Labor Demand Rongsheng Tang Washington U. in St. Louis July, 2016 Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 1 / 53
Overview The production function The employment decision in the short run and long run The long run demand curve for labor Marshall s rules of derived demand Factor demand with many inputs Adjustment costs and labor demand Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 2 / 53
Theory of labor demand Firm s consideration given wage rate, how many workers to hire Trade-off benefit: more worker produce more cost: wage cost Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 3 / 53
The Production Function The production function describes the technology that the firm uses to produce goods and services. For simplicity, we initially assume that there are only two factors of production: the number of employee-hours hired by the firm(e) and capital(k) q = f (E, K ) q is the firm s output, E is the product of the number of workers hired times the average number of hours worked per person, we assume people are homogeneous, meaning that workers have same contribution to the firm s output. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 4 / 53
The Production Function Marginal product of labor(mp E ) is defined as the change in output resulting from hiring an additional worker, holding constant the quantities of all other inputs. Marginal product of capital(mp K ) is defined as the change in output resulting from a one-unit increase in the capital stock, holding constant the quantities of all other inputs. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 5 / 53
The Production Function Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 6 / 53
The Production Function Law of diminishing returns: the marginal product of labor eventually declines The marginal curve lies above the average curve when the average curve is rising, and the marginal curve lies below the average curve when the average curve is falling. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 7 / 53
Profit maximization firm s objective is to maximize its profits, Profit = pq we rk where p is the price at which the firm can sell its output, w is the wage rate, and r is the price of capital. In perfect competitive market, firms take prices as given and choose right amount of labor and capital. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 8 / 53
The Employment Decision in the Short Run Short run : firm can not increase or reduce the size of its plant or purchase or sell physical equipment. How many workers should the firm hire? Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 9 / 53
The Employment Decision in the Short Run Short run : firm can not increase or reduce the size of its plant or purchase or sell physical equipment. How many workers should the firm hire? Firm will hire employee such that the value of marginal product of labor equals the wage rate and the value of marginal product curve is downward sloping, i.e. VMP E = w and VMP E is declining Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 9 / 53
The Employment Decision in the Short Run value of marginal product: the dollar value of what each additional worker produces VMP E = p MP E For convenience, we will restrict our attention to the downward-sloping segment of the VMP E curve. Here we need law of diminishing returns, if VMP E keep rising, the firm would maximize profits by expanding indefinitely, it would then be difficult to maintain the assumption that the firm s decisions do not affect the price of output or the price of labor and capital. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 10 / 53
The Employment Decision in the Short Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 11 / 53
The Employment Decision in the Short Run demand curve for labor: what happens to the firm s employment as the wage changes, holding capital constant. The short-run demand curve for labor is given by the value of marginal product curve The position of the labor demand curve depends on the price of the output, stock of capital, productive efficiency or technology. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 12 / 53
The Employment Decision in the Short Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 13 / 53
The Employment Decision in the Short Run can we get industry s labor demand curve by adding up horizontally the demand curves of the individual firms? Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 14 / 53
The Employment Decision in the Short Run can we get industry s labor demand curve by adding up horizontally the demand curves of the individual firms? No, because the industry level output will affect market price. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 14 / 53
The Employment Decision in the Short Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 15 / 53
The Employment Decision in the Short Run Elasticity of labor demand: percentage change in short run employment(e SR ) resulting from a 1 percent change in the wage: δ SR = percent chage in employment percent change in the wage = E SR/E SR w/w e.g. the industry hire 30 workers when the wage is $20 and hire 56 workers if the wage fall to $10, then the short run elasticity is Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 16 / 53
The Employment Decision in the Short Run Elasticity of labor demand: percentage change in short run employment(e SR ) resulting from a 1 percent change in the wage: δ SR = percent chage in employment percent change in the wage = E SR/E SR w/w e.g. the industry hire 30 workers when the wage is $20 and hire 56 workers if the wage fall to $10, then the short run elasticity is δ SR = percent chage in employment percent change in the wage = (56 30)/30 (10 20)/20 = 1.733 Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 16 / 53
The Employment Decision in the Short Run Firm s hiring decision can have an alternative interpretation: firm should produce up to the point where the cost of producing an additional unit of output equals the revenue obtained from selling that output, the marginal cost equals marginal revenue or the unit cost equals product price. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 17 / 53
The Employment Decision in the Short Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 18 / 53
