Wages and employment under Uncertain Demand OR。 Martin Neil baily The Review of Economic Studies, Vol. 41, No. 1.(Jan, 1974), pp 37-50 http://inks.jstororg/sici?sici0034-6527%28197401%02941%03a1%3c37%3awaeuud%3e2.0.c0%3b2-4 The Review of Economic Studies is currently published by The review of Economic Studies Ltd Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyouhaveobtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the jsTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at Each copy of any part of a JSTOR transmission must contain the same copyright notice that ap on the screen or printed page of such transmission STOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor. org http://www.jstor.org Thu Mar1522:32472007
Wages and Employment under Uncertain Demand Martin Neil Baily The Review of Economic Studies, Vol. 41, No. 1. (Jan., 1974), pp. 37-50. Stable URL: http://links.jstor.org/sici?sici=0034-6527%28197401%2941%3A1%3C37%3AWAEUUD%3E2.0.CO%3B2-4 The Review of Economic Studies is currently published by The Review of Economic Studies Ltd.. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/resl.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Thu Mar 15 22:32:47 2007
Wages and Employment under Uncertain Demand MARTIN NEIL BAILY This paper examines some implications of two postulates for firms wage and emple policies. The first is that firms, or stockholders, have easier access to capital lower costs or higher returns than do small investors, such as workers. Seco are important mobility and turnover costs incurred when a worker moves from to another The existence of mobility costs means that the labour market is not a perfect market. Each firm is not restricted to taking as given some exogenous market wage, period by period, but has some amount of freedom about the wage strategy it sets. The firm annot choose any wage-employment path it wishes, however, and I shall assume that in the long-run the firm must offer the same(expected) utility as that available elsewhere In the short-run there is a constraint that the wage offer must never be so bad that all the firms workers will quit and incur the mobility cost There are solid grounds for believing that great differences exist between stockholders and workers with regard to capital markets. The majority of stocks are held by very wealthy persons indeed, who also hold almost all the state and local bonds and large pro- portions of the property and other assets. In addition, stockholders are frequently company executives or professionals with greater financial expertise and salaries many times that of the average industrial worker. The worker typically has a rather small net worth. his assets are durable goods and a rather small holding of money. He frequently has consumer redit liabilities outstanding He also has much less knowledge of financial assets and institutions bo, a principal function of capital markets is to allow wealth-holders to diversify their Idings and so reduce the risk of their total portfolios. Stockholders, through their greater wealth and expertise, are much better able to bear risks than are workers. The difference in ability to bear risk between the two groups immediately suggests an opportunity to trade. In deciding what wage-employment strategy to set, the firm will be willing to reduce worker risk. By doing so, the firm is offering a joint product, employment plus an insurance or financial intermediation service. The firm does not do this simply because workers prefer it. Risk-reducing policies are the cheapest and hence most profitable way of attracting any given work-force The choice of a risk-reducing policy by the firm will have an important impact on both the wage set and on employment variations-and hence the probability of unemploy ment. The firm will, in general, wish to reduce the uncertainty of the workers'incomes An important feature of the model presented here is that the tendency of the firm to reduce risk has an asymmetrical effect on the wage strategy and on the employment strategy. 1 First version received February 1973 ersion received May 1973(Eds ond the members of the theory omments and criticisms. i reta In addition, one might feel that stockholders as a class are more willing to bear risk simply because of differences in aversion to risk
REVIEW OF ECONOMIC STUDIES Subject to the( somewhat restrictive) assumptions of the model, one can show that a pre-announced non-stochastic wage strategy will be set by the firm. This is true even though the future path of employment is stochastic and hence there is a positive probability of being laid off. An equivalent result is not true for the employment strategy. The firm will wish to vary the size of its work-force Workers dislike income uncertainty and dislike being laid off. The asymmetry etween the wage and employment strategies arises because when a worker is laid off he receives a non-zero income. To attract workers, the firm must pay a higher wage if there is some positive probability of unemployment than it would if employment were guaranteed. As against this, the firm can save on its wage costs by cutting its work-force during periods of slack product demand. Provided workers have some alternative sources of income when they are laid off, the savings from employment variations will outweigh the higher wage necessary, even though workers are risk averse. The alternative sources of income are from unemployment compensation, from working outside the sector considered nd from the income equivalent of avoiding the disutility of work. Workers dislike lay-offs the question is how much do they dislike them relative to how much the firm saves on its One way of thinking about the alternatives facing the firm is to compare two possible policies, one which implies more employment variation and another which implies more yage variation. Such comparisons are an intuitively appealing approach, but it is not the one followed here, nor is it necessary to make comparisons of this type to prove the desired result. This is discussed further in Section IV(including footnote 2, p. 44) The result, that a pre-announced non-stochastic wage is set by firms, is intended to provide an explanation of the phenomenon of sticky wages. In particular, it suggests an explanation for the fact that the real wage does not seem to adjust in the short-run to clear the labour market There is a question of what is meant by sticky wages. In the formal model presented there are a number of rather strong assumptions which allow a clear result. The wage rate is strictly non-stochastic, pre-announced. It does not respond at all to fluctuations in demand. To reach this conclusion firms are assumed to be risk neutral, maximizing the present value of expected profits. Workers are risk averse, and do not operate in capital markets. These assumptions are intended to reflect the asymmetry between workers and capitalists that i described, but clearly they are strong. In Sections VI and VII the consequences of changing these assumptions are discussed . A SINGLE FIRM AND UNCERTAIN DEMAND I shall discuss first the case of a single firm which has a stochastic demand for its product. The simplest assumption to make is that the firm is a perfect competitor in the product market. It is a price-taker and sets quantity as the decision variable. I shall consider in this model a finite time-horizon of T periods Tle assumption 1. The price of the firm's product in period t, P, is a random variable P are jointly distributed and are bounded above and below. pEQ,(t=l,., T) If the joint density function of the prices is F(Pi,.,Pr), then there is a prior or un- conditional expectation of p, defined by E(p)=,… F(p1,…,pr)dlp (1) examining what determines price. One could assume a fluctuating world price. Also ption is not essential a fluctuating demand curve would serve as well
