Chapter 3. Demand for Labor  Study Purposes  to determine how much labor employers will want to employ at different wage rates. Wages change for various reasons: - minimum wage increase - wage increase though collective bargaining - any government policy that mandates wage increases  consider employment and unemployment effects: why are these different?  A major component of a theory of wage determination. Note) Labor demand is derived from the output market.

1. Individual firm ’ s SR demand for labor under competitive output & input markets Under the following five assumptions, each firm demands less labor as wages go up.  Assumption 1: firms seek to maximize profits.  Profit = total revenue (TR) - total cost (TC)  Assumption 2: firms produce their output (Q) by combining two factors of production: labor (L) and capital (K).  Q =  (L, K)

 Assumption 3: both input and output markets are competitive.  firms are price takers both in input and output markets.  TR = P  Q and TC = w  L + c  K  Assumption 4: short-run (SR) analysis  The time period is so short that a firm can not vary its stock of capital. - Delivery and installation lags - Lack of access to funds to buy machines -> Capital utilization???

Definitions  Marginal product of labor (MPL) = the change in physical output (  Q) produced by a change in the units of labor (  L), holding capital constant. - MPL =  Q/  L (holding capital constant) - [MPK =  Q/  K (holding labor constant)]  Marginal revenue (MR) = the additional increment of total revenue that is generated by an extra unit of output. - MR =  TR/  Q = P  Marginal revenue product of labor (MRPL) = the additional increment of total revenue generated by adding an extra unit of labor. - MRPL =  TR/  L = (  TR/  Q)  (  Q/  L) = MR  MPL = P  MPL - [MRPK = MR  MPK = P  MPK]

 Marginal expense (cost) of an added unit of labor (MEL) = the amount of increment in total expense (cost) generated by an extra unit of labor. - MEL = W (the expense of hiring one unit of labor for one time period) - [MEK = C (the interest rate), i.e., the expense of renting one unit of capital for one time period]  Firm ’ s profit (  ) function:  = P  (L, K) – W  L – C  K

Decision rule for profit maximization a. If the income generated by one more unit of labor exceeds the additional expense (MRPL > MEL), then add a unit of labor. b. If the income generated by one more unit of labor is less than the additional expense (MRPL < MEL), then reduce employment of that labor. c. If the income generated by one more unit of an input is equal to the additional expense (MRPL = MEL), then no further changes in that input is desirable. -> Profit is maximized only when employment is such that MRPL = MEL -> P*MPL = W (1) -> or MPL = W/P(2)  Check the consistency of units for both sides of the equation.

 Equation (2) is necessary, but no sufficient, for profit maximization.  Assumption 5: Diminishing MPL;  a sufficient condition  Illustration The marginal Product of Labor in a Hypothetical Car Dealership (capital held constant) - Eventually, as more salesmen are hired, the MPL must fall.

Derivation of a Firm ’ s Demand Curve as a Function of Real wages  Proposition: The firm’s demand for labor in the short run is equivalent to the downward-sloping segment of its MPL schedule.  Illustration: Demand for Labor in the Short Run (Real Wages)  Why downward-sloping part? - If MPL=W/P and MPL is increasing, better increase level of employment

Derivation of a Firm ’ s Demand Curve as a Function of Money Wages Proposition: the firm’s demand for labor in the short run is equivalent to the downward-sloping segment of its MRPL schedule.  and Note) MRPL = MR  MPL = P  MPL. Therefore, MRPL is diminishing with labor as P is fixed and MPL is diminishing with labor. Note: MPL or MRPL is a function of K and L as well as individual characteristics.

Market Demand Curve

2. Firm ’ s LR demand curve under competitive output & input markets: Relaxing Assumption 4  Now firms can adjust capital in response to wage changes.  LR profit-maximizing conditions - MPL  P = W(3) - MPK  P = C(4) - W/MPL = C/MPK(5)  Why is (5) LR profit-maximizing condition? - If W/MPL > C/MPK, reduce L and increase K - If W/MPL < C/MPK, reduce K and increase L

 When the wage rate goes up, other things being equal, the demand for labor is further reduced in the LR than in the SR. Why?  Two things happens in the LR as W  -- SCALE EFFECT  Becomes more costly to produce the same amount of output  Raise output price to maintain profit margins  Demand for the output goes down  Reduce the demand for labor and capital. -- SUBSTITUTION EFFECT  Becomes less costly to use capital than labor (W/MPL > C/MPK)  Substitute capital for labor  Demand for K increase, Demand for L decreases  In sum, the rise in the wage rate has an ambiguous effect on the desired stock of capital. However, both substitution and scale effects serve to reduce the demand for labor.  Conclusion: The labor demand curve is a downward-sloping function of the wage rate even in the LR.

