Efficiency Wages in Weitzman’s Share Economy

DAVID LEVINE‘k

Weitzman proposes widespread profit or revenue sharing as a way of guaranteeing both v e y low levels of equilibrium unemployment and increased stability in the face of aggregate shocks. The benefits of a share economy come from the subsidy that current workers pay to marginal workers. I n an efficiency-wage model, the wage subsidy paid by current workers costs the firm as much in lower productivity as it gains from lower labor costs. There is, therefore, neither a reduction of the equilibrium unemployment rate nor a necessa y increase in macroeconomic stability when the share economy is introduced.

IN PROPOSING PROFIT OR REVENUE SHARING as a solution to stagflation, Martin Weitzman (1984; 1985; 1987) claims that a share economy would lead to high and stable employment, low inflation, and constant competition among firms to hire new workers. His work focuses attention on the critical problems of persistent unemployment and of costly macroeconomic fluctuations, and it contributes to our understanding of monopolistic competition and of the role of increasing returns to scale. More importantly, his policy proposal for tax incentives to encourage profit sharing has been enacted into law in the United Kingdom and has been seriously considered by politicians in the United States.

Unfortunately, Weitzman’s policy program completely neglects both the effects that changes in pay have on productivity and the role that unemployment plays as a worker discipline device. Models that take into account efficiency-wage considerations, such as firms’ difficulties in getting

* School of Business Administration, University of California at Berkeley. Acknowledgements: Ramon Caminal, Bill Dickens, Jennifer Halpern, Steve Marglin, Andy Newman, Juliet Schor, Larry Summers, and Marty Weitzman were very helpful. They are responsible neither for the conclusions nor for any remaining errors.

INDUSTRIAL RELATIONS, Vol. 28, No. 3 (Fall 1989). c 1989 Regents of the University of California 0019/86~6/S9i~01~Zli$10.00

32 1

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workers to work, have been used to explain the equilibrium rate of unemployment. In this paper, by introducing such efficiency-wage considerations as variable work effort and turnover, I show how such models alter not only the equilibrium rate of unemployment, but also the stability of Weitzman’s share proposal. Weitzman’s predictions concerning a reduction in the equilibrium unemployment rate are not supported by the results of the efficiency-wage models estimated here; nor is there evidence that the share system would be more stable than the corresponding wage system.

Efficiency-Wage Models Efficiency-wage models provide a natural explanation for a high rate of

unemployment in equilibrium.2 Weitzman (1987) argues that a share economy lowers the equilibrium rate of unemployment by putting firms in an equilibrium with excess demand for labor, thus reducing frictional and structural unemployment. The share economy also reduces the power of insiders to push up the wage above the competitive level, and it thus reduces any unemployment they might cause.3 Weitzman (1986) further shows that in the face of shocks to aggregate demand, aggregate supply, and labor supply, the share economy vastly outperforms the wage economy.

The benefits of a share economy come from the subsidy that current workers pay to marginal workers. In an efficiency-wage model, the wage subsidy paid by current workers costs the firm as much in lower productivity as it gains from lower labor costs, so firms are not in excess demand for labor in equilibrium. Firms will not want to cut the pay of current workers even when there are unemployed workers. Thus, there is no reduction in

’ Estrin, Grout, and Wadhwani (1987) discuss, and both Elbaum and Stoft (1988) and Koford and Miller (1987) formally derive results similar to those in this paper. The two formal models make stronger assumptions about the shape of the productivity function, and their conclusions are more favorable for the share economy. Other authors have noted that Weitzman’s results are sensitive to his assumptions. Cooper (1988) stresses that partial coverage by the share economy can be destabilizing, and Nordhaus (1988) emphasizes the importance of imperfectly mobile labor. ’ Efficiency-wage models of nominal wage rigidities, Weitzman’s other main concern, are

