Labor Demand. Labor Demand. Output. The marginal product of labor. Production Function: q=f(e,k)

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1 Labor Demand A firm s decision about how much labor to use in production is driven by the firm s desire to maximize profits. Labor Demand Firm s thinking about whether to hire a worker ach worker produces a certain amount to output per hour That output can be sold for money So, each worker generates a certain amount of revenue per hour. If that hourly revenue is greater than the hourly wage, then hire the worker. Just another way of saying marginal benefit must be greater than marginal cost 1 2 Output Production Function: q=f(,k) Some variable definitions: The marginal product of labor Marginal Product of Labor: Change in output resulting from a hiring an additional worker. MP = q / For our example: xample: Note that the MP is decreasing in labor Intuition 3 4 1

2 q Output and the marginal product of labor MP The value of the marginal product of labor Value of the marginal product of labor: the dollar increase in revenue generated by an additional worker. VMP ($) VMP = p MP 5 6 Labor Demand in the Short Run Profit Maximization Profits = pq(,k)-w-rk w = wage rate r = price of capital p = price of output Decision making rule: VMP VMP = p MP In the short run, capital is fixed. VMP > w Value of the Marginal Product of Labor VMP = p MP VMP < w Marginal Cost of Labor MC = w VMP = w 7 8 2

3 Variables q = K 1/3 1/2 w = 2 r=1 p = 12 K = 8 (fixed) xample Capital is fixed, so we can re-write the production function as: MP = -1/2 VMP = 12-1/2 Profit Maximization: VMP =w Profit Π=pq(,K)-w-rK Profit maximization in the short-run: VMP =w -> p MP =w Reconciling Different Conditions for Profit Maximization con 1 p = MC con 139 VMP = w p MP = w MP = q / q / : how much more output firm gets from additional unit of labor. / q: how much more labor firms needs to produce an additional unit of output. p ( q / ) = w p = w ( / q) = MC 9 10 Labor Demand in the Long Run Two conditions must hold in the long run: VMP =w -> p MP =w VMP K =r -> p MP K =r Variables q = K 1/3 1/2 w = 2 r=1 p = 12 xample Profit Π=pq(,K)-w-rK Profit maximization in the long run: p MP = w p MPK = r Profit Maximization: MP =(1/2)K 1/3-1/2 MP K =(1/3)K -1/3 1/2 6K 1/3-1/2 =2 4K -1/3 1/2 =1 Solve for K and

4 Labor Demand in the Long Run Two factors of production: capital and labor. Both capital and labor can be varied. Labor demand curve downward sloping in the long run too. Demand for labor more responsive to wage changes in the long run. W Why does the labor demand curve slope downward? Substitution effect: Describes how input demand changes as the relative price of the inputs changes, holding output fixed. If wages increase, firms may want to substitute out of labor and into other inputs such as capital. Scale effect: Describes how input demand changes as output changes, holding the relative price of inputs fixed. If wages increase, firms may want to scale back production (see next slide). D SR Both of these effects cause the quantity of labor demanded to drop Why wage changes lead to a scale effect: ffect of Wage Change on the Quantity of Labor Demanded $ MC 1 Increase in the Price of Labor Decrease in the Price of Labor p q1* A wage increase will increase the marginal cost of producing an extra unit of output. This will lead the firm to produce less. q Substitution ffect Scale ffect

5 lasticity of Labor Demand How sensitive is the quantity of labor demanded to a change in wages? Why do we care about the elasticity of labor demand? w D In order to understand the elasticity of labor demand, you have to understand many other markets Marshall s Four Rules of Derived Demand Own-wage elasticity is high when: Land Capital supply demand supply Firms supply demand Households RUL 1: Relates to the output market. When the price elasticity of demand for the product is high, the scale effect is big. Labor demand

6 Marshall s Four Rules of Derived Demand, Continued RUL 2: Relates to the production technology. When the technology is such that it s easy to substitute for labor in production, then the substitution effect is big. Marshall s Four Rules of Derived Demand, Continued RUL 4: When the supply of other factors of production is highly elastic, then the substitution effect is big. Increases in the demand for capital do not drive the price of capital up. perfect complements elasticity of substitution = 0 In most cases, inputs are somewhere in the middle perfect substitutes elasticity of substitution RUL 3: When the cost of employing labor is a large share of total costs Changes in the Demand for Labor Factors that Affect Labor Demand Wage 1. Change in the price of output. For example, this could happen if there was an increase in demand for the output. Increase w An increase in output prices. Decrease D VMP =p 1 MP