The Employment Decision in the Short Run Proposition: The condition equating price and marginal cost is identical to the condition equating the wage and the value of marginal product of labor. By definition if then hence MC = w 1 MP E p = MC p = w 1 MP E p MP E = w Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 19 / 53
The Employment Decision in the Long Run In the long run, firm s capital stock is not fixed, therefore, in the long run, the firm maximizes profits by choosing both how many workers to hire and how much plant and equipment to invest in. Isoquants: the possible combination of labor and capital that produce the same level of output. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 20 / 53
The Employment Decision in the Long Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 21 / 53
The Employment Decision in the Long Run Properties: Isoquants must be downward sloping Isoquants do no intersect Higher isoquants are associated with higher levels of output Isoquants are convex to the origin. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 22 / 53
The Employment Decision in the Long Run Similar to indifference curve, the slope of an isoquant is given by the negative of the ratio of marginal products, that is, K E = MP E MP K The absolute value of this slope is called the marginal rate of technical substitution (MRTS). Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 23 / 53
The Employment Decision in the Long Run Isocosts: rewriting it as C = we + rk K = C r w r E Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 24 / 53
The Employment Decision in the Long Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 25 / 53
The Employment Decision in the Long Run Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 26 / 53
The Employment Decision in the Long Run At the cost minimizing solution P, the slope of the isocost equals the slope of the isoquant, that is, marginal rate of technical substitution equal the ratio of prices. MRTS = w/r Intuition: the last dollar spent on labor yield as much output as the last dollar spent on capital MP E w = MP K r Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 27 / 53
The Employment Decision in the Long Run Proposition: a profit maximization conditions imply cost minimization long run profit maximization requires that labor and capital be hired up to the point where w = p MP E and r = p MP K hence MP E MP K = w/r Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 28 / 53
The Long-Run Demand Curve for Labor What happens to the firm s long run demand for labor when the wage changes? Will the firm expand if the wage falls? Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 29 / 53
The Long-Run Demand Curve for Labor scale effect: wage cut reduces the marginal cost of production and encourages the firm to expand, as the firm expands, it want to hire more worker substitution effect: the decline in the wage encourages the firm to readjust its input mix so that it is more labor intensive since the price of labor relative to that of capital decrease. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 30 / 53
The Long-Run Demand Curve for Labor Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 31 / 53
The Long-Run Demand Curve for Labor both scale effect and substitution effect induce the firm to hire more workers as the wage falls, so the demand curve for labor must be downward sloping Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 32 / 53
The Elasticity of Substitution The size of the firm s substitution effect depends on the curvature of the isoquant. perfect substitutes: any two inputs in production can be substituted at a constant rate perfect complements: isoquant between any two inputs is right-angled Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 33 / 53
The Elasticity of Substitution Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 34 / 53
The Elasticity of Substitution In between, the more curved the isoquant, the smaller the size of the substitution effect, to measure the curvature of the isoquant, we define elasticity of substitution as ES = percent chage in(k /E) percent change in (w/r) it gives the percentage change in the capital/labor ratio resulting form a 1 percent change in the relative price of labor. The elasticity of substitution is a positive number. ES = 0, if two inputs are perfect complements ES =, if two inputs are perfect substitute Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 35 / 53
Policy Application: Affirmative Action and Production Costs Affirmative action programs typically encourage firms to alter the race, ethnicity, or gender of their workforce by hiring relatively more of those workers who have been underrepresented in the firm s hiring in the past. A particular affirmative action plan, for instance, might require that the firm hire one black worker for every two workers hired. Suppose there are two inputs in the production process: black workers and white workers, black and white workers are not perfect substitutes in production, the market wage rate for black and white workers are wb and w W respectively Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 36 / 53
Policy Application: Affirmative Action and Production Costs Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 37 / 53
Policy Application: Affirmative Action and Production Costs when firm discriminates against black workers, it will increase cost hence nonprofitable, then the affirmative action program will reduce cost for firms. when government force the color-blind firm to adopt an affirmative action program that mandates the firm hire relatively more blacks, then it will increase firm s production cost. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 38 / 53
Marshall s Rules of Derived Demand Marshall s rules of derived demand describe the situations that are likely to generate elastic labor demand curves in a particular industry. In particular: Labor demand is more elastic the greater the elasticity of substitution Labor demand is more elastic the greater the elasticity of demand for the output Labor demand is more elastic the greater labor s share in total costs Labor demand is more elastic the greater the supply elasticity of capital. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 39 / 53