being developed, although they are not yet fully worked out. Efficiency-wage microfoundations for nominal wage rigidity are based on workers’ norms (Solow, 1980; Akerlof, 1984), asynchronous wage setting (Stiglitz, 1986), or nearly optimal behavior (Akerlof and Yellen, 1985). ’ Weitzman (1987) notes that in an efficiency-wage model, the equilibrium of the share

economy loses its excess demand for labor property. He also claims that “the out-of- equilibrium behavior of a profit-sharing system, when pay parameters are sticky, yields less unemployment than a wage system.” (ibid., p. 104, n. 12) In the formalization of his model used in this paper, it is ambiguous whether the share system is more or less stable than the corresponding wage system.

Efficiency Wages in a Share Economy / 323

the equilibrium rate of unemployment from lower frictional unemployment, and the multipliers on aggregate demand and on labor supply shocks remain approximately the same as in a wage economy, while aggregate supply shocks are magnified. For different reasons, insiders do not lose all of their power over wages.

The productivity function. The novel feature of this paper is the efficiency wage hypothesis: the assumption that the productivity of workers depends on their wages. Numerous variants of efficiency-wage theories have been developed. Higher wages (1) increase the cost of job loss for workers dismissed for providing low effort; (2) reduce the level of costly quits (Salop, 1979); (3) lower the delays and costs in searching for new hires (Lang, 1986); (4) make strikes more costly for workers; (5) reduce the scope for wage gains from strikes; (6) increase the cost of absenteeism; (7) reduce the benefits to workers of spending time on the current job looking for a new job; (8) increase the costs of being caught stealing; (9) lead to a workforce with higher average levels of unobservable human capital (Weiss, 1980); (10) are more likely to be perceived as fair by workers (Akerlof, 1984); (11) often raise morale; (12) forestall union formation or labor strife (Dickens, 1986); and (13) lead to Hicks’ “quiet life” for managers of satisficing monopolies. (Katz [ 19871 and Yellen [ 19841 survey this literature.)

This paper focuses on the incentive variant of efficiency wages. In particular, assume an effort function such that effort depends on the cost to workers of losing their jobs. The cost of job loss in turn depends on the expected duration of unemployment and the difference between the current real wage and the unemployment benefit and the wage expected at the next job. Intuitively, if being fired will lead to a long spell of unemployment, or if unemployment benefits are far below current pay, or if other jobs pay far less than the current job, then workers will work very hard. With identical workers and firms, an exogenously set unemployment benefit, and the assumption that the duration of unemployment is positively associated with the rate of unemployment, in the steady state, effort is a function of real total pay (W/P) and unemployment rates (u),

(1) e = e (W/P, u) e , > O e , > O

e,, < 0 e,, < 0 sign(e12) indefinite

I will also write the short-run effort function as in (l), where the arguments are measured as deviations from long-run values. The effort function will be less responsive to short-run changes in parameter values than to long-

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run changes. The meaning of the effort function should be clear from the context .4

The size of the short-run derivatives depends on what is held constant; if workers do not observe changes in wages at other firms, then e, will be larger than if all wages are observable.

Weitzman’s Model The results concerning the relative stability of wage and share systems

are shown formally using a variant of the model in Weitzman (1985), augmenting the production function with the productivity function described above. Neither Weitzman’s results nor my critique are dependent on the specific model presented here: In a variety of Keynesian models, the beneficial effects of the share economy are eliminated if efficiency wages are being paid.

The aggregate production function has constant returns to effective labor:

Q = g e L

where Q is output, L is labor demand, g is a productivity parameter, and e is the efficiency of labor discussed above.

(3) Q = a A + b M/P where A is autonomous spending, M is outside money, P is the price index, and a and b are the standard Keynesian multipliers.

