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09.03.2017 Labor Demand Sellers’ view of Labor • Sellers view labor as a source of income (potential for increase in consumption of goods and services). • Labor Supply: – Labor as hours devoted to work (T – leisure). – Leisure is a ‘good’, work is a ‘bad’. • Find individual labor supply curves, then aggregate them to find market labor supply curve. – Hours supplied (per period) is an increasing function of wages. – Backward bending labor supply: Hours may decline at very high levels of wages. Chapter 3 © 2016 McGraw‐Hill Education. All Rights Reserved. © 2016 McGraw‐Hill Education. All Rights Reserved, Demand for Labor is «derived demand» Buyers’ view of Labor • Buyers view labor as a factor of production. • Borjas: «workers … differ from other inputs in a number of important ways.» (p.84) • Econ 320 Syllabus: • 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. – Quality is not easily discrenable (Ch.6, 7) – Worker may not apply his/her labor as responsibly as the employer will like (Ch.11) Presently we abstract from these information problems. © 2016 McGraw‐Hill Education. All Rights Reserved. 2 • Central questions: how many workers are hired and what are they paid? 3 Labor is an important input! © 2016 McGraw‐Hill Education. All Rights Reserved. 4 The Firm’s Production Function • Describes the technology that the firm uses to produce goods and services. • The firm’s output can be produced by a variety of capital–labor combinations. • 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 employing one additional unit of capital, holding constant the quantities of other inputs. © 2016 McGraw‐Hill Education. All Rights Reserved. 5 © 2016 McGraw‐Hill Education. All Rights Reserved. 6 1 09.03.2017 The Total Product, the Marginal Product, and the Average Product Curves, Fig. 3‐1 Profit Maximization • Objective of the firm is to maximize profits. • Production function: Q = f(E, K) • Profit function: π = pQ – wE – rK • Total Revenue = pQ • Total Costs = (wE + rK) • Perfectly competitive firms cannot influence prices of output or inputs. • Take p, w, r as given, choose input (E, K) and output (Q) levels to maximize profits. 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 shows the output produced by each additional worker, and the average product curve shows output per worker. See Table 3‐1 for a numerical illustration. 7 © 2016 McGraw‐Hill Education. All Rights Reserved. Short Run Hiring Decision • E = employee‐hours = no. of workers x average hours per worker Consider: 10 workers x 8 hrs/day = 80 hrs/day 20 workers x 4 hrs/day = 80 hrs/day • Will the employer be indifferent between these? • If fixed costs of employement are present, the answer is «NO». 9 The Firm’s Hiring Decision in the Short‐Run (Fig. 3‐2) • Optimal E solves © 2016 McGraw‐Hill Education. All Rights Reserved. . 8 Employment = employee‐hours • Short run: K is fixed. • Value of Marginal Product of Employment (VMPE) is the marginal product of labor times the dollar value of the output. • VMPE indicates the dollar benefit derived from hiring an additional worker, holding capital constant. • Value of Average Product of Employment is the dollar value of output per worker. © 2016 McGraw‐Hill Education. All Rights Reserved. © 2016 McGraw‐Hill Education. All Rights Reserved. © 2016 McGraw‐Hill Education. All Rights Reserved. 10 Labor Demand Curve • The demand curve for labor indicates how many workers the firm hires for each possible wage, holding capital constant. 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. • The labor demand 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 © 2016 McGraw‐Hill Education. All Rights Reserved. 12 2 09.03.2017 The Short‐Run Demand Curve for Labor (Fig. 3‐3) The Firm’s Output Decision Fig. 3‐5 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 (to the right), and increases employment. © 2016 McGraw‐Hill Education. All Rights Reserved. A profit‐maximizing firm produces up to the point where the output price equals the marginal cost of production. 13 The Mathematics of Marginal Productivity Theory Maximizing Profits: Two Rules • Choice of optimal Q: 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). • The cost of producing an extra unit of output: MC = w x (1 / MPE) • The condition: produce to the point where MC = MR = p (for the competitive firm) • Choice of optimal E: (Marginal Productivity Condition) hire labor up to the point where the value of marginal product equals the added cost of hiring the worker (= wage). © 2016 McGraw‐Hill Education. All Rights Reserved. w x (1 / MPE) = p or w = VMPE 15 Critiques of Marginal Productivity Theory 16 © 2016 McGraw‐Hill Education. All Rights Reserved. The Short‐Run Demand Curve for the Industry (Fig. 3‐4) • A common criticism is that the theory bears little relation to the way that employers make hiring decisions. 