Minimum Wages, Employment and. Monopsonistic Competition

Transcription

1 Minimum Wages, Employment and Monopsonistic Competition V. Bhaskar Ted To University of Essex Bureau of Laor Statistics August 2003 Astract We set out a model of monopsonistic competition, where each employer competes equally with every other employer. The employment effects of minimum wages depend on the degree of distortion in the laor market. If fixed costs per firm are high then the laor market is relatively non-competitive and minimum wages increase employment. Conversely, low fixed costs make for a more competitive laor market where minimum wages reduce employment. This contrasts with the results of a Salop style model with localized employer competition where a minimum wage unamiguously raises employment. We also find that the welfare effect of a small minimum wage is unamiguously positive. Keywords: monopsonistic competition, laor theory, minimum wages, monopsony JEL classification codes: J23, J42, L13 We thank Greg Kurtzon, Randy Verrugge and seminar participants at the 2003 Western Economic Association meeting in Denver for helpful comments and suggestions. V. Bhaskar is grateful to the Economic and Social Research Council, UK for its support under research grant L The views expressed are not to e attriuted to the Bureau of Laor Statistics or to the Department of Laor.

2 Minimum Wages, Employment and Monopsonistic Competition Astract We set out a model of monopsonistic competition, where each employer competes equally with every other employer. The employment effects of minimum wages depend on the degree of distortion in the laor market. If fixed costs per firm are high then the laor market is relatively non-competitive and minimum wages increase employment. Conversely, low fixed costs make for a more competitive laor market where minimum wages reduce employment. This contrasts with the results of a Salop style model with localized employer competition where a minimum wage unamiguously raises employment. We also find that the welfare effect of a small minimum wage is unamiguously positive. Keywords: monopsonistic competition, laor theory, minimum wages, monopsony JEL classification codes: J23, J42, L13

3 1 Introduction The view that laor markets are imperfectly competitive, with employers possessing some market power, has gained prominence in recent years. Empirical studies have come up with many findings, such as the positive employment effects of minimum wages Card and Krueger, 1995), that are inconsistent with models of perfect competition. Two alternative approaches to modelling imperfect competition are search models Burdett and Mortensen, 1998) and models of monopsonistic competition Bhaskar and To, 1999). 1 In this paper, we provide a simple model of monopsonistic competition in the laor market. Workers have heterogeneous preferences over employer characteristics, and each employer competes equally with every other employer in seeking to attract workers. This may e contrasted with the circle model of monopsonistic competition in Bhaskar and To 1999), where each employer effectively competes only with her two immediate neighors. Our model may e viewed as a Dixit-Stiglitz type model, since each firm competes with every other firm, and when the numer of firms is large, yields estalishment laor supply curves with approximately constant wage elasticity. However, we emphasize that it is not a representative worker model rather, it is ased on heterogenous workers, each of whom chooses to work for at most one employer. Our model is an adaptation of Sattinger s 1984) model of consumer choice to the laor market. This adaptation results in some technical difficulties, since a realistic model of laor markets must allow for the possiility that some workers may e unemployed. We use this model to study the effects of a minimum wage upon employment in a free entry equilirium. As in other models of monopsonistic competition, a minimum wage has two conflicting effects. First, it has the standard monopsony effect wherey a moder- 1 Bhaskar et al. 2002) provide a discussion of the empirical evidence, and argue that models of oligopsony/monopsonistic competition provide a parsimonious explanation for much of this evidence. Manning 2002) is a textook on laor economics with an approach centered on models with employer market power.

4 ately chosen minimum wage reduces the marginal cost of laor, increasing laor supplied to individual firms. Second, it has a first order negative effect on profits, causing firms to exit, thus reducing employment. We find that the net effect of a small minimum wage can e either positive or negative, depending upon parameter values. If fixed costs are high, so that the equilirium numer of firms is small, and the laor market is relatively non-competitive, then a small minimum wage increases employment. On the other hand, if fixed costs are low, so that the laor market is relatively competitive, a minimum wage reduces employment. In other words, the employment effect of a minimum wage is related to the extent to which the laor market is distorted. These results may e contrasted with those otained in the context of the circle model of the laor market used y Bhaskar and To 1999). Walsh 2001) shows that in the circle model, the effect of a small minimum wage upon employment is unamiguously positive. 2 Interestingly, under some parameter configurations with the current model, minimum wages can increase employment even when the laor market has many employers or when the estalishment level laor supply elasticity is high. This is of importance ecause one common argument is that even if there are laor market distortions, these distortions ecome insignificant in industries like fast food, where many employers compete for workers. Our results show that even when a laor market appears to e competitive, minimum wages can increase employment. Finally, extensive numerical computations suggest that welfare unamiguously increases when a minimum wage is imposed just aove the equilirium wage rate. That is, the welfare gain due to increased wages outweighs the welfare loss resulting from the reduction of jo choices due to employer exit and from potential) disemployment. 2 Walsh corrects and clarifies the formulation in Bhaskar and To. Although Walsh shows that it is possile to modify the circle model to produce negative employment effects, these modifications require somewhat unreasonale parameter restrictions. Further, these restrictions do not have an intuitive interpretation in terms of the extent of laor market distortions. 2