Assume that labor is inelastically supplied, and normalize aggregate labor supply to 1. This implies that the unemployment rate (u) is:

The demand side of the model is an IS-LM reduced form:

(4) u - 1 - L

Long-run equilibrium for a wage economy. Profit maximization implies that prices are a mark-up over marginal cost, and that firms pay efficiency wages. Assume that the elasticity of demand is constant, so the mark-up factor (m) is an exogenous parameter. In a wage economy, total compensation W consists solely of a money wage w. These assumptions imply:

and

‘ The primary results of this paper are unaltered by the type of efficiency wages being paid, as long as the productivity function retains the functional form of equation (1) .

Efficiency Wages in a Share Economy / 325

de W dW e

= 1

The efficiency wage equation (6) implicitly defines the wage that minimizes the firm’s wage per efficiency unit of labor (w/e). Equations (1) through (6) can be solved implicitly for the equilibrium values of Q, P, L, e, and w. With a sufficiently elastic efficiency function, there is unemployment in equilibrium; if a firm lowers wages 1 per cent in the face of unemployment, productivity declines by more than 1 per cent.5

Share vs. wage payment schemes. The formula for W, total pay, is different in a wage than in a share economy. In the share economy, total pay is an increasing function of the firm’s profits or revenues. In a revenue-sharing economy, total compensation is a base wage (wo) plus a share (w,) times total revenues (R = PQ) per worker.

(7) The exercise that Weitzman performs takes w, as set exogenously,

perhaps by custom or by tax incentives. He then contrasts the short-run macroeconomic performance of the wage and share economies, when the other pay parameter (w or wo) is held fixed.

W = wo + w,R/L 0 < w, < 1

Long-run equilibrium for a share economy. In a wage economy, the long- run equilibrium wage is equal to the marginal revenue product of labor (MRPL) at full employment. A share firm paying the same level of total compensation at full employment would have a lower marginal cost of labor (since w,, < w), but it would nevertheless be unwilling to change its pay parameters. Any increase in the base wage w,, made in order to attract new workers would also increase pay for all current workers, leading to a reduction in profits.

Firms are thus in a state of constant excess demand for labor at the current pay parameters. The MRPL is less than the average revenue product, so when a firm hires an extra worker, revenue per worker declines. Thus, part of the marginal worker’s compensation comes from the pockets of other workers.

In the case with no efficiency wage effects, share firms are in an equilibrium similar to that of monopolistically competitive firms that would like to sell more at the going price (price is greater than marginal cost) but are unwilling

Shapiro and Stiglitz (1984), Bowles (1985), Stoft (1983), and Gintis and Ishikawa (1987) all give examples of equilibria with unemployment, using specific functional forms for the effort function (or for the utility functions and technology).

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to expand output. In the share economy, wo is less than the MRPL, but firms are unwilling to raise their pay in order to attract new workers.

In the model with efficiency wages, the wage and share economies have identical long-run equilibria, but for different reasons. Consider a single firm when the unemployment rate and other firms’ total compensation are the same in the share as in the corresponding long-run wage economy’s equilibrium. This firm has no incentive either to set a different level of total compensation or to hire a different number of workers than the corresponding firm in the wage economy.

The efficiency wage equation says that a level of pay lower than that of the corresponding wage firm leads to lower effort, higher turnover, etc. and, therefore, to increased costs. This cost increase is greater than any savings from the pay reduction. Given the same level of unemployment, share firms find it optimal to keep the same pay level as their wage-firm counterparts, thereby maintaining the same cost of job loss.

In the share economy with no efficiency wage effects, firms are always in a state of excess demand because current workers subsidize new ones. In the efficiency wage case, the cost of marginal workers is not lowered to the base wage wo, since firms care about the wage of inframarginal workers. By increasing employment, the firm lowers average revenues. In turn, pay for current workers declines, reducing their productivity. According to the efficiency wage equation, the reduction in efficiency by current workers is greater than or equal to the value of the subsidy to marginal workers. In long-run equilibrium, therefore, firms paying efficiency wages in the share economy have the same marginal cost of labor as firms in the corresponding wage economy.

