CHAPTER 3

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CHAPTER 3. “The laborer is worth his hire.” -The Gospel of St. Luke. Introduction. Firms hire workers because consumers want to purchase goods and services produced by firms. Demand for workers is, thus, derived from the demands of consumers for goods and services.

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CHAPTER 3
• “The laborer is worth his hire.”
• -The Gospel of St. Luke
Introduction

Firms hire workers because consumers want to purchase goods and services produced by firms.

Demand for workers is, thus, derived from the demands of consumers for goods and services.

Central questions: how many workers are hired and how much are they paid?

The Production Function

q = f(E,K) ∆q/∆E > 0 ∆q/∆K > 0

Describes the technology that the firm uses to produce goods and services.

Output can be produced by a variety of input combinations.

The marginal product of labor is the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs.

The marginal product of capital is the change in output resulting from employing one additional unit of capital, holding constant the quantities of other inputs.

Total Product, Marginal Product, and Average Product Curves

The total product curve gives the relationship between output and the number of workers hired by the firm (holding capital fixed). The marginal product curve shows the output produced by each additional worker, and the average product curve shows output per worker.

Profit Maximization

Objective of the firm is to maximize profits.

Technology: q = f(E,K)

The profit equation is:

Π= pq – wE – rK

Total Revenue = pq

Total Costs = wE + rK

Perfectly competitive firms cannot influence the price of output or the prices of inputs (p, w and r are fixed to the firm).

Short-Run Hiring Decision

Value of the Marginal Product of Labor (VMPE) is the marginal physical product of labor times the marginal value of the output produced

VMPE indicates the benefit derived by the firm from hiring an additional worker, holding the amount of capital constant.

Value of the Average Product of Labor (VAPE) is the amount of output produced per worker.

The Demand for Labor in the Short-Run

A profit-maximizing firm hires the number of workers where the wage rate equals the value of the marginal product of labor. If the wage is \$22, the firm hires eight workers.

Short-Run Labor Demand Curve

The demand curve for labor indicates how many workers the firm would hire at each possible wage, holding the quantity of capital constant.

The short-run labor demand curve is downward sloping because, although the marginal product of labor is positive, hiring additional workers reduces the marginal product (Law of Diminishing Returns).

Because w = VMPE at every profit-maximizing amount of employment, the VMPE curve is coincident with the short-run demand curve for labor.

The Short-Run Demand Curve for Labor

A decrease in the wage rate from \$22 to \$18 increases the firm’s employment. An increase in the price of the output produced and sold by the firm shifts the value of the marginal product curve outward and increases employment.

Maximizing Profits:Two Rules

The profit-maximizing firm hires the amount of labor where the value of the marginal product of labor equals the added cost of hiring the extra labor (the wage rate).

The profit maximizing firm produces the amount of output where the cost of producing an additional unit of output (marginal cost) is equal to the revenue obtained from selling that extra output (marginal revenue).

The Algebra of Marginal Productivity Theory

The cost of producing an extra unit of output:

MC = w x (1 / MPE)

The perfectly competitive firm produces output where MC = MR = P

MC = P = w x (1 / MPE)

Critiques of MarginalProductivity Theory

A common criticism is that the theory bears little relation to the way that employers make hiring decisions.

Another criticism is that the assumptions of the theory are not very realistic.

However, employers act as if they know the implications of marginal productivity theory (hence, they try to make profits and remain in business).

The Short-Run Demand Curvefor the Industry

Wage

Wage

T

D

20

20

10

10

D

T

28

Employment

56

15

30

60

30

Employment

Firm

Industry

The Firm’s Output Decision

A profit-maximizing firm produces output where price equals the marginal cost of production.

Labor Demand in the Long Run

In the long run, the firm maximizes profits by choosing how many workers to hire AND how much capital (land, buildings, and equipment ) to use.

An isoquant describe all of the possible combinations of labor and capital that are capable of producing a given level of output.

