Lecture Notes 5 Labour Market
Jie Chen
1. Introduction
Why there is unemployment? Why while many people are not working, there are many vacancies as well? Why it is often obrved that big shifts in labour demand will lead to large fluctuations in employments but only small changes in the real wage?
The topic of unemployment is a central subject of macroeconomics. There are two main issues: first, what determines the unemployment rate in one economy? Second, what motivates the cyclical behaviour of the labour market? The starting point to understand labour market is that we can not treat the labour market as Walrasian so that labour supply is sufficiently elastic. There are various theories arguing that the labour market may depart from a competitive, textbook market. If the labour market is Walrasian, it should exclude the possibility of unemployment since unemployed workers should immediately bid the wage down until the supply and demand are in balance. If the labour market is not Walrasian, we can start from its non-Walrasian features to understand the possibility of unemployment and its cyclical behaviour.
2. A Generic Efficency-Wage Model
Potential Reasons for Efficiency Wages
The central idea of efficiency-wage models is that there is a benefit as well as a cost to a firm of paying a higher wage. That is to say, paying lower wages may harm a firm. The reasons are:
First and most imply, a higher wage can increa workers’ food consumption, and therefore cau them to be better nourished and more productive. Obviously this possibility is not important in developed economies. Nonetheless, it provides a concrete argument of the advantage of paying a higher wage. Second, a higher wage can increa worker’s effort becau the opportunity cost is higher. This is especially important when the firm cannot monitor the workers perfectly. In a Walrasian labour market, workers are indifferent about losing their jobs, since identical jobs are immediately available. Thus workers in such a labour market have no incentive to exert effort. But if a firm pays more than the market-clearing wage, its jobs become valuable. Workers are then afraid to lo the jobs and willing to exert more efforts.
Third, paying a higher wage can improve worker’s ability when the ability is unobrvable. Offering a higher wage rais the average quality of the applicant pool, and thus rais the average ability of th
e workers the firm hires.
Finally, a high wage can build loyalty among workers and hence induce high effort; converly, a low wage can cau anger, anxiety and desire for revenge, and thereby lead to shirking or sabotage.
Other potential advantages of a higher wage are: it can reduce turnover (and hence recruitment and training costs); it can lower the likelihood that the workers will unionize; it can rai the utility of managers who have some ability to pursue objects other than maximizing profits.
Here, we don’t exclude the possibility to obtain the benefits of a higher wage through other compensation schemes and polices, which may appear cheaper than raising the wage. The nutritional advantage of a higher wage, for example, can be obtained by compensating workers partly in kind (such as providing free lunch). But we can always generalize the compensation in the form of a conventional wage.
Assumptions
坚强的理由歌词
There is a large number of firm, N , of identical competitive firms. The reprentative firm eks to maximize its real profits,
(5.2.1) π = Y − wL
where Y is the firm’s output, w is the real wage that it pays, and L is the amount of labour it hires.宝宝消化不良
花的古诗词
A firm’s output depends both on the number of workers it employs and on their effort. For simplicity we neglect other inputs and assume that labour and effort enter the production function multiplicatively. (5.2.2) Y = F (eL ), F'(•) > 0, F''(•) < 0
where e denotes workers’ effort.
The crucial assumption of efficiency-wage model is that effort depends positively on the wage the firm pays. Thus,
(5.2.3) e = e (w ), e '(•) > 0
Finally, there are −
L identical workers, each of whom supplies 1 unit of labour inelastically.
Analyzing the model
The problem facing the reprentative firm is
(5.2.4) wL )L )w (e (F max w L,−
When the firm is unconstrained, the F.O.C for L and w are
(5.2.5) 0w )w (e )L )w (e ('F =−
(5.2.6) 0L )w (Le')L )w (e ('F =−
Let’s rewrite (5.2.5) as
(5.2.7) )
w (e w )L )w (e ('F = Substituting (5.2.7) into (5.2.6) and dividing both sides by L yields
(5.2.8) 1)
提纲挈领的意思w (e (w)we'=
Equation (5.2.8) states that at the optimum, the elasticity of effort with respect to the wage is 1. Note
that the cost per unit of effective labour is w /e (w ). Since (5.2.8) is F.O.C for the problem of choosing w to minimize the cost of effective, the wage satisfying this condition is known as the efficiency wage .
