1. Chapter 4. Labor Demand Elasticities
Chapter 3: Is the demand for labor a downward-sloping function of the wage rate? (DIRECTION)
Ex) If the government raises the minimum wage level, will the amount of job opportunities be reduced?
Chapter 4: How responsive labor demand is to changes in the wage rate (cost of labor).
Ex) If the government raises the minimum wage level, how many job opportunities will be lost?  (MAGNITUDE)

2. Case A. Relatively Small Impact on Employment and Unemployment
Demand curve is relatively steep.

3. Case B. Relatively Large Impact on Employment and Unemployment
Demand curve is relatively flat.

4. Own-Wage Elasticity of Demand
Definition of the own-wage elasticity of demand for a category of labor (i)
 ii = % Ei/% Wi
i = skilled labor, unskilled labor, teenage labor, …
 ii <0 always. Ex) ii = -1.5
 The larger its absolute value, the larger will be the percentage decline in employment associated with any given percentage increase in wages.
If the absolute value of ii >, =, < 1, then the labor demand curve is said to be elastic, unitary elastic, or inelastic.
Different Elasticities along a Demand Curve
 See <Figure 4.2>

5. D1 is generally more elastic than D2

6. Hicks-Marshall Laws of Derived Demand
Other things equal, ii is high under the following conditions:
1) When the price elasticity of demand for the product being produced is high;
2) When other factors of production can be easily substituted for the category of labor;
3) When the supply of other factors of production is highly elastic;
4) When the cost of employing the category of labor is a large share of the total costs of production.

7. Chain of Events Revisited

8. More on Each Law
Law 1) demand for the final product (related with scale effect)
Implications
The demand curve for labor for the individual firm will be more elastic, other things equal, the more competitive the product market in which it operates.
The demand curve for an entire industry should be less elastic than the labor demand curve for any one individual firm in the industry.

9. Law 4) The share of labor in total cost (related with scale effect)
The impact of a rise in wages on production costs depends on how high labor costs are relative to other costs of production.

10. Law 2) Substitutability of other factors (related with substitution effect)
 Substitution possibilities are limited not only by technological constraints but also institutional rules.
- Example: Union shop
 However, substitution possibilities that are not feasible in the short run may well become feasible over longer periods of time.
- The firm can build new plants in less unionized states or states with “right-to-work” laws; 22 States
- These adjustments would occur only in the long run, which is another reason why the demand for labor is more elastic in the long run than in the short run.

12. Law 3) The elasticity of supply of other inputs (related with substitution effects)
The extent of the increase in the price of capital depends on the elasticity of its supply curve.

13.  Empirical evidence <Table 4.1>
 Estimated long run labor demand elasticity is close to –1.
 to which short run scale effect (holding production technology constant) and substitution effects (holding output constant) contribute approximately equally.

14. Mathematical Discussion
Assumptions & Definitions
- Competitive output and input markets
- Constant returns to scale production
- Own-wage elasticity of labor demand
Price elasticity of demand for the product
Elasticity of substitution between K and L

15. - Labor cost as a share of total cost
Want to derive
The more elastic is product demand, the larger (in absolute value) is the scale effect.
The larger is labor’s share of costs, the larger (in absolute value) is the scale effect.
The easier is the substitution between K and Li, the larger (in absolute value) is the substitution effect.
The larger is labor’s share of costs, the smaller (in absolute value) is the substitution effect.

16. Demand for labor
- Once we know Q and W/C, we know L
Then, the following equations hold.
scale effect + substitution effect
So, the elasticity of demand for labor in response to a wage change = scale + substitution

17. Scale Effect
,because, with constant returns to scale, the least-cost way of increasing Q by some proportion is to increase both L and K by that same proportion.
; the definition of elasticity.
,because the profit-maximizing competitive firm choose Q to equate P and MC.

18. , because, with CRS, MC=AC.
, because each one percent increase in W increases costs by (the labor’s share of costs) of a percent.

19. Substitution effect
, because C is not changed. Alternatively,
(**)
As we are interested in dlnL, not dlnK, we need to “solve it out”
As the firm is minimizing cost initially,
Dividing both sides by K, we have
(***)

20. Plug (***) into (**)
;substitution effect
Finally, we have
So, increases in only when ?

21. The cross-wage elasticity of demand
Percentage change in the demand for input h induced by a 1 percent change in the price of input k.
hk = % Dh/% Pk
The signs of cross-elasticities are determined by the relative sizes of the scale and substitution effects.
 If substitution > scale, two inputs are gross substitutes, and the cross-elasticity is positive.
 If scale > substitution, gross complements, and the cross-elasticity is negative.
 When the two inputs are complements in production (no substitution effect), then gross complements, so negative cross-elasticity

22. Magnitudes of cross-elasticities : Are the Hicks-Marshall laws of derived demand still applicable to cross-elasticities?
 What would happen to the demand for adult workers if the wages of teenage workers were to fall?
Empirical Findings on Cross-Elasticities
Skilled (well-educated) labor is more likely to be a gross complement with capital than unskilled labor.  
Other things equal, ii will be larger in magnitude for unskilled than skilled workers.
 A policy that reduces the costs of capital investments could create a larger reduction in the demand for unskilled labor than in skilled labor.

