y)MP(z)MRP(z)=MR(y)MP(z) Similarly, average revenue product Similarly, average revenue product

equals the price of the output times equals the price of the output times average product of the variable input:average product of the variable input:

ARP(z)=pAP(z) ARP(z)=pAP(z)


Figure 11.6 The firm’s demand forFigure 11.6 The firm’s demand forone variable inputone variable input


The Firm’s Demand Curve for One The Firm’s Demand Curve for One Variable InputVariable Input

For input prices less than the maximum values For input prices less than the maximum values of ARP, the firm’s demand function is the of ARP, the firm’s demand function is the downward-sloping portion of MRP.downward-sloping portion of MRP.

For input prices greater than the maximum For input prices greater than the maximum value of ARP, the firm will demand none of the value of ARP, the firm will demand none of the variable input.variable input.

Given an initial positive quantity of the input Given an initial positive quantity of the input demanded, an increase in the price of an input, demanded, an increase in the price of an input, will cause the firm to reduce the quantity will cause the firm to reduce the quantity demanded of that input.demanded of that input.


The Firm’s Demand Curve for One The Firm’s Demand Curve for One Variable InputVariable Input

The value of the marginal product (MRP) The value of the marginal product (MRP) of the variable input (VMPof the variable input (VMPzz) is output ) is output price time marginal product: price time marginal product: VMPz=pMP(z).VMPz=pMP(z).

For a perfect competitor VMP =MRP For a perfect competitor VMP =MRP (since p=MR).(since p=MR).

For a monopolisy MRP<VMP since MR<P.For a monopolisy MRP<VMP since MR<P.


Input Demand with Many Variable InputsInput Demand with Many Variable Inputs

In the long-run all inputs are variable.In the long-run all inputs are variable. In the long run, the firm’s response In the long run, the firm’s response

to an input-price change will via both to an input-price change will via both the substitution effect and the output the substitution effect and the output effect, produce a downward sloping effect, produce a downward sloping input demand curveinput demand curve


Figure 11.7 The substitution effect Figure 11.7 The substitution effect of an input price changeof an input price change


Figure 11.8 Comparing long-run and Figure 11.8 Comparing long-run and short-run input demand functionsshort-run input demand functions


Elasticity Rules for Derived DemandElasticity Rules for Derived Demand The response to an input price The response to an input price

change in both the short and long change in both the short and long run is to demand more (less) of an run is to demand more (less) of an input as its price fall (rises).input as its price fall (rises).

The response to a input price change The response to a input price change is greater in the long run than in the is greater in the long run than in the short run.short run.


Equilibrium in a Competitive MarketEquilibrium in a Competitive Market In the long run, a firm that is a perfect In the long run, a firm that is a perfect

competitor in both its output and input market competitor in both its output and input market will chose a input bundle such that for each will chose a input bundle such that for each input:input: wwe=MRP(ze=MRP(z)=pMP(z)=VMP(z))=pMP(z)=VMP(z)

In long-run equilibrium, a firm that is a perfect In long-run equilibrium, a firm that is a perfect competitor in its input markets but a competitor competitor in its input markets but a competitor in its output market, will choose an input in its output market, will choose an input bundle such that for each input: bundle such that for each input:

wwee=MRP(z)=MR(y)MP(z)<pMP(z)=VMP(z) =MRP(z)=MR(y)MP(z)<pMP(z)=VMP(z)


Figure 11.9 Equilibrium in a Figure 11.9 Equilibrium in a competitive input marketcompetitive input market


Monopsony in Input MarketsMonopsony in Input Markets A monopsonist has significant control A monopsonist has significant control

over what it pays for an input.over what it pays for an input. The relationship between input price The relationship between input price

(w) and quantity of the input (z) is (w) and quantity of the input (z) is determined by the market supply determined by the market supply function for the input: w=S(w).function for the input: w=S(w).


