Eaton Micro 6e Ch11

7/27/2019 Eaton Micro 6e Ch11

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2005 Pearson Education Canada Inc.11.1

Chapter 11

Input Markets and the

Allocation of Resources


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Perfectly Competitive Input Markets

There are two types of input markets:

1. Primary inputmarkets include resourcesthat have not been processed by otherfirms, such as land, oil and labour.

2. Intermediate inputmarkets are theprocessed output from other firms, suchas iron ingots, hog bellies and rolledsteel.


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The Supply of Non-Labour Inputs

Renewable resources, such as land, can

be used over and over again.

Non-Renewable resources, like oil, onceused it is gone.

In the analysis that follows, it is assumed

that the supply of non-labour inputs is

perfectly price-elastic.


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The Supply of Labour

An individual faces two constraints:

1. The time constraint says that totaltime available (T) equals work time(h) plus leisure time (x1): h+x1=T

2. The income constraintsays that apersons income (x

2

) is the sum ofwork income (wage x h) and non-workincome (A): X2=wh+A


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The Leisure-Income Constraint

The leisure income constraint:wx1+x2=A+wT

The wage (w) is the price of leisure and

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

The utility maximizing bundle of

leisure/labour is where the indifferencecurve is tangent to the leisure-incomeconstraint in Figure 11.1


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Figure 11.1 The demand for

leisure and the supply of labour


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Figure 11.2 Leisure as a normal good


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Figure 11.3 Income and substitution

effects for a wage change


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Response to a Change in Wage Rate

When leisure is a normal good, the hours ofwork may increase or decrease in response to awage increase depending upon whether the

income effect is greater than or less than theincome effect.

When leisure is an inferior good, an increase inwage rate invariably leads to a decrease in

leisure hours and an increase in work hours


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Figure 11.4 (a & b) The demand for

leisure and the supply of labour


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Firms Demand for One variable Input

The short-run demand functionrelates to a scenario where only oneinput is variable.


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Input Demand in a One-Good Economy

For any wage less than themaximum value of the averageproduct, the firms demand function

is the downward sloping portion ofthe marginal product curve.

For any wage rate greater than themaximum value of the averageproduct, the firm maximizes profitsby hiring no labour.


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Figure 11.5 Input demand in a one-good economy


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Transforming the Product Curves

into Revenue Curves

Marginal Revenue Product is the marginalproduct from an addition unit of labourtimes the marginal revenue when the

additional output is sold:MRP(z)=MR(y)MP(z)

Similarly, average revenue productequals the price of the output timesaverage product of the variable input:

ARP(z)=pAP(z)


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Figure 11.6 The firms demand for

one variable input


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The Firms Demand Curve for One

Variable Input

The value of the marginal product (MRP)of the variable input (VMPz) is outputprice time marginal product:

VMPz=pMP(z).For a perfect competitor VMP =MRP

(since p=MR).

For a monopolisy MRP


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Input Demand with Many Variable Inputs

In the long-run all inputs arevariable.

In the long run, the firms responseto an input-price change will via boththe substitution effect and the outputeffect, produce a downward sloping

input demand curve


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Figure 11.7 The substitution effect

of an input price change


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Figure 11.8 Comparing long-run and

short-run input demand functions


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Elasticity Rules for Derived Demand

The response to an input pricechange in both the short and longrun is to demand more (less) of an

input as its price fall (rises).

The response to a input price changeis greater in the long run than in the

short run.


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Equilibrium in a Competitive Market

In the long run, a firm that is a perfectcompetitor in both its output and input marketwill chose a input bundle such that for eachinput:

we=MRP(z)=pMP(z)=VMP(z)

In long-run equilibrium, a firm that is a perfectcompetitor in its input markets but a

competitor in its output market, will choose aninput bundle such that for each input:

we=MRP(z)=MR(y)MP(z)


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Figure 11.9 Equilibrium in a

competitive input market


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Monopsony in Input Markets

A monopsonist has significant controlover what it pays for an input.

The relationship between input price(w) and quantity of the input (z) isdetermined by the market supplyfunction for the input: w=S(w).


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The monopsonist buys all units of aninput at the same price (averagefactor cost or AFC).

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

TFC(z)=zS(z)


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The marginal factor cost (MFC) is the rateat which TFC changes as the quantity ofoutput (z) changes.

When a monopsonist buys a positivequantity of the input, the MFC exceedsprice (w) or average factor cost.

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


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Figure 11.11 A monopsonists

profit-maximizing decision


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Profit Maximizing Input Decisions

The general profit-maximizing rule in aninput market is to buy an input up to thepoint where marginal factor cost is equal

to marginal revenue product.

For a competitive input market:

MRP(z*)=MFC(z*)=w*

For a monopsonist:

MRP(z*)=MFC(z*)>w*


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Figure 11.13 The inefficiency of monopsony


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Figure 11.15 Resource allocation summarized


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The Firms Demand for Capital Inputs

Since capital is durable, the sum of presentvalues of MRP through time is:

MRP=MRP0+[MRP1/(1+i)]++[MRP1/(1+i)D-1]

The optimal quantity of capital input is thequantity where the present value of themarginal revenue products over its life is equalto the present value of all costs of this input

(p= MRP). The MRP is the firms demand curve for

gadgets.


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Figure 11.16 The demand for a capital input


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Human Capital Decisions Over Time

Human capital-investments in educationand training.

Human capital production function:

R=F(H)Which says additional income (return on

human capital investment) (R), is a

diminishing function of the quantity ofhuman capital (H).


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Figure 11.17 Investing in human capital


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From Figure 11.17

Invest in an additional dollar ofhuman capital if the marginalproduct (MP) exceeds the rate at

which current foregone consumptioncan generate future consumption(1+i).

To maximize the present value of netincome, invest in human capital upto the point where MP=(1+i).


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Figure 11.18 Another perspective on

the human capital investment


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2005 Pearson Education Canada Inc11 38

Figure 11.19 The life-cycle choice

Eaton Micro 6e Ch11

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