3. Demand for an input as a function of the prices of other inputs  Want to investigate how the demand for an input (e.g., L) is changed by the price changes of other inputs (e.g., C).  Suppose C   Scale effects: demand for K , and demand for L   Substitution effects: demand for K , and demand for L   Sign of the change in labor demand is indeterminate.  Definitions  Gross complements  scale effect > substitution effect  demand for an input and price of the other input move in opposite directions.  Gross substitutes  substitution effect > scale effect  demand for an input and price of the other input move in the same direction.

 When the two inputs are substitutes in production, then the two inputs are either gross complements (Figure 3.3-a) or gross substitutes (Figure 3.3-b)  When the two inputs are complements in production (no substitution effects), then the two inputs are always gross complements.  Demand for L  as C .  Our textbook example: Snowplows, skilled labor, and unskilled labor  What happens to the demand for skilled workers 1) when the wages of skilled workers go up? 2) when the wages of unskilled workers increase? 3) when the price of snowplows increases?

Chain of Events: Understanding Firm ’ s LR Demand

4. Monopoly: Relaxing Assumption 3  All the other assumptions still hold except that the product market is monopolistic.  General profit maximization condition  MRPL (= MR  MPL) = MEL  Profit maximization condition for a monopolist  As MR  P(price maker), and MEL = W (taker), M RPL = MR  MPL = W  SR demand for labor as a function of real wages.  (MR/P)  MPL = W/P(6) In comparison, MPL = W/P (2) for a competitor.

 MR = P for a competitive firm, but MR < P Why?  A monopolist is the single supplier to the product market.  In order to sell extra unit of output, it must lower price, i.e., a monopolist faces a downward-sloping market demand curve.  Since the firm must lower price on all units of output, and not just on the extra units to be sold, the marginal revenue associated with an additional unit is below price.  Numerical example QPTR MR of 10 th unit = 10 < 19 = P of all units

 Implication of MR < P  Demand less labor than an otherwise identical competitor  Since labor is the only input in the SR, output is lower under monopoly than under competition.  However, as long as the monopolist behaves competitively in the labor market, the wage rate need not be different.  a local utility company

5. Policy Application: The Labor Market Effects of Payroll Taxes and Wage Subsidies 1) What is an employer payroll tax?  Employers (in some cases employees) must pay taxes based on the size of their payrolls.  To finance social insurance programs - Social Security retirement, disability, and Medicare programs: both employers and employees. - Unemployment insurance, worker ’ s compensation: employers.  To simplify our discussion, assume only employers pay payroll taxes

2) Who bears the burden of a payroll tax?  Initially, /H, and employ E 0 workers.  T he government imposes a payroll tax of $ X/H.  Therefore, the demand curve shifts down by $X.  With D 1, the market wage rate is set at $ /H, and the E 1 amount of labor are employed.  Therefore, $ of the tax gets shifted to employees in the form of wage cut.  Employment also goes down by E 0 – E 1.  Employers also bear $ of the tax because the average labor costs rise to $.  With an upward-sloping labor market supply curve, employees withdraw labor as their wages fall, and it becomes more difficult for firms to find workers.

3) Conclusion  The party legally liable for the contribution (the employer) is not necessarily the one that bears the full burden of the actual cost.  Who bears more burden of the tax depends on the slope of the supply curve. -The less responsive labor supply  the fewer the employees withdraw from the market  the higher the proportion of the tax gets shifted to workers in the form of a wage decrease. -Two extreme cases vertical labor supply horizontal labor supply?

 To the degree employee wages do not fall, employment levels will. -When wages do not fall much, employer labor costs are increased, and employers greatly reduce the demand for labor. -In extreme, horizontal labor supply curve,  Winners? -Both employers and employees share the burden of payroll taxes. -Disadvantaged groups those social insurance programs are targeted for  Empirical Evidence - Most of a payroll tax is eventually shifted to wages, with little long-run effect on employment.

4) Gender differences in the burden of payroll taxes -Women ’ s labor supply is more wage-elastic than men ’ s. -Compared with women, men tend to bear the burden of payroll taxes relatively more in the form of wage cut. -Compared with men, women tend to get the burden of payroll taxes relatively more in the form of employment cut.

Graphical Derivation of a Firm ’ s Labor Demand Curve Mathematical Discussion of the Labor Market Effects of Employer Payroll Taxes/Wage Subsidies See question 1 of assignment 1