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3. Labor Demand 3A. Labor Demand Model 3B. Short-Run Labor Demand 3B. Short-Run (Cont.)

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3. Labor Demand 3A. Labor Demand Model 3B. Short-Run Labor Demand 3B. Short-Run (Cont.) 3. Labor Demand 3A. Labor Demand Model E151A: C.Cameron n What happens when wage changes? 1. Firms maximize profit (rev - cost). In short-run? Implies produce where marginal profit = zero. In long-run? Maintained assumption throughout course. n What happens if markets are not 2. Two homogeneous factors of competitive due to monopoly or production: labor and capital. monopsony? Q = f(K, L) (Relaxed later) n What is effect of payroll tax? a. Short-run (capital is fixed) b. Long-run (capital may vary) 3A. Model (cont.) 3A. Model (cont.) 3. Price of labor = hourly wage rate. 4. Firms are price-takers in input and output markets. Implies no fringe benefits and no distinction Then marginal cost equals price between increasing labor by increasing the and marginal revenue equals price. number of workers and increasing labor by having current workers work more. Relax to allow: Monopoly: Price-maker in output good market Relax this assumption in ch. 5. Monopsony: Price-maker in input good market 3B. Short-Run (cont.) 3B. Short-Run Labor Demand n Price-taker in labor market: n MRP = Marginal Revenue Product of L L Then always MEL = w = Increase in Revenue due to So hire until MRPL = w one unit increase in Labor So MRPL curve is labor demand curve. = MR x P (P is price) n Price-taker in output market n ME = Marginal Revenue Product of L L Then always MRPL = MPLxP = Increase in Expenses due to n So in competitive markets hire until one unit increase in Labor MPLxP = w or MPL= w/P n L L Profit-maximizer hires until MRPL = MEL n MPL slopes down Þ DL slopes down 1 MRPL IS LABOR DEMAND CURVE 3C. Long-Run Labor Demand MRPL n Hire inputs until increasing output costs same if by more labor or more capital. w n Cost of one more unit of output = w/MPL if labor used MRPL = DL = c/MPK if capital used (c=user cost of K) n So w/MPL = c/MPK or w/c = MPL/MPK L n L* e.g. wskilled/wunskilled = MPskilled/MPunskilled 3C. Long-Run (cont.) 3D. Net Substitutes/Complements n When wage increases n Substitutes in production (net substitutes) 1. Scale effect: Greater use of one input can compensate output ¯ Þ L ¯ for reduced use of the other 2. Substitution effect: e.g. unskilled labor & capital K • as relatively cheaper Þ L ¯ n Complements in prodn (net complements) n Overall: wage • Þ labor demand ¯ Greater use of one input requires more use of the other e.g. skilled labor & capital n Need more than 2 inputs for complements. 3D. Gross Substitutes/Complements Wage n When price of capital increases both Gross substitutes D (high c) 1. Scale effect: output ¯ Þ L ¯ c • Þ L • 2 D (low c) 2. Substitution effect: 1 Labor Capital relatively more expensive Þ a. Substitutes in prodn: L • Wage b. Complements in prodn: L ¯ Gross complements n c • Þ L ¯ Overall: price capital • Þ labor D ? D1 (low c) n Labor demand • then gross substitutes D2 (high c) Labor demand ¯ then gross complements Labor 2 3E. Monopoly labor demand EFFECT OF MONOPOLY W/P Real wage n Monopolist: MR < P as only producer so faces market demand curve. n Then MRPL = MR x MPL with MR < P n Hire labor until MRPL = w MPL (competitive) Þ MRxMPL = w (MR/P)xMPL (monopoly) Þ (MR/P) x MPL = w/p Þ Hire less labor as MR/P < 1 Labor n Expect as monopolist has lower output. MONOPSONY 3F. Monopsony labor demand W MEL Money n Firm only user of labor so faces upward- wage SL sloping labor supply curve. Þ MEL > w (as increase w to all) n Hire labor until MRPL = MEL > w MRPL Þ Further back up MRPL Þ Hire less labor n e.g. coal miners, nurses in remote areas Employment 3G. Payroll Tax PAYROLL TAX W Wage n S Payroll tax is tax physically paid by received employer to government by worker n It leads to difference in wage paid by w0 employer and wage received by worker. w1 $T D0 n Cost is borne in part by employer and in part by worker. D1 Actual amounts depend on elasticities E E1 E0 of labor demand and supply. 3 3H. Cobb-Douglas Production 3I. Labor Demand Summary n Example: Q = 100xK.5xL.5 n 1. Firms maximize profit. 2. Q = f(K, L): Short-run and long-run n Then MPL = dQ/dL 3. Price of labor = hourly wage rate .5 -.5 = 100xK x.5xL 4. Firms are price-takers. = 50xK.5/L.5 which decreases as L increases n SR and LR conditions Monopoly and monopsony n Given K, w and P can solve for L Substitutes and complements using hire L until P x MPL = w Payroll Tax 4.
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