Isoquant Curves

Capital

X

K

Y

q1

q0

Labor

E

All capital-labor combinations that lie on a single isoquant produce the same level of output. The input combinations at points X and Y produce q0 units of output. Combinations of labor and capital that lie on higher isoquantsproduce more output.

The isocost line indicates all labor–capital combinations that represent a specified amount of total expenditure

Isocost lines indicate equally costly combinations of capital and labor.

Higher isocost lines indicate higher total expenditure on labor and capital

Isocost Lines

Isocost Lines

All capital-labor combinations that lie on a single isocost curve are equally costly. Capital-labor combinations that lie on a higher isocost curve are more costly. The slope of an isoquant equals the (negative of) the ratio of input prices (-w/r).

Capital

C1/r

Isocost with Cost Outlay C1

C0/r

Isocost with Cost Outlay C0

Labor

C0/w

C1/w

The Cost-MinimizingCombination of Inputs

Capital

C1/r

A

C0/r

P

175

B

q0

Labor

100

A firm minimizes the cost of producing q0 units of output by using the capital-labor combination at P, where the isoquantfor q0 is tangent to the isocost line. All other capital-labor combinations (such as A and B) lie on a higher isocost line.

Cost Minimization

Profit maximization implies cost minimization.

The firm chooses the least-cost combination of capital and labor.

This least-cost combination is where the isocost line is tangent to the isoquant.

The marginal rate of substitution equals the ratio of input prices, w/r, at the least-cost combination

Long-Run Demand for Labor

When the wage rate decreases, two effects arise:

The firm responds to the lower price of labor by expanding production (the scale effect)

The firm takes responds to the wage decrease by rearranging its mix of inputs, employing more labor and less capital, holding output constant (the substitution effect)

The Impact of a Wage ReductionHolding Expenditure Constant

Capital

C0/r

R

P

75

q0

Wage is w1

Wage is w0

L

25

40

A wage reduction flattens the isocost curve. If the firm were to hold the initial cost outlay constant at C0 dollars, the isocost would rotate around C0 and the firm would move from point P to point R. A profit-maximizing firm, however, will not generally want to hold the cost outlay constant when the wage changes.

q0

Dollars

Capital

MC0

MC1

R

p

P

150

100

Labor

100

150

Output

25

50

The Output and Employment Effects of a Wage Decrease

• A wage-rate decrease reduces the marginal cost of production, and induces the firm to expand output (from 100 to 150 units).
• The firm’s optimal combination of capital and labor changes from point P to point R, indicating an increase in the number of workers hired from 25 to 50.
Substitution and Scale Effects

Capital

D

C1/r

Q

C0/r

R

P

200

D

100

Wage is w1

Wage is w0

50

40

25

Labor

A wage-rate decrease generates both a substitution effect and a scale effect. The scale effect (from P to Q) increases the firm’s employment. The substitution effect (from Q to R) induces the firm to use a more labor-intensive method of production, further increasing employment

Two Special Isoquants

Capital and labor are perfect substitutes if the isoquant is linear (so that two workers are identical in production to one machine). Capital and labor are perfect complements if the isoquant is right-angled, in which case the two inputs are always used in fixed proportions to minimize the cost of producing a given amount of output.

Elasticity of Substitution

The elasticity of substitution () is the percentage change in the ratio of capital to labor (K/L) associated with a one-percentage-point change in the ratio of the price of labor to the price of capital (w/r).

 = %∆(K/L)  %∆(w/r)

0 <  < + ∞

Elasticity of Substitution

Example:

If the elasticity of substitution is 1/2, then a 10% increase in the ratio of the price of labor to the price of capital would result in an increase in the capital-to-labor ratio of 5%.

Long Run Demand Curve for Labor

Dollars

w0

w1

DLR

25

50

Labor

The long-run demand curve for labor gives the firm’s profit-maximizing level of employment at a given wage

The Short- and Long-Run DemandCurves for Labor

Dollars

Short-Run Demand Curve

Long-Run Demand Curve

Labor

In the long run, the firm can optimally adjust both the amount of capital and the amount of labor induced by a change in the wage. As a result, the long-run demand curve is more elastic than the short-run demand curve.

