Chapter 3 Labor Demand

Chapter 3 Labor Demand 3.1 Introduction The objective of this chapter is showing the concept of labor demand, how to derive labor demand both short run and long run, elasticity, and relating policy. We will start with analysis of short - run labor demand that depends on the competitive equilibrium framework. Next, we will analyze the long run labor demand with specific tools, which are isoquant and isocost, and then we try to decompose the scale and substitution effect when the wage rate changes. The first important framework is about profit maximization. Firm wants to * maximize profit which is π = pq we rk, so given the output level q, firm needs to appropriately allocate unit of worker and unit of capital. Note that, the * state of decision is two steps, first firm choose the optimal level of output ( q ) applying marginal cost and marginal revenue concept. At the second step, firm will choose the optimal level of capital and employee, so we call demand of labor as derived demand. Last of chapter, we will focus on the impact of government policies on labor demand and its adjustment. These examples of policies are anti-race workplace, minimum wage, and overtime pay. In addition, we will use the global data about minimum wage rate as one of the empirical analyses. 3. Short Run Labor Demand We mainly assume that labor market is competitive. So, the conditions of marginal cost and marginal revenue will be used in this framework. Firm faces the production function depending on hired labor ( E ) and capital ( K ) with specific function that call production function which is q = f( E, K). In general, the production function is concave to both variables (increasing function but with the decreasing rate of change). The example of production function is Cobb- 1 Douglas production function which is q= E α K α. In this case, we can find the α 1 α 1 α q E K α 1 1 α K marginal product of labor which is = = αe K = α and 1 α E E E α 1 α α q E K α α E marginal product of capital which is = = (1 α) E K = (1 α). α K K K The meaning of marginal product for labor is that if the labor change one unit the quantity will be changed MP E units. Note that both of marginal products follow the law of diminishing marginal return, the combination of both may be inappropriate and leads to lower output. In short run, we have to assume that one input fixed (we assume fixed capital) and another can vary. The average product and marginal product of labor will be the hump shape that means to the increasing at the first stage and 1

will go down at second stage. The figures of MP and AP show in figure 3.1. The first can count the value of additional one unit of labor can produce as value of marginal product. Generally, the constant fixed price is assumed for framework of competitive market, so the value of marginal product will be VMPE = p MPE. This condition states that one unit increase of labor will generate the revenue as the value of addition units from one unit of addition labor. Note that, we treat price of product as exogenous variable depended on the market equilibrium. We can derive the value of average product which is VAPE = p AP E, so both of these will be created by scaling the graph in Figure 3.1 by price that is already presented by figure 3.1. Figure 3.1 Graph of output, marginal product, average product The key decision still applies the marginal framework that equates marginal cost from hiring one unit of labor and marginal revenue from one unit of input (VMP). The cost of this case is very obvious that is the wage rate per one unit of labor, so the optimal condition will be w= p MPE. This condition also stats that wage rate is valuable for the value of product getting from additional worker. The figure 3. shows this condition. The alternative explanation of this condition may come from the cost side that is at profit maximization marginal cost equaling the marginal revenue. At competitive equilibrium, p = MC, so w= MC MP E, and w MC = (try to explain this condition by economic reason). MP E

Figure 3. Optimal point in the short run production We can derive the demand curve from each firm, which is the same condition on law of demand. If wage rate falls, firm want to hire more labor the demand for labor may be shifted to the right. However, we have to think about the industry decision too. Industry may hire more labor leading to increase an output level, and then the price will decrease implying to the lower VMP that shifts demand back to original level or less than an original level. For industry, we should think about the expansion of production and price of output that affects the decision of labor hiring through the VMP. The industry labor demand is not the sum of every firm s demand; this is different from labor supply because the interaction of firm s production and mechanism of price on VMP. The figure 3.3 shows an industry demand curve. The figure 3.3 shows the industry demand curve. 3