BAILY WAGES AND EMPLOYMENT The unsubscripted expectations operator will be used to denote this expected value, i.e. when the state variables from 1, ., T(the prices Pi,..., Pr in the above case)are unknown The operator Er will denote the expected value of a variable when state variables up to period t are known. It is the conditional expectation defined in the usual way It is convenient to take the technology and capital equipment to be constant. It is doubtful if any essential features of the results depend upon this, but a number of awkward Assumption 2. The firms output in period t is x, and is given by x1=9(L)g′>0,g"<0, where L, is employment in period t 3 Let a worker's income in period t be The values (,., yr), which depend upon the wage and employment prospects of the worker, will in general be stochastic variables. Each worker's decision function is of the form given by Assumption 3. A worker making a decision in t-I which affects his path of income yu., yr will maximize Vt-1 given by U()(1+p) where U>0, U"<O and p is a constant The assumption implies all workers are alike in their preferences. This makes life much easier, as I shall comment later, but obviously is pretty strong. The firm and industry are assumed small relative to the rest of the economy. The overall price level is constant ects in the rest of the are given exogenously. There may, in fact, be many choices open to a worker who is not employed with the firm we are analysing. But just as one assumes an equilibrium wage prevailing in the economy in the standard textbook theory, I shall assume a given(possibly stochastic) path of income available elsewhere Assumption 4. The path of income available to a worker elsewhere in the economy is yi,..., yT. The y2 are stochastic and may be jointly distributed Consider a worker who does join the firm we are analysing. If he is employed in criod t his income is simply the firm wage wr. If there were no mobility or information costs in this economy the firm would have no real choice. It would pay w,= yo in each riod as a perfect competitor in the labour market. more realistically, however, although a firm may face a long-run horizontal supply of labour, this is not true period by period because of information and mobility costs The fact that mobility costs exist has been well recognized in the literature. - In ctual practice the cost of changing jobs may be quite different from one worker to another. Some workers may have many jobs open to them in the same location and have a general skill needed in many industries. There would seem to be many workers, however, for whom changing jobs would involve considerable costs. These might be moving expenses search expenses, income foregone and possible retraining. For almost all firms there are significant costs involved when a new worker joins the company. He may have to be fROTh us. E ( p) is t te the ite ral r Feo eh conditional density of Pr, defined as the ratio of the integral 3 The length of the period can be taken as the order of er Is as an analysis of very short-run fluctuations and overtime
REVIEW OF ECONOMIC STUDIES given some on-the-job training or equivalently his productivity may be lower during the first few periods after he is hired, as he learns by doing It is hard to do justice to the full complexity of the factors described, particularly differences between workers at different skill levels and different geographical locations Instead the following simple parametrization is used Assumption 5. If a worker leaves the firm where he has been seeking work and moves to another firm in period t he suffers a mobility cost in periodτ given by C≥0τ≥t The mobility cost experienced by the worker he pays directly. The firm's turnover cost is assumed to take the form of a reduced wage for the first few periods after the worker ns the firm I L FIRM WAGE AND EMPLOYMENT STRATEGIES Once we include mobility and information costs the single firm has a measure of freedom about the wage and employment policies it can set. To model this the distributions of the state variables are assumed known and the firm announces at time zero a strategy with respect to wages and employment. The strategy will consist of two decision rules con- ditional on the values of the state variables, which are the prices Pi,., Pr and the incomes available elsewhere yi, .. yT2 A particular(and not in fact very likely) strategy would be to choose a constant level of employment and let the wage always equal the marginal product times price in each period. The announced strategy can be defined by two sets of mappings from the state variables into employment and wages Assumption 6. The firm announces at time zero a strategy s defined by two sets of mappings(a1,…,ar)and(b1,…,br) such that L=a1(P1,…,2y3,…,y9) (4) y,…,y) These mappings could be analytic functions or perhaps integral equations where L, and w,depend on some function of the expected values. This assumption is very weak in the ense that the class of possible strategies is very general. The announced strategy together with the known distribution of the variables mean that the worker can evaluate the expected utility of seeking work at the firm The knowledge requirements of this formulation are quite considerable but the stylized model makes the framework seem more unrealistic than it actually Workers learly do not make complex calculations upon announced joint probability distributions They are, however, concerned with the past behaviour of firms, how frequently lay-offs occur and what is the likely path of wages. Firms are concerned about their reputations as employers, suggesting that short-sighted decisions do not necessarily imply long-run profit maximization. In terms of the model, they stick to an implicit strategy since it is in their long run- interests to do so. In addition, the conclusions of this paper suggest that the wage strategy will be one of setting a non-stochastic pre-announced wage path; this is the strategy which reduces the knowledge requirements and simplifies the calculation of This section deals with an easy case. Employment variations are excluded so that the wage strategy is considered given a constant employment level. This keeps everything revious periods in prefcrence toha ntew thaknawnworkeh. hence the ost expaerehced iven dene far as the firm is concerned, the product price and incomes available elsewhere have exogenously