1. In response to a wage reduction, and individual firm would like to increase employment and increase output. 2. If all firms did this, output increase will reduce the output price, and the labor demand curve of the individual firm will shift in. Wage • Another criticism is that the assumptions of the theory are not very realistic. Wage T D • However, employers act as if they know the implications of marginal productivity theory (hence, they try to earn profits and remain in business). © 2016 McGraw‐Hill Education. All Rights Reserved. 14 © 2016 McGraw‐Hill Education. All Rights Reserved. 20 20 10 10 D T 15 28 30 Employment Firm 17 30 56 60 Employment Industry © 2016 McGraw‐Hill Education. All Rights Reserved. 18 3 09.03.2017 Elasticity of Labor Demand The Employment Decision in the Long Run • As a result, the demand curve for the industry (b) is steeper (less elastic) than the demand curve for an individual firm (a). • Short run elasticity of labor demand: • In the long run, the firm maximizes profits by choosing how many workers to hire AND how much plant and equipment to invest in. % % • In figure (b): 56 10 ∆ / ∆ / 30 /30 20 /20 • Isoquant curves describe the possible combinations of labor and capital that produce the same level of output 1.73 © 2016 McGraw‐Hill Education. All Rights Reserved. 19 © 2016 McGraw‐Hill Education. All Rights Reserved. Isoquant Curves (Fig. 3‐6) X K Y q1 q0 E Isocost Lines All capital‐labor combinations that lie on a single isoquant produce the same level of output. The input combinations at points X and Y produce q0 units of output. Combinations of input bundles that lie on higher isoquants must produce more output. Capital • The isocost line indicates all labor–capital bundles that exhaust a specified budget for the firm. • Isocost lines indicate equally costly combinations of inputs. • Higher isocost lines indicate higher costs. Employment © 2016 McGraw‐Hill Education. All Rights Reserved. 21 Capital C1/r Isocost with Cost Outlay C1 Isocost with Cost Outlay C0 © 2016 McGraw‐Hill Education. All Rights Reserved. All capital‐labor combinations that lie on 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). Capital C1/r A C0/r P 175 B q0 C0/w 100 C1/w © 2016 McGraw‐Hill Education. All Rights Reserved. 22 The Firm’s Optimal Combination of Inputs (Fig. 3‐8) Isocost Lines (Fig. 3‐7) C0/r 20 23 A firm minimizes the cost 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. Employment © 2016 McGraw‐Hill Education. All Rights Reserved. 24 4 09.03.2017 Cost Minimization Long Run Demand for Labor • When the wage drops, two effects arise. • Profit maximization implies cost minimization. • The firm chooses the 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 ratio of input prices, w / r, at the least‐cost choice. – The firm takes advantage of the lower price of labor by expanding production (the scale effect). – The firm takes advantage of the wage change by rearranging its mix of inputs, by employing more labor and less of other inputs, even if holding output constant (the substitution effect) or © 2016 McGraw‐Hill Education. All Rights Reserved. 25 The Impact of a Wage Reduction Holding Costs Constant (Fig. 3‐9) Capital C0/r R P 75 q0 The Impact of a Wage Reduction on the Output and Employment of a Profit‐ Maximizing Firm (Fig. 3‐10) 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. Dollars 100 100 150 Output 25 50 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. 27 Capital D C1/r Q C0/r R P 200 D 100 Wage is w1 Wage is w0 A wage cut generates substitution and scale effects. The scale effect (from P to 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 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. Employment © 2016 McGraw‐Hill Education. All Rights Reserved. © 2016 McGraw‐Hill Education. All Rights Reserved. Two Special Cases of Isoquants (Fig. 3‐12) 50 R P 150 Substitution and Scale Effects 40 MC1 p 40 © 2016 McGraw‐Hill Education. All Rights Reserved. 25 Capital MC0 Wage is w1 Wage is w0 25 26 © 2016 McGraw‐Hill Education. All Rights Reserved. 29 © 2016 McGraw‐Hill Education. All Rights Reserved. 30 5 09.03.2017 Elasticity of Substitution Elasticity of Substitution • The elasticity of substitution is the percentage change in the capital to labor ratio given a percentage change in the price ratio (wages to real interest). • Example: If the elasticity of substitution is 5, then a 10% increase in the ratio of wages to the price of capital would result in the firm increasing its capital‐ to‐labor ratio by 50%. – Formula: %∆(K/L) %∆(w/r). – Interpret a particular elasticity of substitution number as the percentage change in the capital– labor ratio given a 1% change in the relative price of labor to capital © 2016 McGraw‐Hill Education. All Rights Reserved. 