Equation (5.2.7) states that the firm hires workers until the marginal product of effective labour equals its cost. This is analogous to the condition in a standard labour-demand problem that the firm hires labour up to the point where the marginal product equals the wage.
Equation (5.2.7) and (5.2.8) describes the behaviour of a single firm. It is straightforward to describe the economy-wide equilibrium. Let w t * and L t * denote the values of w and L that satisfy (5.2.7) and (5.2.8) at period t . Since firms are identical, each firm choos the same values of w and L. Total labour demand at period t is therefore NL t *. If labour supply at that time, L t 0, exceeds this amount, firms are unconstrained in their choice of w and then the economy-wide equilibrium wage will be w t * , the number of employed workers will be NL t *, while there will be unemployment appeared as amount of L t S −NL t *. But if however, labour supply at that time, L t S , is less than NL t *, the wage will be bid up to the point where the demand and supply of labour are matched and there will be no unemployment.
Implications
This model shows how unemployment can ri due to the efficiency wage consideration. In addition, the model implies that the real wage is unresponsive to demand shifts. Suppo the demand for labour increas, it will lead to a growth in the employment, L *. Since the efficiency wage, w *, is determined entirely by the properties of the effort function, e (•), there is no reason for firms to adjust their wages. Thus the model provides a candidate explanation of why shifts in labour demand lead to large movements in employment but small changes in the real wage. In addition, the fact that the real wage and effort do not change implies that firm’s labour costs do not change. As a result, in a model with price-tting firms, the incentive to adjust prices is small.
猫怎么写However, the model appears less promising to explain the long run pattern of labour market. The model suggests that although the real wage remains unchanged when the economic growth shifts up the demand for labour, unemployment should trend down. Then eventually, unemployment reaches zero, at which point further increas in demand lead to increas in the real wage. However, in practice we do not obrve a clear pattern of unemployment rate over a long period.
Extensions
With many of the potential sources of efficiency wages, the wage is unlikely to be the only determina
nts of effort. For example, the cost of a worker of being fired depends not just on the wage the job pays, but also on how easy it is to obtain other jobs and on the wages tho jobs pay. Therefore workers are more likely to exert more efforts at a given wage when unemployment is higher, and to exert less effort when the wage paid by other firms is higher. Similar arguments apply to situations where the wage affects effort becau of unobrved ability or feelings of gratitude or anger.
Thus a natural generalization of the effort function, (5.2.3), is
(5.2.9) e = e (w , w a , u ), e 1 (•) > 0, e 2 (•) < 0, e 3 (•) > 0
where w a is the wage paid by other firms and u is the unemployment rate.
Each firm takes w a and u as given. The reprentative firm’s problem is the same as before, except that w a and u now affect the effort function. The F.O.C can therefore be rearranged to obtain
(5.2.10) )u ,w w,(e w )L )u ,w w,(e ('F a a =
(5.2.11) 1)
w (e u),w (w,we a 1= The conditions are analogous as before. Given the assumption that the effort function is sufficiently well behaved so that there is unique optimal w for a given w a and u , equilibrium requires w = w a . The extended version of the model can account for both the abnce of any trend in unemployment over the long run and the fact that shifts in labour demand appear to have large effects on unemployment in the short run. It can
be shown that equilibrium unemployment depends only on the parameters of the effort function; the production function is irrelevant (Romer 2000, pp419).
3.The Shapiro-Stiglitz Model
There is another possibility of efficiency wages: firms have limited monitoring abilities of workers’ efforts; this forces them to provide with an incentive to exert effort. This idea is first developed in Shapiro and Stiglitz (1984). Here just prents an intuitive version of this model:
Think of a worker gets paid at wage w when employed but during employment he needs to decide either exert effort e = e m or exert no effort at all, e =0. Therefore, at any moment the worker must be one of three states: employed and exerting effort (denoted E), employed and not exerting effort (denoted S, for shirking), or unemployed (denoted U). The utilities at each state are denoted as V E,
V S and V U, respectively. Let b denote the exogenous probability that this worker los his job, due to for example the economic business reasons. Let q denote the probability of being fired due to caught in shirking. The discount rate of utility is denoted ρ. Let α be the job acquisition rate of unemployed.