In summary, when firms pay efficiency wages, the share and wage economies reach the same equilibrium. The share economy with efficiency wages differs from the case Weitzman analyzes because firms do not have excess demand for labor in equilibrium. This latter result has important implications for the short-run behavior of the model.

The Share Economy and the Equilibrium Rate of Unemployment

Weitzman (1984; 1987) has shown that in a full-employment world, share and wage economies reach the same long-run equilibrium. He has noted that the share economy reduces the equilibrium unemployment rate if it is caused either by frictions after local shocks that lead to layoffs, or by insiders pushing up wages above the competitive level. These beneficial effects may not be present when efficiency wages are being paid.

Efficiency Wages in a Share Economy / 327

Equilibrium and fn’ctional unemployment. Weitzman’s (1984) analysis of a share economy and frictional unemployment suggests that firm- or industry- specific negative shocks in general do not result in layoffs, since a marginal worker’s revenue product is greater than hidher cost to the firm. When the shock is too big for a firm to keep all of its workers, any workers who leave or are laid off will be hired by other firms that are still in a state of excess demand for labor.

In the share economy with efficiency wages, since firms are not in a state of excess demand for labor, they lay off workers as soon as there is a decline in demand. Furthermore, other firms do not race to hire the newly laid off workers, and the frictional level of unemployment is not necessarily lower than in a wage economy.

Insider resistance to outsiders. Weitzman (1987) shows how the share economy can lower unemployment by reducing the market power of insiders vis-a-vis outsiders. If pay parameters are set so that pay is above that of similar workers, then the firm will find it profit-maximizing to hire the workers attracted to the supra-competitive wage and to expand output. The firm will keep doing this until it has diluted revenues per worker enough so that it is paying a competitive level of total compensation and can no longer attract new workers (Weitzman, 1984; 1987).

In motivating his model of insiders and outsiders, Weitzman (1987) refers to numerous sources of insider power. He specifically cites Lindbeck and Snower’s ( 1986) observation that insiders may choose not to cooperate with new hires, to have poor personal relations with them, and to engage in disruptive activities in order to stop the firm from hiring outsiders (see also Summers, 1986).

When resistance by insiders lowers the effective labor that new employees provide, the favorable benefits of the share system are reduced. As in the efficiency wage model, the marginal wage subsidy provided by insiders is counteracted by a fall in the productivity of labor. In the efficiency wage model, it is the current workers’ productivity that falls; in Lindbeck and Snower’s version, it is the marginal workers who have lower productivity.

Short-Run Equilibrium

Multipliers without efficiency wage effects. In the short run, wages and pay parameters (w, and w,) are fixed; thus, output is determined by the aggregate demand equation (3). The economy has textbook Keynesian output and employment multipliers:

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(8) dQ dA = a

(9) dL a dA- ge

-

The novel result of Weitzman’s (1985) article comes from the short-run behavior of the share firm. Even with fixed-pay parameters, there is no unemployment after a modest negative shock. After a modest demand shock lowers workers’ marginal revenue products, the marginal worker is still worth more to the firm than the base wage, wo. Thus, the response to negative aggregate demand shocks is to remain at full employment, and the multipliers for output and employment are zero.

Multipliers in a wage economy with efficiency wages. The multipliers are different if the productivity level of workers varies with wages. A negative shock that lowers aggregate demand and employment will raise productivity in a wage economy by raising the cost of job loss. This higher productivity then has implications for the price level and the level of real pay.

Linearizing the system (2), (3), (4), (6) , and (8) around equilibrium yields the output and employment multipliers when there are efficiency wage effects. Derivatives of the effort function are for short-run deviations from the long-run wage level.

a 1 Pe - PLe, -we,

a

L I

dL

The terms [Pe - PL e, - we,] and [e - e,W/P] capture the feedbacks from higher effort leading to lower prices and thus to higher pay, which again increases effort. I assume that these feedbacks are well behaved, and that the system is stable.