Monopsony in Input MarketsMonopsony in Input Markets The monopsonist buys all units of an The monopsonist buys all units of an

input at the same price (average input at the same price (average factor cost or AFC).factor cost or AFC).

Total factor cost (TFC) is quantity (z) Total factor cost (TFC) is quantity (z) times AFC or price S(z):times AFC or price S(z):

TFC(z)=zS(z)TFC(z)=zS(z)


Monopsony in Input MarketsMonopsony in Input Markets The marginal factor cost (MFC) is the rate The marginal factor cost (MFC) is the rate

at which TFC changes as the quantity of at which TFC changes as the quantity of output (z) changes.output (z) changes.

When a monopsonist buys a positive When a monopsonist buys a positive quantity of the input, the MFC exceeds quantity of the input, the MFC exceeds price (w) or average factor cost.price (w) or average factor cost.

The MFC=w+z(slope of supply curve):The MFC=w+z(slope of supply curve):


Figure 11.11 A monopsonist’s Figure 11.11 A monopsonist’s profit-maximizing decisionprofit-maximizing decision


Profit Maximizing Input DecisionsProfit Maximizing Input Decisions

The general profit-maximizing rule in an The general profit-maximizing rule in an input market is to buy an input up to the input market is to buy an input up to the point where marginal factor cost is equal point where marginal factor cost is equal to marginal revenue product.to marginal revenue product.

For a competitive input market:For a competitive input market:MRP(z*)=MFC(z*)=w*MRP(z*)=MFC(z*)=w*

For a monopsonist:For a monopsonist:MRP(z*)=MFC(z*)>w*MRP(z*)=MFC(z*)>w*


Figure 11.13 The inefficiency of monopsonyFigure 11.13 The inefficiency of monopsony


Figure 11.15 Resource allocation summarizedFigure 11.15 Resource allocation summarized


The Firm’s Demand for Capital InputsThe Firm’s Demand for Capital Inputs

Since capital is durable, the sum of present Since capital is durable, the sum of present values of MRP through time is:values of MRP through time is:ΣΣMRP=MRPMRP=MRP00++[MRP[MRP11/(1+i)]+…+[MRP/(1+i)]+…+[MRP11/(1+i/(1+i)D-1)D-1]]

The optimal quantity of capital input is the The optimal quantity of capital input is the quantity where the present value of the quantity where the present value of the marginal revenue products over its life is equal marginal revenue products over its life is equal to the present value of all costs of this input to the present value of all costs of this input (p= (p= ΣΣMRP).MRP).

The The ΣΣMRP is the firm’s demand curve for MRP is the firm’s demand curve for gadgets.gadgets.


Figure 11.16 The demand for a capital inputFigure 11.16 The demand for a capital input


Human Capital Decisions Over TimeHuman Capital Decisions Over Time

Human capital-investments in education Human capital-investments in education and training.and training.

Human capital production function:Human capital production function:R=F(H)R=F(H)

Which says additional income (return on Which says additional income (return on human capital investment) (R), is a human capital investment) (R), is a diminishing function of the quantity of diminishing function of the quantity of human capital (H).human capital (H).


Figure 11.17 Investing in human capitalFigure 11.17 Investing in human capital


From Figure 11.17 From Figure 11.17 Invest in an additional dollar of Invest in an additional dollar of

human capital if the marginal human capital if the marginal product (MP) exceeds the rate at product (MP) exceeds the rate at which current foregone consumption which current foregone consumption can generate future consumption can generate future consumption (1+i).(1+i).

To maximize the present value of net To maximize the present value of net income, invest in human capital up income, invest in human capital up to the point where MP=(1+i).to the point where MP=(1+i).


Figure 11.18 Another perspective on Figure 11.18 Another perspective on the human capital investmentthe human capital investment


Figure 11.19 The life-cycle choiceFigure 11.19 The life-cycle choice

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Chapter 11 Input Markets and the Allocation of Resources