国庆节黑板报图片
Following three conditions should satisfy
(5.3.1) ρV E = (w−e m) −b (V E −V U)
(5.3.2) ρV S = w− (b+q) (V E −V U)
(5.3.3) ρV U = α(V E −V U)女人梦见别人家办丧事
Note that (5.3.1) can be re-expresd as
(5.3.4) V E = [(w−e m) + bV U]/(ρ + b)
The no-shirking condition
The firm choos w so that V E just equals V S:
(5.3.5) V E = V S
Using (5.3.1) and (5.3.2), this is equivalent to,
(5.3.6) (w−e m) −b (V E −V U) = w− (b+q) (V E −V U)
=> V E−V U = e m/q
自我介绍1分钟
This equation implies that firms t wage high enough that workers strictly prefer employment to unemployment. Thus workers earn rent premium. We can e that the size of premium is increasing in the cost of exerting effort and decreasing in firm’s efficacy in detecting shirkers.
Using (5.3.1) and (5.3.3),
(5.3.7) ρ(V E −V U) = (w−e m) − (a + b) (V E −V U)
This expression implies that for V E−V U = e m/q, the wage must be
(5.3.8) w = e m + (a + b + ρ) e m/q
This conditions states that the wage needed to induce effort is increasing in the cost of effort, the eas
e of finding jobs, the rate of job break-up, and the discount rate, and is decreasing in the probability that shirkers are detected.
We would like to express the rate at which the unemployed find jobs in terms of the job break-up rate b, employment per firm L, and the total labor supply L S.
(5.3.9) a = NLb/(L S −NL)
This equation implies that a + b = L S b /(L S −NL ). Thus, we can rewrite (5.3.8) as
(5.3.10) w = e m + [L S b /(L S −NL )+ ρ] e m /q
This is the no-shirking condition , which shows the wage that firms must pay to induce workers to exert effort is an increasing function of employment.
To clo the model, we need the condition where the marginal product of labour to equal the wage, (5.3.11) w )L e ('F e m m =
Extensions
The model implies the existence of equilibrium unemployment and suggests various factors that may influence it. But it also has limitations in that it is too stylized and thus difficult to gauge its quantitative implications. Recently this model has received a number of uful extensions.
First, an important puzzle about the labor market is why, employers tend to layoff workers rather than work-sharing arrangement when their demand for labor drops. Workers are expected to accept a lower wage to work rather being fired. However, modified Shapiro and Stiglitz’s model can be a possible explanation for this puzzle. A reduction in hours of work lowers the surplus that workers are getting from their jobs and will lead to increasing shirking. But layoffs however do not need increa the wage needed.
Second, Bulow and Summers (1986) extends the model to explain the relationship between wage levels and turnover rate. It is also uful to understand stories of occupational gregation , primary and condary jobs and dual labor markets .
Third, firms t high wages to improve the average quality of job applicants, especially when the ability required is not perfectly obrvable.
4. Other Important Models
Implicit contracts model: many jobs involve long-term attachment and considerable firm-specific skills on part of workers. The possibility of long-term relationships implies that the wage does not have to adjust to clear to the labor market each period. It also implies the strong rigidity of real wage.
Insider-outsider model: great insider power reduces employment by raising wage and reducing firm’s labor demand.
Hysteresis model: insiders’ bargaining power is related to the number of insiders. The changes in the number of insiders affect future wage-tting and employment, cau one-time shock to have permanent effects. Such dynamics of employment fluctuation is obrved in Europe (Blanchard and Summers,1986).
S earch and matching model: workers and jobs are highly heterogeneous, workers and firms meet in a decentralized, one-on-one fashion, and engage in a costly process of trying to match up idiosyncratic preferences, skills, and needs. Since this process is not instantaneous, it results in some unemployment.
5. Emprical Applications
Contracting effects on wages and employment; Union effects; Inter-industry wage differences; evidences on wage rigidity; ….