31 © 2016 McGraw‐Hill Education. All Rights Reserved. 32 The Short‐ and Long‐Term Demand Curves for Labor Long Run Demand Curve for Labor (Fig. 3‐11) Dollars Dollars Short-Run Demand Curve The long‐run demand curve for labor gives the firm’s employment at a given wage and is downward sloping. w0 w1 Long-Run Demand Curve 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. DLR 25 50 Employment Employment © 2016 McGraw‐Hill Education. All Rights Reserved. 33 34 Factor Demands When There Are Several Inputs Marshall’s Rules • Labor Demand is more elastic when: • There are many different inputs. – The elasticity of substitution is greater. – Skilled and unskilled labor – Old and young – Old and new machines – The elasticity of demand for the firm’s output is greater. (Remember: The demand for labor is derived demand.) – Labor’s share in total costs of production is greater. • Cross‐elasticity of factor demand. – Percent change in xi Percent change in wj – If cross‐elasticity is positive, the two inputs are said to be substitutes in production. – The elasticity of supply of other factors of production such as capital is greater. © 2016 McGraw‐Hill Education. All Rights Reserved. © 2016 McGraw‐Hill Education. All Rights Reserved. 35 © 2016 McGraw‐Hill Education. All Rights Reserved. 36 6 09.03.2017 The Demand Curve for a Factor of Production Affected by the Prices of Other Inputs Labor Market Equilibrium Dollars Price of input i Price of input i In a competitive labor market, equilibrium is attained at the point where supply equals demand. The market‐ clearing wage is w* at which E* workers are employed. Supply whigh w* D0 D1 D0 wlow D1 Employment of input i Employment of input i Demand ED 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. E* 37 © 2016 McGraw‐Hill Education. All Rights Reserved. Application: The Employment Effects of Minimum Wages ES Employment © 2016 McGraw‐Hill Education. All Rights Reserved. 38 The Impact of the Minimum Wage on Employment Dollars • The unemployment rate is higher the higher the minimum wage and the more elastic are the labor supply and demand curves. S w w* • The benefits of the minimum wage accrue mostly to workers who are not at the bottom of the distribution of permanent income. D E 39 © 2016 McGraw‐Hill Education. All Rights Reserved. Minimum Wages in the United States, 1938‐2011 0.5 0.4 4 © 2016 McGraw‐Hill Education. All Rights Reserved. 40 Evidence from Turkey, 2005 Monthly labor market earnings = real wage x hours Ratio 5 Employment Evidence from around the World is mixed! Why? Compliance with the Law is not perfect. 7 6 ES Employment effects of minimum wages 0.6 8 E* A minimum wage set at w results in employers cutting employment from E* to E. The higher wage also encourages ES – E* workers to enter the market. Thus, under a minimum wage, U = ES – E– workers are unemployed. 3 0.3 2 Nominal Minimum Wage 1 0.2 0 1938 1944 1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010 Year left axis: min wage right axis: ratio ratio = min. wage / average manufacturing wage © 2016 McGraw‐Hill Education. All Rights Reserved. 41 © 2016 McGraw‐Hill Education. All Rights Reserved. 42 7 09.03.2017 The Impact of Minimum Wages on the Covered and Uncovered Sectors Employment Protection Legislation Makes adjustment of employment level costly. Adjustment costs: • Firing costs In Turkey if firm wants to fire a «permanent» worker, it must pay penalties («severnace pay» and «advanced notice pay»). • Hiring costs Dollars Dollars SU SC (If workers migrate to covered sector) SU w SU (If workers migrate to uncovered sector) w* w* DC E EC DU Employment EU EU EU Employment (b) Uncovered 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. © 2016 McGraw‐Hill Education. All Rights Reserved. 43 Asymmetric Variable Adjustment Costs Slow Transition to a New Labor Equilibrium Employment 150 B 100 A C 50 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. © 2016 McGraw‐Hill Education. All Rights Reserved. 44 © 2016 McGraw‐Hill Education. All Rights Reserved. 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. Time 45 46 © 2016 McGraw‐Hill Education. All Rights Reserved. Problems with Estimating Labor Demand Estimating Labor Demand S0 • One can identify the slope of the labor demand curve, which can be used to calculate the elasticity of labor demand, when the supply curve shifts. Dollars S1 Z P w0 R w2 • Problem: Must make sure the labor demand curve is not also changing. Z Q w1 D1 D0 E0 © 2016 McGraw‐Hill Education. All Rights Reserved. 47 E1 E2 © 2016 McGraw‐Hill Education. All Rights Reserved. Employment 48 8 09.03.2017 The Impact of Wartime Mobilization of Men on Female Labor Supply © 2016 McGraw‐Hill Education. All Rights Reserved. The Impact of Wartime Mobilization of Men on Female Wages 49 © 2016 McGraw‐Hill Education. All Rights Reserved. 50 9