The output multiplier is smaller with efficiency wages because effort rises and marginal costs decline following an increase in unemployment. Lower marginal costs imply lower prices, higher real balances (M/P), and higher aggregate demand. The employment multiplier is larger with efficiency wages-with higher unemployment and effort, fewer workers are needed to produce a given level of output.

Efficiency Wages in a Share Economy / 329

Multipliers in a share economy with efficiency wages. The marginal product of labor (MP,) is lower in the share economy than in the corresponding wage economy, and it is also lower than in Weitzman’s fixed-productivity case. A new worker lowers the average revenue per worker, thus lowering all of the current workers’ pay slightly (by wl d(R/L)/dL per current worker). This lower pay then lowers productivity for current workers.

The change in average revenue when a new worker is added is the difference between the marginal and average revenue product of labor. The marginal revenue product of labor in turn is marginal revenue (P/m) times the marginal product of labor. This gives:

Solving the firm’s profit maximization problem gives the optimal price: m wo/(l -wl)

As in equation (9, price is a mark-up over the cost of hiring a new worker divided by the productivity of the marginal worker.

As before, we linearize the model around equilibrium and solve for the output and employment multipliers. After tedious algebra, the results are:

where

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I [(A - 1)Pg c2 + [d(R/L)/dL]P gw1c4 cg = 1 - Pgelwl

(Assume 1 - elwlg > 0 and 1 - Pelwlg > 0 for stability.) Each term has an interpretation: cz, c4, and c6 measure the responsiveness

of e, el, and [Ld(WL)/dL] to changes in L; c3, c5, and c7 measure the corresponding responsivenesses to changes in P. It is not possible to determine whether the multipliers in the share economy are larger or smaller than those in the wage economy (equations 10 and 11). In the share firm, a negative shock cuts revenues and therefore pay. It might appear that since a share economy automatically cuts total pay after a negative shock, and since total pay will eventually need to fall to restore long-run equilibrium, a share economy will yield less unemployment than a wage system.

This intuition ignores the difference between the average cost of labor (total pay), and the marginal cost of effective labor. The whole point of the share economy is to uncouple these two variables. The fall in revenue affects the former, while the firm's hiring decision depends only on the latter.

The decline in pay after a negative shock reduces labor productivity, but it has no effect on the marginal cost of labor ( ~ d ( 1 - w ~ ) ) . Without a fall in marginal cost, there is no reduction in prices, and thus no expansion of output occurs. The fall in productivity does imply an expansion in labor demand since more workers are needed to produce a given level of output.

Inspection of equation (12) shows that any increase of el or [Ld(R/L)/dL] will increase marginal costs and therefore raise prices and contract demand (compared to a wage economy). We will examine how each of these is affected by an increase in the share fraction wl.

The curvature of the effort function implies diminishing returns to pay (ell < 0). Thus, after a decline in pay, el (the responsiveness of effort to total pay) rises. A larger w1 implies a larger decline in pay, and thus a larger increase in el. When el is large, the marginal product of labor is low, since

Efficiency Wages in a Share Economy I 331

the productivity of old workers is more responsive to the cut in pay caused by a new worker. Firms will tend to raise prices and to reduce labor demand, destabilizing both output and employment.

There is also a change in el after a negative shock raises unemployment. When there is a longer expected duration of unemployment, any increase in total pay is considered more important because a fired worker would be losing more dollars for a longer period of unemployment. For example, when the expected duration of unemployment doubles from six months to one year, paying $1 per hour more than the unemployment benefit becomes approximately twice as important. Thus, firms see a larger response of productivity to pay and will have an incentive to reduce labor demand in order to increase revenue per worker. This will tend to amplify the employment multiplier .6

There is a counteracting effect. After a negative shock, the firm could observe that workers are being motivated by unemployment and will therefore not lower their productivity much, even if wages are lowered further. The firm will then expand its own employment compared with a wage firm, even at the expense of cutting total pay, to take advantage of the high productivity workers are providing. This effect is the only one present if firms need to maintain a specific level of the cost of job loss, and if the rise in unemployment raises the cost of job loss more than the fall in revenues lowers it.