3.3 Long Run Labor Demand For the long run, we use the concept of isoquant and isocost as main analyzing tools. The isoquant represents the combination of inputs that produces the same level of out put. The idea is as same as the isoquant when we analyze the labor supply. The slope of isoquant shows the marginal rate of technical substitution (MRTS) which means that in order to maintain the level of output, when we change the one input (for example increasing unit of labor) we have to decrease the level of another input (in this case is unit of capital). The figure 3.4 presents the picture of isoquants corresponding to level of output surface. With the same analogy, the isocost represents the combination of inputs that uses the same level of cost. The cost function is C = we+ rkthat returns the * lowest cost when we specify the level of output ( q ). The tangent point between isocost and isocost show the condition of the least cost combination, i.e. given level of output, the optimal point will be the best combination to get the lowest cost 1. The tangent of both also show the important condition that both slopes MPK MPE equal that are =, marginal product of capital per one unit of its cost r w equals marginal product of labor per one unit of its cost (explain if not, what s happen and how to adjust to optimal point). The optimal situation is derived from the idea that given the level of output, firm minimizes their cost. On the other hand, firm may specify the level * of cost and then try to maximize the level of output. If the level of output ( q ) process is the same firm must have the same cost, this is called duality. The graphical idea is shown in figure 3.5. In addition, at the optimal point, we also conclude that w= p MP E and r = p MPK. In appendix 3.1, I show formal derivation of labor demand function. In the case changing in wage rate (in the long run), firms can extend their production. Given the fixed capital, the isocost will rotate at the same point of fixed capital. This situation is shown in figure 3.6. However, firm may change their capital because firm freely change input combination due to long run production. The key question is that where is a new isocost. The answer is the cost such that is a new least cost combination, so new isocost may not be a rotate a line from the original one. 1 Note that, the least cost combination is not the maximized profit combination because the maximized profit condition is determined by both marginal cost and marginal revenue. 4

Figure 3.4 Isoquants corresponding to level of output surface Complementary inputs Imperfectly substitute (Cobb-Douglas) Capital Intensive Pure Capital 5

Figure 3.5 Duality of cost minimization and output maximization Figure 3.6 Duality of cost minimization and output maximization 6

3.3 Analysis of Substitution and Scale Effect The change in wage rotates the isocost line, so firm will make a new decision on resource allocation. The total change of decision (unit of hiring labor) can be decomposed into two effects, which are substitution effect and scale effect. The scale effect is the change in demand for labor when keep the wage rate constant, this can compare to the income effect in labor supply derivation. For the substitution effect, we try to find the change in demand when wage rate changes and maintaining the constant output. The graph of how to decompose the effect is presented by figure 3.7. As I mention earlier, firm may not use the same level of cost due to the ability to change the inputs combination in long run production, so the new isocost may not be parallel with the previous isocost. Figure 3.7 substitution and scale effect From figure 3.7, the original optimal point is on point E, with wage rate w1, firm hires labor x1 unit. If the wage rate in labor market decreases from w1 to w, the isocost changes to w line with new tangent point F, so firm hires labor x units (the total change is x x1, we hire more labor). This figure assumes that firm may not change level of capital that is the WRONG analysis framework. However, I will use this figure in order to simplify the idea and will move on to correct one in the next figure. In order to classify both effects, I create the new line with same slope as w1 which is w1* and attach the isoquant q at point G. This line can show the effect of wage holding the quantity constant that is substitution effect (x to x3). The substitution effect generally be positive due to the trade off between both inputs when we assume input price changes (relative price of inputs changes). In the second step, we analyze point E to G that is different only cost (shift in cost). So this can be call scale effect (x1 to x3). The correct figure is shown in figure 3.8. 7

Figure 3.8 The capital is not fixed We can analyze the labor market and substitutable between labor and capital from elasticity of substitution. The substitutable of both has many powerful implications because firm will know the degree of substitute and may planning for resource. Moreover, government can apply it to manage the labor, poverty, and many policies. The measurement of elasticity of substitution is the K % Δ E ratio between changes in relative input price to relative input used, σ =. w % Δ r The other implications of elasticity of substitution help us to understand the firm s behavior when there is some change about wage rate. The Marshall s rules of derived demand are the one implication from elasticity of substitution (this summarize from Borjas, 010). a) labor demand is more elastic the greater the elasticity of substitution: we can notice about the curvature of isoquant. b) labor demand is more elastic the greater the elasticity of demand for the output: this rules is very well presentation about derive demand that links between output and demand for inputs. We can also analyze the elasticity of demand applying the concept of elasticity that is the ratio between percentage change in employment and percentage change in wage, i.e. ΔE E ΔE w δ = =. Δw Δw E w 8

c) labor demand is more elastic the greater labor s share in total cost: link age between input price and production through specific input intensive d) the demand for labor is more elastic the greater supply elasticity of other factors of production, such as capital: we may see the cross elasticity of % ΔX i factor demand which is ε c = % Δ w. j 3.4 Minimum Wage (this section based on Tito and Jan Van Ours [008]) Minimum wage is a government policy to enforce employer paying the wage rate at a specific minimum (floor) level. In general, minimum wage is greater than the equilibrium wage rate, so this policy may generate the deadweight loss for economy. However, the counter argument is the way to protect the worker in order to live at specific standard. The dynamic of a minimum wage relates to the covered and uncovered sectors, that they may mobilize between both. The outcome in the covered sector is lowering the employment and wage increasing to minimum wage rate. On the other hand, the outcome of uncovered may not be specified because there are two effects from increasing minimum wage rate in the covered sector. The first effect comes from the migrating worker from covered sector to the uncovered sector that leads to increase labor supply. The second effect comes from migration of labor in the uncovered sector to the covered sector in order to get more pay. So, the analysis of the uncovered sector has to weight between both effects that are very difficult to exactly measure. There are at least three forms of minimum wage rate policy (Tito and Jan Van Ours, 008). a) A national, government legislated minimum wage b) A national minimum wage (outcome of collective bargaining agreement) c) An industry level minimum wage (industry collective bargaining) In table 3.1, Tito and Jan Van Ours (008) show the minimum wage in OECD countries and their system. Discuss: Policy Issues a) Should the minimum wage be reduced or increased? b) Is the minimum wage effective in reducing earning inequality and poverty? c) Why does a minimum wage exist? 9

