1、1Chapter 16LABOR MARKETSCopyright 2005 by South-Western,a division of Thomson Learning.All rights reserved.2Allocation of Time Individuals must decide how to allocate the fixed amount of time they have We will initially assume that there are only two uses of an individuals time engaging in market wo
2、rk at a real wage rate of w leisure(nonwork).3Allocation of Time Assume that an individuals utility depends on consumption(c)and hours of leisure(h)utility=U(c,h)In seeking to maximize utility,the individual is bound by two constraintsl+h=24c=wl.4Allocation of Time Combining the two constraints,we g
3、etc=w(24 h)c+wh=24w An individual has a“full income”of 24w may spend the full income either by working(for real income and consumption)or by not working(enjoying leisure)The opportunity cost of leisure is w.5Utility Maximization The individuals problem is to maximize utility subject to the full inco
4、me constraint Setting up the LagrangianL=U(c,h)+(24w c wh)The first-order conditions areL/c=U/c-=0L/h=U/h-=0.6Utility Maximization Dividing the two,we get)for(/chMRSwhUcU To maximize utility,the individual should choose to work that number of hours for which the MRS(of h for c)is equal to w to be a
5、true maximum,the MRS(of h for c)must be diminishing.7Income andSubstitution Effects Both a substitution effect and an income effect occur when w changes when w rises,the price of leisure becomes higher and the individual will choose less leisure because leisure is a normal good,an increase in w lead
6、s to an increase in leisure The income and substitution effects move in opposite directions.8Income andSubstitution EffectsU1U2LeisureConsumptionABCThe substitution effect is the movementfrom point A to point CThe individual chooses less leisure as a result of the increase in wThe income effect is t
7、he movementfrom point C to point Bsubstitution effect income effect.9Income andSubstitution EffectsU1U2LeisureConsumptionABCThe substitution effect is the movementfrom point A to point CThe individual chooses more leisure as a result of the increase in wThe income effect is the movementfrom point C
8、to point Bsubstitution effect income effect.10A Mathematical Analysisof Labor Supply We will start by amending the budget constraint to allow for the possibility of nonlabor incomec=wl+n Maximization of utility subject to this constraint yields identical results as long as n is unaffected by the lab
9、or-leisure choice.11A Mathematical Analysisof Labor Supply The only effect of introducing nonlabor income is that the budget constraint shifts out(or in)in a parallel fashion We can now write the individuals labor supply function as l(w,n)hours worked will depend on both the wage and the amount of n
10、onlabor income since leisure is a normal good,l/n 0,l/w 0 the individual will always choose to spend n on leisure Since leisure costs w per hour,an increase in w means that less leisure can be bought with n.23Cobb-Douglas Labor Supply Note that l/n 0 an increase in nonlabor income allows this person
11、 to buy more leisure income transfer programs are likely to reduce labor supply lump-sum taxes will increase labor supply.24CES Labor Supply Suppose that the utility function ishchcU),(Budget share equations are given by)1(1wnwcsc)1(1wnwwhsh where =/(-1).25CES Labor Supply Solving for leisure gives1
12、wwnwh and111),(wwnwhnwl.26Market Supply Curve for LaborlllwwwsAsBTo derive the market supply curve for labor,we sumthe quantities of labor offered at every wageIndividual Assupply curveIndividual Bssupply curveTotal laborsupply curveSlA*lB*w*l*lA*+lB*=l*.27Market Supply Curve for LaborlllwwwsAsBNote
13、 that at w0,individual B would choose to remain out of the labor forceIndividual Assupply curveIndividual Bssupply curveTotal laborsupply curveSw0As w rises,l rises for two reasons:increased hours of work and increased labor force participation.28Labor Market Equilibrium Equilibrium in the labor mar
14、ket is established through the interactions of individuals labor supply decisions with firms decisions about how much labor to hire.29Labor Market Equilibriumreal wagequantity of laborSDw*l*At w*,the quantity of labor demanded is equal to the quantity of labor suppliedAt any wage above w*,the quanti
15、ty of labor demanded will be less than the quantity of labor suppliedAt any wage below w*,the quantity of labor demanded will be greater than the quantity of labor supplied.30Mandated Benefits A number of new laws have mandated that employers provide special benefits to their workers health insuranc
16、e paid time off minimum severance packages The effects of these mandates depend on how much the employee values the benefit.31Mandated Benefits Suppose that,prior to the mandate,the supply and demand for labor arelS=a+bwlD=c dw Setting lS=lD yields an equilibrium wage ofw*=(c a)/(b+d).32Mandated Ben
17、efits Suppose that the government mandates that all firms provide a benefit to their workers that costs t per unit of labor hired unit labor costs become w+t Suppose also that the benefit has a value of k per unit supplied the net return from employment rises to w+k.33Mandated Benefits Equilibrium i
18、n the labor market then requires thata+b(w+k)=c d(w+t)This means that the net wage isdbdtbkwdbdtbkdbacw*.34Mandated Benefits If workers derive no value from the mandated benefits(k=0),the mandate is just like a tax on employment similar results will occur as long as k t,the new wage falls by more th
19、an the cost of the benefit and the equilibrium level of employment rises.36Wage Variation It is impossible to explain the variation in wages across workers with the tools developed so far we must consider the heterogeneity that exists across workers and the types of jobs they take.37Wage Variation H