Application

Affirmative action and production costs:

A firm is “color blind” if race does not enter the hiring decision.

Discrimination shifts the hiring decision away from the cost minimization tangency point on the isoquant.

Affirmative Action

Black Labor

Q

P

q*

White Labor

The discriminatory firm chooses the input mix at point P, ignoring the cost-minimizing rule that the isoquant be tangent to the isocost line. An affirmative action program can force the firm to move to point Q, resulting in more efficient production and lower costs.

Black Labor

Q

P

q*

White Labor

Affirmative Action

A color-blind firm is at point P, employing relatively more whites because of the shape of the isoquants. An affirmative action program will increase this firm’s costs if it must further increase its quantity of black labor.

Hicks-Marshall Rules of Derived Demand

Labor demand is more elastic the larger is:

The elasticity of substitution between capital and labor

The elasticity of demand for the firm’s output

Labor’s share in total costs of production

The elasticity of supply of other factors of production, such as capital

Input Demands With Many Inputs

Labor and capital can be separated into many “types”:

Skilled and unskilled labor

Native-born and immigrant workers

Equipment and structures

Cross-price elasticity of demand.

i,j = %∆xi%∆wj

If the cross-elasticity is positive (negative), then inputs i and j are substitutes (complements) in production.

The Demand Curve for a Factor of Production is Affected by the Prices of Other Inputs

Price of input i

Price of input i

D0

D1

D0

D1

Employment of inputi

Employment of input i

(a)

(b)

The labor demand curve for inputishifts when the price of another input changes. (a) If the price of a substitute input rises, the demand curve for input i shifts up. (b) If the price of a complement rises, the demand curve for input i shifts down.

Labor Market Equilibrium

Dollars

Supply

whigh

w*

wlow

Demand

ED

ES

E*

Employment

In a competitive labor market, equilibrium is attained at the point where supply equals demand. The market-clearing wage is w* at which E* workers are employed.

The Effects of a Minimum Wage

Employment is lower and unemployment is higher

the higher is the minimum wage

the more elastic are the labor supply and demand curves.

The benefits of an increase in the minimum wage accrue mostly to workers who are not poor

The Impact of a Minimum Wage on Employment

Dollars

S

w

w*

D

Labor

E

E*

ES

A minimum wage set at w results in employers cutting employment from E* to E. The higher wage also encourages ES – E* workers to enter the market. Thus, under a minimum wage, ES – E– workers are unemployed.

Dollars

Dollars

(If workers migrate to covered sector)

SU

SC

SU

w

SU

(If workers migrate to uncovered sector)

w*

w*

DU

DC

Employment

Employment

E

EC

EU

EU

EU

(b) Uncovered Sector

(a)Covered Sector

If the minimum wage applies only to jobs in the covered sector, the displaced workers might move to the uncovered sector, shifting the supply curve to the right and reducing the uncovered sector’s wage. If it is easy to get a minimum wage job, workers in the uncovered sector might quit their jobs and wait in the covered sector until a job opens up, shifting the supply curve in the uncovered sector to the left and raising the uncovered sector’s wage.

Changing employment quickly is costly, and these costs increase at an increasing rate. If government policies prevent firms from firing workers, the costs of trimming the workforce will rise even faster than the costs of expanding the firm.

Slow Transition to a New Labor Equilibrium

Employment

150

B

A

100

C

50

Time

Variable adjustment costs encourage the firm to adjust the employment level slowly. The expansion from 100 to 150 workers might occur more rapidly than the contraction from 100 to 50 workers if government policies “tax” firms that cut employment.

Estimating Labor Demand

One can identify the slope of the labor demand curve, which can be used to calculate the elasticity of labor demand, when the supply curve shifts.

Problem: Must make sure the labor demand curve is not also changing.

Problems with Estimating Labor Demand

S0

Dollars

S1

Z

P

w0

R

w2

Z

Q

w1

D1

D0

E1

E0

E2

Employment