Country Table 3.1 Minimum Wages in OECD Countries (005) Minimum wage to average wage ratio 1 (%) Minimum wage ( per hour) Minimum wage ( per month) PPP Determination 3 Setting Level Coverage 4 Australia 7.5 177 - - 80 Austria CB-L P 95 Belgium 43 6.93 10 CB N 90 Canada 35 4.75 836 L F-P 100 Czech Republic 39 1.58 78 L N 100 Denmark CB - 80 Finland CB N 90 France 5 7.51 13 L N 100 Germany CB - 68 Greece 3.9 578 L N 100 Hungary 38 1.8 5 L N 100 Iceland CB - - Ireland 53 7.43 1308 CB N 100 Italy CB N 80 Japan 40 4.15 731 L P 100 a Korea 7.64 464 - - 10 Luxembourg L N 100 b Netherlands 39 7.30 184 L N 100 c New Zealand 48 4.98 877 L N 5 Poland 40 1.35 37 L N 100 Portugal 53.08 366 L N 100 Slovak Republic L N 100 Spain 40 3.40 599 L N 100 Turkey.78 489 L - 100 United Kingdom 39 6.40 117 L N 100 d United States 31 3.48 613 L N 100 Sources: OECD, LFS Database; ILO Minimum Wage Database. Tito and Jan Van Ours (008) Notes: 1 Minimum wage as percentage of the wage of an average production worker (APW). Real hourly minimum wage in Purchasing Power Parity times monthly number of hours. 3 Indicates whether wage floors are set by statutory rules defined by law or by collective negotiation and the levels of this agreement. CB= collective bargaining; L= set by law; P= provincial; F= federal; N= national. 4 Coverage is equal to 100 if the minimum wage is set by law, or where the coverage of collective agreements is extended to all workers; otherwise it measures the fraction of workers covered by the collective agreements defining contractual minima. a At the end of the 1990s. b For workers over 18 years old. c For workers over 3 years old. d For workers over years old. 10

Reading Lists: *** Bojas (Chapter 3) ** Bosworth et al. (Chapter 8) Hamermesh, Daniel. "The Demand for Labor in the Long Run." Chapter 8 in Handbook of Labor Economics. Vol. 1. Amsterdam, Netherlands: North-Holland, 1986. Tito Boeri and Jan Van Ours (008). The Economics of Imperfect Labor (Chapter Minimum Wage). Princeton University Press. 11

Appendix 3.1 Formal derivation of Labor Demand Function (Silberberg, 1978) Given firm wants to minimize cost of two factor inputs ( X1 and X ) with input prices ( and w ). So the cost of input is C = wx and subject to production function, w1 = Min w X w X λ[ Y f ( X, X )] Y f( X, X ). The Lagrangian equation is 0 1 The first order condition is i= 1 i i I= + +. 1 1 0 1 I a) = 1 = w1 λ f1 b) I I = = w λ X1 X f c) = λ = Y0 f( X1, X) λ We have three unknown variables ( X 1, X, λ ) and we have three conditions, so we can derive for unknown variables which is the function of each input prices and specific output level X1( w1, w, Y 0), X ( w1, w, Y 0), and λ ( w1, w, Y0) The last variable is called shadow price. We have to important notices as following. * * X ( w 1 1, w, Y0) X ( w 1 1, w, Y0) a) The general condition for variables is < 0, > 0, this w1 w condition also presents about the substitutable between two inputs. b) In advanced analysis, we need to check the second order condition to make sure that this problem is the cost minimization problem by check the Bordered Hessian Matrix, λf11 λf1 f1 Δ= λf1 λf f < 0. f f 0 1 Practice Given firm wants to minimize cost of two factor inputs ( X1 and X ) with input prices ρ ρ ρ ( w1 and ). Production function isy0 = f ( X1, X ) = η ax + bx. Show the output 1 level and condition in important notices. w ( ) θ 1