5 2 The Model To ensure that laor supply is imperfectly elastic, we assume that different jos have different non-wage characteristics. These include the jo specification, hours of work, distance of the firm from the worker s home, the social environment in the workplace, etc. The importance of non-wage characteristics has een recognized in the theory of compensating differentials, which is a theory of vertical differentiation. Some jos are good while other jos are ad, and wage differentials compensate workers for these differences in characteristics. We assume that jos are horizontally differentiated so that workers have heterogenous preferences over these characteristics. McCue and Reed 1996) provide survey evidence of horizontal heterogeneity in worker preferences. Heterogeneous preferences over non-wage characteristics ensures that each employer has market power in wage setting, even if it competes with many other employers. Our modelling of the laor market is inspired y Sattinger s 1984) model of the product market. The key difference is that we allow for unemployment home production ). Let us suppose that the individual worker has the following utility function: U = W 1 γ L γ 1) where W is the worker s jo-adjusted income defined elow) and L is time spent at leisure activities. Let firms e indexed y j {1, 2,..., n}. Each firm offers a jo that has characteristics that differ from its rivals and workers have heterogeneous preferences over these characteristics. We shall also assume that the alternative to outside employment is home production which we denote as jo 0. The worker s preferences over this set of n + 1 alternatives are parameterized y the n + 1 vector r whose generic component r j is a measure of the worker s disutility from activity j. In particular, a larger value of r j reduces the value of working for employer j, 3

6 at the offered wage w j. More specifically, we model this as follows. If a worker works h j hours for wage w j and has disutility r j for working at jo j then her disutility-adjusted earnings from jo j are w j h j /r j and her total jo-disutility-adjusted income from all jos is W = n j=0 w jh j /r j. Workers have likes and dislikes over jo characteristics and an unpleasant jo i.e., one for which r j is large) reduces the pleasure that a worker gets from her income. We assume that the return to home production,, is exogenously specified. If L is the total amount of leisure time availale then she enjoys L = L n j=0 h j hours of leisure. Taking the first order conditions yield: U = 1 γ) w ) γ ) 1 γ j L W γ 0 2) h j r j W L for j = 0, 1,..., n. For generic values of r, this condition will hold with equality for exactly one employer and with strict inequality for all other employers. This implies that individual workers will work for at most one employer. Let j = arg max k {w k /r k } represent the employer for whom the first order condition holds with equality. Solving equation 2), the worker s laor supply to employer j is h j = 1 γ) L and for all employers k j is h k = 0. If j happens to e home production, the worker will e unemployed. Suppose that there is a unit mass of workers and that for each worker, her disutilities, r j, are independently and identically distriuted with a continuous distriution function F and corresponding proaility density function f. The conditional proaility given r j that the worker prefers employer j to employer k is 1 F r j w k /w j ). Thus the conditional proaility given r j that the worker prefers employer j to all other employers and to staying at home is k j [1 F r jw k /w j )]. Multiplying individual laor supply y this 4

7 proaility and integrating over all r j yields laor supply to firm j L j = 1 γ) Ls j 3) where s j is firm j s share of total laor supplied either for work or for home production) and is given y: [ s j = 1 F k j rj w k w j )] fr j )dr j. 4) For the case when all firms ut j offer wage w j, this ecomes: s j = [ 1 F rj w j w j )] n 1 [ 1 F rj w j )] fr j )dr j. 5) Suppose that F is the Pareto distriution so that F x) = 1 /x) a and fx) = a a /x a+1 where a, > 0 and x. Consider employer j s laor supply when all rival employers offer wage w j and w j, w j >. The equation for firm j s share of laor supplied can e written as: [ ) a ] [ ) a ) an 1) ) ] a ) an 1) w j 1 w j + 1 w j n w j w j w j + 1 n+1 w j s j = [ ) an 1) ) an 1) ) ] a ) an 1) ) a 1 wj n w j w j w j + 1 n+1 w j w j ) a w j if w j w j if w j w j 6a) For the case when w j, w j <, s j can e written as: s j = 1 2 [ ) a ) a ) a ] ) a ) a wj w j w j w j + 1 w j w j n+1 w j if w j w j ) an 1) ). 6) a wj wj w j if w j w j 1 n+1 These expressions are rather complicated, however, for the case with symmetric wages i.e., w j = w j = w), the estalishment level elasticity of laor supply is given y the 5

