2. Labor Economics, 4th edition
Chapter 4
Labor Demand
Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin
Labor Economics, 4th edition

3. Introduction
Firms hire workers because consumers want to purchase a variety of goods and services
Demand for workers is derived from the wants and desires of consumers
Central questions: how many workers are hired and what are they paid?

4. The Firm’s Production Function
Describes the technology that the firm uses to produce goods and services
The firm’s output is produced by any combination of capital and labor
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 hiring one additional unit of capital, holding constant the quantities of other inputs

5. More on the Production Function
Marginal products of labor and capital are positive, so as more units of each are hired, output increases
When firms hire more workers, total product rises
The slope of the total product curve is the marginal product of labor
Law of Diminishing Returns: eventually, the marginal product of labor declines
Average Product: the amount of output produced by the typical worker

6. The Total Product, the Marginal Product, and the 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 gives the output produced by each additional worker, and the average product curve gives the output per worker.

7. Profit Maximization Objective of the firm is to maximize profits
The profit function is:
Profits = pq – wE – rK
Total Revenue = pq
Total Costs = (wE + rk)
Perfectly competitive firm cannot influence prices of output or inputs

8. Short Run Hiring Decision
Value of Marginal Product (VMP) is the marginal product of labor times the dollar value of the output
This indicates the benefit derived from hiring an additional worker, holding capital constant
Value of Average Product is the dollar value of output per worker

9. The Firm's Hiring Decision in the Short-Run
VMPE
VAPE
Number of Workers
A profit-maximizing firm hires workers up to the point where the wage rate equals the value of marginal product of labor. If the wage is $22, the firm hires eight workers.

10. Labor Demand Curve
The demand curve for labor indicates how the firm reacts to wage changes, holding capital constant
The curve is downward sloping
This reflects the fact that additional workers are costly and alter average production due to the Law of Diminishing Returns

11. The Short-Run Demand Curve for Labor
Because marginal product eventually declines, the short-run demand curve for labor is downward sloping. A drop in the wage from $22 to $18 increases the firm’s employment. An increase in the price of the output shifts the value of marginal product curve upward, and increases employment.
VMPE
VMPE
Number of Workers

12. Maximizing Profits: a general rule
The profit maximizing firm should produce up to the point where the cost of producing an additional unit of output (marginal cost) is equal to the revenue obtained from selling that output (marginal revenue)
Marginal Productivity Condition: this is the hiring rule, hire labor up to the point when the added value of marginal product equals the added cost of hiring the worker (i.e., the wage)

13. The Mathematics of Marginal Productivity Theory
The cost of producing an extra unit of output:
MC = w x 1/MPe
The condition: produce to the point when MC = P (for the competitive firm, P = MR)
W x 1/MPe = P

14. Critique of Marginal Productivity 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)

15. The Short-Run Demand Curve for the Industry20 10 30 15
Wage
Employment 28 60 D 56 T

16. The Firm's Output Decision
A profit-maximizing firm produces up to the point where the output price equals the marginal cost of production. This profit-maximizing condition is the same as the one requiring firms to hire workers up to the point where the wage equals the value of marginal product.

17. The Employment Decision in the Long Run
In the long run, the firm maximizes profits by choosing how many workers to hire AND how much plant and equipment to invest in
Isoquant: describes the possible combinations of labor and capital that produce the same level of output (the curve “ISOlates the QUANTity of output). Isoquants…
Must be downward sloping
Cannot intercept
That are higher indicate more output
Are convex to the origin
Have a slope that is the negative of the ratio of the marginal products of capital and labor

18. Isocost
The Isocost line indicates the possible combinations of labor and capital the firm can hire given a specified budget
Isocost indicates equally costly combinations of inputs
Higher isocost lines indicate higher costs

19. Isoquant Curves
Capital
Employment q1 q0 X K E Y
All capital-labor combinations that lie along a single isoquant produce the same level of output. The input combinations at points X and Y produce q0 units of output. Input combinations that lie on higher isoquants produce more output.

20. Isocost Lines
Capital
C1/r
Isocost with Cost Outlay C1
C0/r
Isocost with Cost Outlay C0
Employment
C0/w
C1/w
All capital-labor combinations that lie along 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 ratio of input prices (-w/r).

21. The Firm's Optimal Combination of Inputs
Capital
Employment q0 B P A
175
100
C1/r
C0/r
A firm minimizes the costs of producing q0 units of output by using the capital-labor combination at point P, where the isoquant is tangent to the isocost. All other capital-labor combinations (such as those given by points A and B) lie on a higher isocost curve.

22. Cost Minimization Profit maximization implies cost minimization
The firm chooses a least cost combination of capital and labor
This least cost choice is where the isocost line is tangent to the isoquant
Marginal rate of substitution equals the price ratio of capital to labor

23. Long Run Demand for Labor
If the wage rate drops, two effects take place
Firm takes advantage of the lower price of labor by expanding production (scale effect)
Firm takes advantage of the wage change by rearranging its mix of inputs (while holding output constant; substitution effect)

24. The Impact of A Wage Reduction, Holding Constant Initial Cost Outlay at C0
Capital 40 25 75 q0  R P
C0/r
Wage is w1
Wage is w0
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

25. The Impact of a Wage Reduction on the Output and Employment of a Profit-Maximizing Firm
150
100
MC1
MC0 p
Dollars
Output 50 25 R P
Capital
Employment
A wage cut reduces the marginal cost of production and encourages the firm to expand (from producing 100 to 150 units).
The firm moves from point P to point R, increasing the number of workers hired from 25 to 50.