Marshall s Rules of Derived Demand An application: Union Behavior Consider in competitive firm, a union wants to organize the firm s workers, and promises the worker that collective bargaining will increase the wage substantially. Since labor demand curve is downward sloping, the firm may respond to the higher wage by moving up its demand curve and cutting back employment. Then the union s organizing drive has a greater chance of being successful when the demand curve for labor is inelastic. It is the union s best interests, therefore, to take whatever actions are available to lower the firm s elasticity of demand Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 40 / 53
Marshall s Rules of Derived Demand Unions often resist technological advances that increase the possibilities of substituting between labor and capital. e.g The typesetters unions long objected to the introduction of computerized typesetting equipment in the newspaper industry. Unions want to limit the availability of goods that compete with the output of unionized firms. e.g. United Auto Workers(UAW) was a strong supporter of policies that made it difficult for Japanese cars to crack into the US market. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 41 / 53
Marshall s Rules of Derived Demand Unions that organize small groups of workers such as electricians or carpenters tend to be very successful in getting sizable wage increases. Unions often attempt to raise the price of other inputs, particularly nonunion labor. e.g. the Davis-Bacon Act requires that contractors involved in publicly financed projects pay the prevailing wage to construction workers. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 42 / 53
Factor Demand with Many Inputs It is easy to extend two inputs model to multi-input model q = f (x 1, x 2,..., x n ) similarly the profit-maximizing firm hires the ith input up to the point where its price equals the value of marginal product of that input: w i = p MP i Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 43 / 53
Factor Demand with Many Inputs We want to know the change of demand for input i when changing the price of input j, we define the cross-elasticity of factor demand as Cross-elasticity of factor demand = percent change in x i percent change in w j If the cross-elasticity is positive, the two inputs are said to be substitutes in production. If the cross-elasticity is negative, the two inputs are said to be complements in production. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 44 / 53
Factor Demand with Many Inputs Capital-skill complementarity hypothesis: empirical studies suggest that unskilled labor and capital are substitutes and that skilled labor and capital are complements. This hypothesis suggests that subsidies to investments in physical capital will have a differential impact on different groups of workers. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 45 / 53
Adjustment Costs and Labor Demand Adjustment costs: The expenditures that firms incur as they adjust the size of their workforce. Hiring and firing may both induce adjustment costs variable adjustment costs: depends on number of workers fixed adjustment costs Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 46 / 53
Adjustment Costs and Labor Demand Figure: Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 47 / 53
Adjustment Costs and Labor Demand Because of variable adjustment cost, firm will adjust firm size slowly In term of fixed adjustment cost, firm might as well adjust to the optimal level immediately as long as it is profitable. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 48 / 53
Adjustment Costs and Labor Demand Employment protection legislation: To enhance the job security of workers, many developed countries have enacted legislation that imposes substantial costs on firms that initiate layoffs, for instance, many countries mandate that firms offer severance pay to laid-off workers. The theory suggests these policies would be expected to slow down the rate at which workers are laid off and may prevent layoffs altogether. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 49 / 53
Adjustment Costs and Labor Demand These policies may also discourage firms from hiring new workers during an economic expansion. European countries that impose higher costs on layoffs have smaller fluctuations in employment over the business cycle. At the same time, mandating that employers pay three months severance pay to laid-off workers with more than 10 years of seniority reduces the aggregate employment rate by about 1 percent. The employment protection legislation affects the amount of effort that workers supply to their jobs. In Italy, it is difficult to fire workers after the 12th week of employment, a recent study shows that workers are much more likely to be absent from their jobs after the employment protection kicks in. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 50 / 53
Adjustment Costs and Labor Demand The distinction between workers and hours The firm can adjust the number of employee-hours it wants by either changing the number of workers or changing the length of the workweek. hiring more workers: induce adjust cost, more health insurance lengthening workweek: overtime premium Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 51 / 53
Adjustment Costs and Labor Demand The evidence indicates that firms do substitute between workers and hours as the relative costs of the two factors of production change. It has been estimated that an increase in the overtime premium from time-and-a-half to double time may substantially change the number of full-time workers that the firm wishes to hire. There is also evidence that employers prefer to hire full-time workers(rather than part-time workers) when the fixed costs of hiring are substantial. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 52 / 53
Adjustment Costs and Labor Demand Job creation and job destruction The analysis of adjustment cost suggests that small firms would have an advantage in creating jobs if they could respond to favorable changes in the marketplace much faster than bigger firms. It also might be that small businesses have carved out a niche in the fastest-growing areas of the economy. In manufacture sector in a typical year, nearly 11.3 percent of manufacturing jobs disappear, whereas nearly 9.2 percent of manufacturing jobs are newly created. Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 53 / 53