8 following, relatively simple expression: an+1)n 1)+ w ) an ) ε = n+1) w ) if w w an 0. 7) an if w This is a weakly decreasing, continuous function of w and is ounded y an 1) and an. That is, as the market wage rate rises, the elasticity of laor supply falls. This is what should e expected since if the wage is high relative to the return from home production, home production ecomes a less attractive sustitute. Moreover, ε is an increasing function of the numer of firms, n. Differentiating ε with respect to n we get: ε n = an+1) 2 2n+1) w ) an +n+1) w ) an ln w ) an ) if w w n+1 w ) an ) ) a if w Consider the case when w. Since 2n+1)x+n+1)x ln x is strictly decreasing for all x 1, it follows that the minimum value of numerator is an 2. Thus we can conclude that ε/ n > 0. As should e expected, estalishment level laor supply ecomes more elastic as the numer of employers increases. In particular we have the desirale result that as the numer of firms, n, grows large, the laor market approaches perfect competition with estalishment laor supply curves ecoming perfectly infinitely) elastic. For a fixed numer of firms in a symmetric equilirium, wages will e set according to the rule, wn) = φ ε 1 + ε 9) where φ is the marginal revenue product of laor. 3 Thus wages are a strictly increasing 3 The assumption, that the marginal revenue product of laor is constant, is not really necessary. If oth capital and laor are required, and there is constant returns to scale and a competitive capital market, Bhaskar and To 1999) show that when the capital laor ratio adjusts optimally, the net revenue product 6

9 function of the laor supply elasticity. This implies that there is a unique, symmetric equilirium wage, w n), satisfying equations 7) and 9). 4 Moreover, since laor supply elasticity rises with the numer of employers, equilirium wages do so as well. Given the equilirium wage rate, w n), the equilirium share of laor per firm is given y s n) = 1 n [ 1 1 n+1 w n) ) an ] + 1 n+1 w n)) an if w n) w n) ) a if w n). 10) As should e expected, if w n) = then each of the n + 1 activities garners an equal share of laor supplied i.e., s n) = 1/n + 1). The equilirium profits of the firm are given y π n) = φ w n))l n) 11) where L n) = 1 γ) Ls n). This is decreasing in the numer of firms for two reasons. First, laor supply per firm is decreasing in n, and second, the wage is also higher with n. To see the former, examine equation 13). The numerator is a scalar multiple of the numerator of 8) and y similar argument we can show that ε n < 0. Since laor supply falls and wages rise with n, profits must fall with n. The free entry numer of firms is an n such that π n ) c = 0 where c is the fixed cost of production. 3 The effects of a minimum wage When a minimum wage is imposed, estalishment level employment rises due to the monopsony effect, ut total employment may fall ecause of induced firm exit. Recall is constant. 4 As noted y Sattinger 1984), there may well exist other, asymmetric equiliria. For tractaility, we focus only on the symmetric equilirium. 7

10 that estalishment level employment is given y: Ln) = 1 γ) Ls j where s j is as given in equations 6a) and 6). Let E denote total employment, Ln. In order to work out the employment effect of a minimum wage under free entry, we utilize the following decomposition, due to Walsh 2001): de dw = Ln ε ε ) j m w ε n where ε is the elasticity of firm laor supply with respect to the own wage, ε j is the elasticity with respect to competitor firm wages, and ε n is the elasticity with respect to n. The own wage elasticity of laor supply is given y equation 7). From the equation for laor supply, ε j and ε n are as follows: ε n = ε j = an 1) 12) n+1)2 2n+1) w ) an +n+1) w ) an ln w ) an n+1){n+1 n w ) an } if w n+1 if w. 13) It is straightforward to show that there exist parameter values such that the employment effect of a minimum wage is positive. For example, consider parameter values such that w. 5 In this case, ε = an and ε n = n/n + 1), so that de dw m = L w a That is, if the equilirium wage is sufficiently small relative to the return from home 5 Since the equilirium wage, w, is ounded aove y φ, we may choose φ so that w is smaller than. 8

11 production, a minimum wage increases employment. Unfortunately, general conditions for negative employment effects are not possile ecause of the non-linearity of the equilirium system of equations. For this reason, we numerically compute the equiliria for a wide range of parameters to estalish that minimum wages can lower employment. We present a selection of these results in Tale 1. These results show that fixing other parameter values, the minimum wage effect depends upon the fixed cost c. When fixed costs are relatively low, a minimum wage reduces employment. When the fixed cost is large, minimum wages increase employment. Since fixed costs are the factor which prevent perfect competition from occurring, our results have an intuitive interpretation minimum wages raise employment when the laor market is distorted, ut reduce employment when the market is relatively competitive. Note however that even for laor markets that appear to e highly competitive to a casual oserver e.g., n > 850 or ε > 90), a minimum wage can still have a positive employment effect. That is, even if a laor market appears, prima facie, to e competitive, a minimum wage may increase employment under monopsonistic competition. 3.1 Welfare Effects Let us now consider the utility of an individual with disutilities r = r 0, r 1,... r n ). Suppose the equilirium wage profile is w =, w 1,... w n ). This worker will spend 1 γ) L hours at activity j where j = arg max w j /r j and γ L hours at leisure activities. Her indirect utility can e written as: Uw, r) = K max wj r j ) 1 γ 14) 9