7 Factors that Affect Labor Demand Factors that Affect Labor Demand 2. Firm s technology choice. For example, the firm could switch to a technology for which the marginal productivity in labor is higher. 3. Change in the price of other inputs. $ Capital Market S2 S1 Supply decreases w An increase in the MP VMP =p MP xample: Supply of capital decreases, leading to an increase in the price of capital. $ D K Substitution ffect (S) increases the demand for labor Labor Market?? Output Market S2 $ S1 D Q Scale ffect (SC) decreases the demand for labor D Gross Substitutes and Gross Complements Labor Demand When the Labor Market Is Not Perfectly Competitive Labor demand increases Labor demand decreases If a market is characterized by monopsony, it means that there are many sellers and only one buyer. r increases In the case of the labor market, it means that there s only one firm that buys labor. Prototypical example: a coal mine in a remote location. w increases Capital demand increases Capital demand decreases However, the most important feature of a monopsony is that if a firm wants to hire more workers, it must raise wages. This could happen if there are Mobility costs Firms have to pay workers higher and higher wages as the firm gets bigger to prevent the workers from shirking

8 Differences in Labor Supply Curves Under Perfectly Competition and Monopsony The Marginal Cost of Hiring For Monopsonists $ Competitive Labor Market $ Monopsony S Intuitively, profit maximization is the same for a monopsonist as it is for a perfectly competitive firm. S=W ach firm s profit maximizing demand for labor is the quantity of labor such that: VMP = MC. L Note: in this class, we will examine the case of a monopsonist who cannot price discriminate. What does that mean? L However, the MC of hiring a worker does not equal w. Why? Because when the monopsonist hires an additional unit of labor, it must increase the wages it pays to all workers xample of why MC increasing Graphically Labor supply curve: w= workers, w = 30 Total Cost = = workers, w = 32 Total Cost = = 352 w Marginal Cost of 11 th worker = (=$32 for 11th worker plus $20 for extra $2 paid to 10 original workers)

9 Profit Maximization Comparison with Perfect Competition w How do you draw the labor demand curve for a monopsonist? The monopsonist simultaneously picks w* and *, so there is no labor demand curve for a monopsonist. w w* MC S Fewer people are hired than in a perfectly competitive market and wages are lower. This is because the marginal cost of hiring an additional worker is higher for a monopsonist than for a perfectly competitive firm. 33 * VMP VMP = MC Workers worse off relative to perfectly competitive labor market. 34 Monopsony in Professional Sports Sports owners are a small and interconnected group. Supplemental Reading 3 Kahn, Lawrence, The Sports Business as a Labor Market Laboratory, p76-p83. Possibly can band together and act as monopsonists. Main issue here is that the owners can set wages that is, wages are not determined by perfect competition. Two implications The greater is a league s monopsony power, the lower will be player salaries. Players will be paid below their VMP

10 Salaries of Major League Baseball Players, vidence on the Degree of Monopsonistic xploitation If an employer is a monopsony, then workers are paid less than their marginal product 1879: Reserve Clause 1891: American Association nds 1901: Start of American League 1915 nd of Federal League How does a player s marginal revenue product (or value of marginal product of labor) compare with that player s salary? Two steps Calculate how various measures of player performance affect a team s winning percentage (MP ) Calculate how a team s winning percentage affects revenue (p) VMP = p MP stimates Late 1960s: players paid 15-20% of VMP. Late 1980s: players paid 29-45% of VMP. Reserve clause effectively ends in : Start of National Baseball League 1882: Start of American Association 1903: Start of Major League 1913: Start of Federal League Labor Demand Application: Minimum Wage Laws Minimum Wage Laws Basic Facts Federal minimum wage is $5.15/hour. California minimum wage is $6.75/hour. Not all sectors are covered. Farmworkers employed on small farms mployees of season recreational establishments Salespeople at automobile dealerships In 2001, 3.1 percent of workers earned at or below the Federal minimum wage, and 71 percent of those workers earned below $5.15 per hour