23. Policy Application: Effects of Minimum Wage Laws
Purpose of the minimum wage (MW)
 to guarantee each worker a reasonable wage for his/her work effort and thus to reduce the incidence of poverty.
 by putting a floor under the income of a particular subgroup of the population, “working poor.”
Federal MW and Coverage
7.25/hour for about 90% of all nonsupervisory workers.

24. Who are working poors? (2005)

25. Minimum wage and poverty
- In 2010, the official federal poverty line for a family of three with two children was $22,500/$22,200.
; A full-time worker (working 2,080 hours a year) earning $7.25 an hour would earn $15,080 a year, well below the 2010 federal poverty line.
Things to be considered in the above analysis
i) Only a small portion (about 25%) of the low-wage workers (earning $7.25 or less) are living in poverty households.
 Many low-wage workers are not household heads, but rather so-called “secondary” earners, such as teenagers and spouses.

26. ii) Not all workers can find full-time work.
iii) The federal poverty line is viewed by many as an inadequate measure of the income needed to support a family
iv) Consideration of other welfare measures, EITC, food stamps
v) Consideration of state MW
As of 2011, sixteen states have enacted higher minimum wages.

27. <Figure 4.3> Problem of Minimum Wages
; For the minority of low-wage workers who are single-earner family heads, particularly female household heads, the minimum wage is too low.
; However, if the government raises the minimum wage further,
(i)    job opportunities for low-wage workers will be reduced further due to the reduced labor demand for those low-wage workers, and
(ii) even for those low-wage workers who have jobs, most benefits in terms of the increased wage go to nonpoor families.
History of the Minimum Wage: Nominal and Real
<Figure 4.3>

28. Coverage
- textbook; about 10% of all nonsupervisory workers are not covered by the Federal MW law.
- Non-compliance; ???
 Covered sector
i)employees of companies with revenues of at least $500,000 a year ii) employees of smaller firms in interstate commerce or in the production of goods for commerce iii) employees of federal, state, or local government agencies, hospitals, and schools iv) domestic workers
 Uncovered sector
i) executive, administrative, and professional personnel, ii) those employed in small scale firms in the retail trade and services industries, iii) household workers and agricultural workers etc.

29. Employment Effects of the Minimum Wage
Nominal vs Real MW
 As real MW falls toward a new congressional action, its negative employment impact declines.
Holding other things constant
 The predictions of job loss associated with higher minimum wages are made, holding other things equal (+competitive labor market, not monopsonized one).
 What happens when other things change?
<figure 4.4>

30.  Effects of uncovered sectors
Uncoverage: about 10% of nonsupervisory workers plus NONCOMPLIANCE
<Figure 4.5>
The overall loss of employment is likely to be less than the loss of employment in the covered sector.
In the above example, all workers remained employed after the minimum wage was imposed.
The average wage increase tends to smaller than the MW increase.

31. What is the matter with these findings?
Empirical findings
Generally speaking, the employment effects of the minimum wage are ambiguous.
Even for teenagers, it is estimated that when the minimum wage goes up by one percent their employment goes down approximately by 0.2%.
Some recent research (Card and Krueger (1998)) suggests that the employment effect is negligible or, in some cases, positive.
What is the matter with these findings?
The elasticity of demand for labor (unskilled + skilled) = - 1.
The demand for labor is more elastic for unskilled than for skilled.
 So, we expect that the elasticity would be greater than 1 (absolute value) for unskilled, low-wage workers.

32. Possible explanations
1) Measurement problems:
 In order to make other things constant, researchers often compare employment levels just before and after the law
 Time period is so short that firms can not adjust their behavior, therefore, many researches estimated short-run effects
 Estimating long-run effects is more difficult because it becomes more difficult to make “other things” constant in the long-run.
2) Uncovered sector:
 The actual job losses among teenagers (low-wage workers) are small because uncovered sector – legal or illegal – absorb those workers displaced from covered sector.
 If this occurs, the wages among teenagers will not increase as much as the minimum wage increase because the teenage wages in the uncovered sector will decrease.
 However, this hypothesis is rejected as recent studies finds that teenage wages significantly increase with the increase in the minimum wage.
3) A competitive model vs monopsony-type model
 Theory prediction of monopsony model

33. Does the minimum wage fight poverty?
If the short-run response of low-wage employment to changes in MW is really inelastic,
 we expect that an increase in MW would increase the total earnings going to low-wage workers.
However, studies found that only 25% of all minimum wage workers lived in poor families.
 the minimum wage is a relatively blunt instrument with which to reduce poverty; most of its benefits go to workers in nonpoor families.
Is there any better measure to help the working poor?
Earned Income Tax Credit? Is the EITC a replacement for a minimum wage increase?