12 Tale 1: Employment and welfare effects a c n w l ε employment effect welfare effect Notes: The employment and welfare effects are elasticities with respect to the minimum wage. For these computations, we fix various scale parameters as follows: γ = 0.5, = 1, φ = 1 and L = 1. These numeric results were computed using a FORTRAN program employing the non-linear equation solver from the Argonne National Laoratory s collection of optimization suroutines, MINPACK-1. 10

13 where K = 1 γ) 1 γ γ γ L. For symmetric wage profiles where wj = w for j = 1, 2,... n, indirect utility can e rewritten as: Ux e, x u ) = K max{x e, x u }) 1 γ 15) where x e = max{w/r j } n j=1 and x u = /r 0. Each ratio, x j = w j /r j has cumulative distriution 1 F w j /x j ). The random variale x e is an order statistic with cumulative distriution [1 F w/x)] n. Thus x = max{x e, x u } is a random variale that has cumulative distriution Gx) = [1 F w/x)] n [1 F /x)]. Differentiating yields density function: gx) = nw[ 1 F )] w n 1 [ x 1 F w0 )] x f w ) [ x + w0 1 F w )] n x f w0 ) x 16) x 2 Average utility is equal to a typical worker s expected utility and can therefore e written as EU = K x 1 γ gx)dx. 17) As efore, consider the case when F is the Pareto distriution. If w then we can write g as gx) = an+1) x an x x w x w ) an ) a x if x ) an if x w. 18) If w then g can e written as: gx) = an+1) x a x ) an x ) a x if x w w ). 19) a x if w x 11

14 Thus EU = K an+1) an+1)+1 γ an+1) an+1)+1 γ w0 ) an w0 w w ) a w an an+1 γ ) 1 γ + ) 1 γ + a a+1 γ [ w [ w0 ) 1 γ w0 ) an w0 w ) 1 γ w ) a w ) ] 1 γ ) ] 1 γ if w 20) if w where n = n and w = w n ). Given the complexity of this expression, analytic welfare calculations are not possile. However, numeric computations can e used to evaluate the welfare consequences of a minimum wage. Some of these results are presented in Tale 1. What appears to e true is that for this model, assuming that the r j are distriuted Pareto, minimum wages unamiguously increase welfare. Since as is common with monopsonistic competition, minimum wages have opposing welfare effects increasing wages vs declining jo choices and potentially declining employment), we do not elieve that this unamiguous welfare result is roust to modelling changes or even changes in the assumed distriution of the r j. Nevertheless, it is useful to oserve that welfare can increase even as employment falls so that the literature s preoccupation with the employment effects of minimum wages may e misguided. 4 Concluding Comments We have developed a simple model of monopsonistic competition, where each employer competes equally with all other employers for workers. This is similar to a Dixit-Stiglitz style model, although it is ased on heterogeneous workers, each of whom only works for one employer. We find that the effect of a small, inding minimum wage is amiguous: it will e positive if the laor market is relatively distorted, and negative otherwise. One point worth emphasizing is that even for laor markets that to all appearances is competitive, a moderately chosen minimum wage can increase employment. For ex- 12

15 ample laor market concentration might e considered a useful statistic for judging the competitiveness of the laor market. However, as we have demonstrated, even for quite large n, a minimum wage can still increase employment. References Bhaskar, V., A. Manning and T. To, Oligopsony and Monopsonistic Competition in Laor Markets, Journal of Economic Perspectives, 162): , Bhaskar, V. and T. To, Minimum Wages for Ronald McDonald Monopsonies: A Theory of Monopsonistic Competition, Economic Journal, 109: , Burdett, K. and D. T. Mortensen, Wage Differentials, Employer Size, and Unemployment, International Economic Review, 392): , Card, D. and A. B. Krueger, Myth and Measurement: The New Economics of the Minimum Wage, Princeton, New Jersey: Princeton University Press, Manning, A., Monopsony in Motion, London, UK: London School of Economics Press, McCue, K. and W. R. Reed, New Empirical Evidence on Worker Willingness to Pay for Jo Attriutes, Southern Economic Journal, 623): , Sattinger, M., Value of an Additional Firm in Monopolistic Competition, Review of Economic Studies, 51: , Walsh, F., Comment on: Minimum Wages for Ronald McDonald Monopsonies: A Theory of Monopsonistic Competition, Economic Journal, ): ,