26. Long Run Demand Curve for Laborw1 w0 50 25
Dollars
Employment
DLR
The long-run demand curve for labor gives the firm’s employment at a given wage and is downward sloping.

27. Substitution and Scale Effects
100
200 D R P Q 50 25 40
Capital
Employment
Wage is w1
Wage is w0
C0/r
C1/r
A wage cut generates substitution and scale effects. The scale effect (the move from point P to point Q) encourages the firm to expand, increasing the firm’s employment. The substitution effect (from Q to R) encourages the firm to use a more labor-intensive method of production, further increasing employment.

28. Elasticity of Substitution
When two inputs can be substituted at a constant rate, the two inputs are called perfect substitutes
When an isoquant is right-angled, the inputs are perfect complements
The substitution effect is large when the two inputs are perfect substitutes
There is no substitution effect when the inputs are perfect complements (since both inputs are required for production)
The curvature of the isoquant measures elasticity of substitution

29. Isoquants
Capital and labor are perfect substitutes if the isoquant is linear (so that two workers can always be substituted for one machine). The two inputs are perfect complements if the isoquant is right-angled. The firm then gets the same output when it hires 5 machines and 20 workers as when it hires 5 machines and 25 workers.

30. Elasticity Measurement
Intuitively, elasticity of substitution is the percentage change in capital to labor (a ratio) given a percentage change in the price ratio (wages to real interest)
%∆K/L%∆w/r
This is the percentage change in the capital:labor ratio given a 1% change in the relative price of the inputs

31. The Short- and Long-Run Demand Curves for Labor
Dollars
Short-Run Demand Curve
Long-Run Demand Curve
Employment
In the long run, the firm can take full advantage of the economic opportunities introduced by a change in the wage. As a result, the long-run demand curve is more elastic than the short-run demand curve.

32. Isoquants when Inputs are either Perfect Substitutes or Perfect Complements

33. Application Affirmative action and production costs
A firm is “color blind” if race does not enter the hiring decision at all
Discrimination shifts the hiring decision away from the cost minimization tangency point on the isoquant

34. Affirmative Action q* P Q
Black Labor
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. An affirmative action program can force the firm to move to point Q, resulting in more efficient production and lower costs.

35. Affirmative Action q* Q P
Black Labor
White Labor
A color-blind firm is at point P, hiring relatively more whites because of the shape of the isoquants. An affirmative action program increases this firm’s costs.

36. Marshall’s Rules Labor Demand is more elastic when:
Elasticity of substitution is greater
Elasticity of demand for the firm’s output is greater
The greater labor’s share in total costs of production
The greater the supply elasticity of other factors of production (such as capital)

37. Factor Demand with Many Inputs
There are many different inputs
Skilled and unskilled labor
Old and young
Old and new machines
Cross-elasticity of factor demand
%∆Di%∆wj
If cross-elasticity is positive, the two inputs are said to be substitutes in production

38. The Demand Curve for a Factor of Production is Affected by the Prices of Other Inputs
Price of input i
Employment of input i D0 D1
(a)
(b)
The labor demand curve for input i shifts when the price of another input changes. (a) If the price of a substitutable 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.

39. Labor Market Equilibrium
Dollars
Supply
whigh w* ES ED E*
wlow
Demand
Employment
In a competitive labor market, equilibrium is attained at the point where supply equals demand. The “going wage” is w* and E* workers are employed.

40. Application: The Employment Effects of Minimum Wages
The unemployment rate is higher the higher the minimum wage and the more elasticity the supply and demand curves
The benefits of the minimum wage accrue mostly to workers who are not at the bottom of the distribution of permanent income

41. Minimum Wages in the United States, 1938-2005
Source: U.S. Bureau of the Census, Statistical Abstract of the United States. Washington, DC, Government Printing Office, various issues; U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1970, Washington, DC, 1975; and U.S. Bureau of Labor Statistics, Employment and Earnings, Washington, DC, Government Printing Office, January 2006.

42. The Impact of the Minimum Wage on Employment
Dollars S D
Employment w* w ES E* E
A minimum wage set at w forces employers to cut employment (from E* to E). The higher wage also encourages (ES - E*) additional workers to enter the market. The minimum wage, therefore, creates unemployment.

43. The Impact of Minimum Wages on the Covered and Uncovered SectorsSU
Dollars SC
Employment EU EC
(b) Uncovered Sector E w w* DU DC
(If workers migrate to covered sector)
(If workers migrate to 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.

44. Adjustment Costs and Labor Demand
The expenditures that firms incur as they adjust the size of their workforce are called adjustment costs
Variable adjustment costs are associated with the number of workers the firm will hire and fire
Fixed adjustment costs do not depend on how many workers the firm is going to hire and fire

45. Asymmetric Variable Adjustment Costs
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.

46. Slow Transition to a New Labor Equilibrium
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.
Employment B
150 A
100 C 50
Time

47. Shifts in Labor Supply and Labor Demand Curves Generate the Observed Data on Wages and Employment
Dollars S0 w0 E1 E0 D0
Employment w1 S1 D1 w2 E2 Z P Q R

48. The Impact of Wartime Mobilization of Men on Female Labor Supply

49. The Impact of Wartime Mobilization of Men on Female Wages

50. End of Chapter 4