11 1982 Dollars $6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $0.00 The Real and Nominal Value of the Federal Minimum Wage, Year Nominal Min. Wage Real Min Wage Theoretical ffect of Minimum Wage Laws Perfect Competition: Minimum wages are a type of price floor. ffectively change supply curve. Decrease employment. xtent to which demand drops depends on the elasticity of labor demand. $ w* * S D Monopsony and Minimum Wages Criticisms of the Minimum Wage $ MC It only helps teenagers. It causes unemployment. S Are these criticisms valid? w* When minimum wage laws are implemented in a monopsonistic market, then employment may actually increase. VMP * mployment

12 Who arns the Minimum Wage? (Age Groups) Who arns the Minimum Wage? (Relationship in Household) One third are teenagers. Almost one half are over the age of 25. About 25% are heads of a households. About 35% are children Who arns the Minimum Wage? (Race and Gender) Mostly women. 63.7% of minimum wage earners are women. Mostly White. 80% of minimum wage earners are white. What is the ffect of the Minimum Wage on mployment Issues to consider: 1. We observe employment and the timing of minimum wage increases. 2. Looking at what happens in a small number of firms can be misleading

13 What is the ffect of the Minimum Wage on mployment 3. Other changes in the economy also affect employment. w min wage w0 S Need Variation! Sources of Minimum Wage Variation: State to state variation in the nominal and real value of the minimum wage. Can relate state variation in real value of minimum wage to state variation in employment rates. Time series variation in nominal and real minimum wage. Can relate variation over time in the real value of the minimum wage with variation over time in employment rates. D min * State variation in minimum wage? Time Series Variation Real Value of Minimum Wage and Average Wages of Manufacturing Production Workers Two problems: 1. States with high minimum wage laws might be states with strong economies and, thus, low unemployment rates. 2. Many states have minimum wages that are the same as the Federal minimum wage

14 Teenage mployment Rate With Dates of Minimum Wage Changes Randomized xperiment Study Design What would be the ideal way to study the effect an increase in minimum wage on employment? How might a doctor test the effectiveness of a new drug? Why would the doctor have a control group? Problem: mployment fluctuations large compared to employment fluctuations that you would expect from minimum wage increases. 53 How would you design a randomized experiment to study the effect of a minimum wage? 54 Study by Card and Krueger Study by Card and Krueger Data Collection Can t conduct a randomized experiment. Alternatively, use natural experiments. Prior to April 1992, the minimum wage in NJ and PA is $4.25/hour April 1, 1992 NJ raises its minimum wage to $5.05/hour The minimum wage in PA doesn t change. Survey 400 fast food establishments Burger King, Roy Rogers, KFC, Wendy s etc. New Jersey and Pennsylvania Asked them number of full-time and part-time employees Before: March, 1992 After: December,

15 Difference-in-Difference stimation Number of Full-Time quivalent Non-supervisory mployees Implications of Card and Krueger Study Suggests that the labor demand curve is upward sloping. NJ PA Difference Before 20.4 (A) 23.3 (C) After 21.0 (B) 21.2 (D) Difference Monopsony? Suggests that employment increased! Criticisms of the Card and Krueger Study No attempt to collect data on hours worked. Big drop in employment in PA over 8 month time period. Overall increase masks huge variation in both directions. Hungry teenager theory What are we to make of minimum wage laws? Theoretically, they can reduce employment rates. But, not a lot of empirical evidence that increases in the minimum wage lead to lower employment rates. Still, not clear that increases in the minimum wage are the best means of fighting poverty

16 Living Wage Campaigns Currently Very Active A total of 130 places have living wage ordinances and living wage campaigns are underway in another 119 cities, counties and universities. Selected Cities with Living Wages CITY Living Wage Living Wage With No Health Benefits Sacramento CA Sebastopol CA Port Hueneme CA Lansing MI Orlando FL Dayton OH Arlington VA Prince George's County MD Santa Fe NM Impact of Living Wage Law Theoretical effects are complex because living wages only cover a relatively small number of companies. Covered sector Non-covered sector Not a lot of evidence that living wage ordinances decrease employment. Some evidence that they reduce poverty. Who really pays for living wage ordinance? Unknown. To what extent might employers cut back on other benefits? Unknown. Still an area of active research