When prices fall after a negative shock, ld(R/L)/dLI declines, which reduces the responsiveness of current workers’ pay to the hiring of new workers. On the other hand, any increase in effort following an increase in unemployment increases ld(R/L)/dLI and acts to lower the marginal product of labor, increase prices, and destabilize output.

Summary of effects. The most important effect is arguably the fall in effort that follows the cut in pay. Since there is a fall in pay similar to the fall in productivity, there are lesser effects on prices, and therefore on output. Most of the second-order effects work to increase the output multiplier compared to the corresponding wage economy, but the relative sizes cannot be determined. The fall in productivity acts to increase labor demand.

Responses to Aggregate Supply Shocks and Labor Supply

Aggregate supply shocks. While the response of the share economy is similar

In the case where productivity is a linear function of the cost of job loss, this effect is always dominant.

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to that of a wage economy in the face of aggregate demand shocks, the share economy magnifies the effects of aggregate supply shocks. In the framework used in this paper, a negative supply shock can be heuristically modeled as a decrease in g, the labor productivity parameter in the production function (2). (See Weitzman, 1985.)

The results of a supply shock are similar in a wage or share economy with fixed effort, and in the share economy with fixed wages. When there is an increase in costs in a wage economy with constant efficiency, there is a decrease in the maximum level of output for the economy and an increase in the labor needed to produce any level of output. There is also an increase in prices that leads to a decline in real balances and aggregate demand. As long as the effect of lower productivity on labor demand dominates the contractionary effect from rising prices, unemployment will not rise after a productivity shock.

In the share economy with efficiency wages, a negative productivity shock leads to a fall in compensation and a decrease in effort. This further fall in effort from the reduction in pay magnifies the shock’s effects of higher prices, lower output, and higher employment. There are also effects on el,, d(R/L)/dL, and e, that can magnify or reduce the shock.

Labor supply shocks. In the short run of a wage system with rigid pay, an increase in labor supply does not affect aggregate demand and thus will raise unemployment. In a share system with no efficiency wage effects, labor’s marginal revenue product is above its marginal cost to the firm, so any increase in labor supply is immediately utilized.

With efficiency wages and either fixed wages or the share economy, an increased labor supply is not immediately utilized. The increase in unemployment leads to a rise in effort; in the share economy, this implies changes in total pay, e,,, and d(R/L)/dL. As with the demand multipliers, the share economy can be slightly more or less stable than the corresponding wage economy.

Conclusions Weitzman proposes widespread profit or revenue sharing as a way of

guaranteeing both very low levels of equilibrium unemployment and enormous stability in the face of aggregate shocks. In a share economy, when a new worker is hired, the revenue or profit pie increases; and the pie is sliced into more pieces. When firms are maximizing profits, the latter effect is always larger than the former effect (since the marginal revenue product of labor is below the average revenue of labor). Thus, when a new worker is hired, pay for all current workers falls.

Efficiency Wages in a Share Economy I 333

worker is hired, pay for all current workers falls. This reduction of pay for current workers acts as a wage subsidy for

marginal workers. Weitzman claims that with this subsidy the economy will reach full employment and shocks will have no effect on output or employment. All of the beneficial effects of the share economy come from this reduction in the pay of current workers when new workers are hired.

In an efficiency-wage model, worker effort and turnover depend upon the total compensation that the firm pays. The firm thus sets total pay so that profits decrease when pay is lowered. Firms do not want to decrease total pay since work effort will decline and turnover will rise.

In this situation, the subsidy paid by current workers in a share economy costs the firm as much in lower productivity as it gains from lower wages. Therefore, there is no reduction of the equilibrium unemployment rate when the share economy is introduced, and the stability of the economy remains approximately the same as that of the corresponding wage economy.

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