20、uman Capital differences in human capital translate into differences in worker productivities workers with greater productivities would be expected to earn higher wages while the investment in human capital is similar to that in physical capital,there are two differences investments are sunk costs o
21、pportunity costs are related to past investments.38Wage Variation Compensating Differentials individuals prefer some jobs to others desirable job characteristics may make a person willing to take a job that pays less than others jobs that are unpleasant or dangerous will require higher wages to attr
22、act workers these differences in wages are termed compensating differentials.39Monopsony in theLabor Market In many situations,the supply curve for an input(l)is not perfectly elastic We will examine the polar case of monopsony,where the firm is the single buyer of the input in question the firm fac
23、es the entire market supply curve to increase its hiring of labor,the firm must pay a higher wage.40Monopsony in theLabor Market The marginal expense(ME)associated with any input is the increase in total costs of that input that results from hiring one more unit if the firm faces an upward-sloping s
24、upply curve for that input,the marginal expense will exceed the market price of the input.41Monopsony in theLabor Market If the total cost of labor is wl,thenlllllwwwME In the competitive case,w/l=0 and MEl=w If w/l 0,MEl w.42Monopsony in theLabor MarketLaborWageSMElDl1Note that the quantity of labo
25、r demanded by this firm falls short of the level that would be hired in a competitive labor market(l*)l*w1w*The wage paid by the firm will also be lower than the competitive level(w*).43Monopsonistic Hiring Suppose that a coal mines workers can dig 2 tons per hour and coal sells for$10 per ton this
26、implies that MRPl=$20 per hour If the coal mine is the only hirer of miners in the local area,it faces a labor supply curve of the forml=50w.44Monopsonistic Hiring The firms wage bill iswl=l2/50 The marginal expense associated with hiring miners isMEl=wl/l=l/25 Setting MEl=MRPl,we find that the opti
27、mal quantity of labor is 500 and the optimal wage is$10.45Labor Unions If association with a union was wholly voluntary,we can assume that every member derives a positive benefit With compulsory membership,we cannot make the same claim even if workers would benefit from the union,they may choose to
28、be“free riders”.46Labor Unions We will assume that the goals of the union are representative of the goals of its members In some ways,we can use a monopoly model to examine unions the union faces a demand curve for labor as the sole supplier,it can choose at which point it will operate this point de
29、pends on the unions goals.47Labor UnionsLaborWageDMRSThe union may wish to maximize the total wage bill(wl).This occurs where MR=0l1 workers will be hired and paid a wage of w1l1w1This choice will create an excess supply of labor.48Labor UnionsLaborWageDMRSThe union may wish to maximize the total ec
30、onomic rent of its employed members This occurs where MR=Sl2 workers will be hired and paid a wage of w2l2w2Again,this will cause an excess supply of labor.49Labor UnionsLaborWageDMRSThe union may wish to maximize the total employment of its members This occurs where D=Sl3 workers will be hired and
31、paid a wage of w3l3w3.50Modeling a Union A monopsonistic hirer of coal miners faces a supply curve ofl=50w Assume that the monopsony has a MRPL curve of the formMRPl=70 0.1l The monopsonist will choose to hire 500 workers at a wage of$10.51Modeling a Union If a union can establish control over labor
32、 supply,other options become possible competitive solution where l=583 and w=$11.66 monopoly solution where l=318 and w=$38.20.52A Union Bargaining Model Suppose a firm and a union engage in a two-stage game first stage:union sets the wage rate its workers will accept second stage:firm chooses its e
33、mployment level.53A Union Bargaining Model This two-stage game can be solved by backward induction The firms second-stage problem is to maximize its profits:=R(l)wl The first-order condition for a maximum isR(l)=w.54A Union Bargaining Model Assuming that l*solves the firms problem,the unions goal is
34、 to choose w to maximize utilityU(w,l)=Uw,l*(w)and the first-order condition for a maximum isU1+U2l=0U1/U2=l.55A Union Bargaining Model This implies that the union should choose w so that its MRS is equal to the slope of the firms labor demand function The result from this game is a Nash equilibrium
35、.56Important Points to Note:A utility-maximizing individual will choose to supply an amount of labor at which the MRS of leisure for consumption is equal to the real wage rate.57Important Points to Note:An increase in the real wage rate creates income and substitution effects that operate in differe
36、nt directions in affecting the quantity of labor supplied this result can be summarized by a Slutsky-type equation much like the one already derived in consumer theory.58Important Points to Note:A competitive labor market will establish an equilibrium real wage rate at which the quantity of labor su
37、pplied by individuals is equal to the quantity demanded by firms.59Important Points to Note:Monopsony power by firms on the demand side of the market will reduce both the quantity of labor hired and the real wage rate as in the monopoly case,there will be a welfare loss.60Important Points to Note:Labor unions can be treated analytically as monopoly suppliers of labor the nature of labor market equilibrium in the presence of unions will depend importantly on the goals the union chooses to pursue.
