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Profit-sharing in a unionised economy with imperfect competition
International Journal of Industrial Organization 6 (1988) 47-57. North-Holland
PROFIT-SHARING IN A UNIONISED ECONOMY IMPERFECT COMPETITION
WITH
Richard JACKMAN London School of Economics and Political Science, London WC2A ZAE, UK
Final version received November 1987 This paper sets up a simple model of a unionised economy and shows that the introduction of profit-sharing unambiguously reduces the unemployment rate. The result arises because unions are assumed to care about the employment of their members but cannot bargain over employment directly. Profit-sharing reduces the perceived cost, in terms of worker income foregone, of increasing employment in the firm. In the economy as a whole, the equilibrium unemployment rate falls.
1. Introduction This paper investigates the effect on the equilibrium rate of unemployment of the introduction of profit-sharing in an economy where wages are determined by trade uni0ns.l The analysis is based on a particular, and perhaps very specific, model but given the assumptions of the model it is shown that profit-sharing unambiguously reduces equilibrium unemployment. The paper has been stimulated by Weitzman’s challenging claim [see Weitzman (1983, 1984, 1985)] that the introduction of profit-sharing is likely to lead to a radical transformation of an economy’s macroeconomic performance. Whereas, he claims, a conventional wage economy (with no profitsharing) is prone to recession and unemployment, a system with protitsharing is likely to enjoy conditions of permanent excess demand for labour. Under profit-sharing, firms ‘will cruise around like vacuum cleaners on wheels, searching in nooks and crannies for extra workers to suck in at existing compensation parameter values’ (1983, p. 777). The basic intuition is quite simple. If workers receive part of their income in the form of a profit share and if, as a result, wages are lower than otherwise the marginal cost of labour to the firm is reduced. Firms would then wish to hire more workers and given a sufficient degree of profitsharing, an excess demand for labour could be generated. These claims for profit-sharing clearly depend on a theory of wage determination which enables one to demonstrate that wages would indeed be ‘By equilibrium, I mean a steady state where expectations are fulfilled and the real variables of the system are in a state of rest, but there is no requirement that markets clear.
48
R. Jackman, Profit-sharing in a unionised economy
lower under profit-sharing than otherwise. In Weitzman’s papers cited above, wages are essentially determined by a competitive labour market modified by ‘the realpolitik of wage capitalism, with its less than perfect labour markets and downward inflexible wages’ (1985, p. 943). To simplify without I think doing injustice to Weitzman, his argument is that in a conventional wage economy, wages are set at the market-clearing level phs a supplement of, say, x percent for realpolitik, etc. The x percent supplement is taken to be unaffected by the introduction of profit-sharing, so that, provided that wages can be reduced by more than x percent the economy moves into an excess demand for labour regime. Since Weitzman believes x percent is quite small [the wage economy operates, he suggests ‘most of the time, hopefully not too far from the full employment boundary’ (1985, p. 943)], a modest degree of profit-sharing could well do the trick. This model of wage determination is widely regarded as insufliciently rigorous. In this paper I develop an earlier note [Jackman (1985)] which modelled the introduction of profit-sharing in long-term equilibrium with wages determined by trade unions. In the meantime, papers by Estrin et al. (1987), Holmlund (1986), Wadhwani (1988), and in particular Weitzman (1987), have addressed similar issues. Section 2 of the paper sets out the assumptions and establishes the equilibrium rate of unemployment in the absence of profit-sharing. Section 3 introduces profit-sharing and establishes the main results. Section 4 offers some concluding thoughts.
2. The model of the wage economy 2.1. Production The economy consists of a large number of identical imperfectly competitive firms. I make the assumption of imperfect competition for three reasons. First, it seems the empirically relevant assumption for most sectors of the economy. Second, it sits more easily with the assumption of union power at the level of the individual firm. Imperfectly competitive firms have market power and may make excess profits (at least temporarily); these factors provide scope for the exercise of union power. Third, Weitzman’s papers assume imperfect competition in the product market and one can better focus on the effects of different models of wage determination if one maintains the same product market assumptions throughout. The assumption of imperfect competition is, however, not crucial. One could assume perfect competition in the product market and industry wide unions setting a common wage rate within each industry. The wageemployment trade-offs facing the industrial unions in this model are much
R. Jackman,
Profit-sharing
in a unionised economy
49
the same as those facing the firm-based unions of the imperfect competition model. What is crucial, however, is that firms face (at least initially) increasing returns to scale, for reasons that will become apparent. While imperfect competition sits well with increasing returns, it is not essential. The exact form of the imperfection competition model follows Weitzman (1985) both for simplicity and to facilitate comparisons. Thus, the firm’s production function is written
(1)
Q=f+Yi, where n, is employment, f is fixed overhead output. Its demand curve is
labour
requirements
and yi is
where a is aggregate demand divided by the number of firms in the economy, pi the firm’s relative price and v] the elasticity of demand it faces in the product market. (We assume firms’ production and sales are the same.) Let the real consumption wage in firm i (i.e., the money wage in firm i deflated by the general price level) be wi. Then if firms maximise their profits (pi =piyi- wini) subject to (1) and (2) it follows that (3)
Pi=(Ul(V-ll))wi=Pwi,
and hence
ni = f + a(pwi) where An which firm’s
,u( _=n/q increase in turn demand
(4)
‘,
- 1) is the firm’s mark-up of prices over variable wage costs. in the wage in firm i will cause it to raise its product price, will lower sales and hence production and employment. The for labour is thus a decreasing function of the wage it faces.
2.2. Bargaining I assume a ‘monopoly union’ model where unions set the wage and firms determine employment given the wage. The first of these assumptions is made for simplicity; allowing bargaining over wages does not alter the qualitative nature of the results. 2 The second is made because in practice firms do not appear to bargain over employment [Oswald (1987)] and in part because in the face of continually changing circumstances it is hard for a union to make credible a threat to hold a firm to any particular predetermined level of employment [Farber (1987)]. ‘See Holmlund alters the relative
(1986). A more complex question, not pursued bargaining power of firms and unions.
here, is whether
profit-sharing
R. Jackman, Profit-sharing in a unionisedeconomy
50
2.3.
Union preferences
Unions are assumed to be concerned both about their members’ wages and about the level of employment. The assumption that unions care about employment is crucial to the intuition underlying our results, and the main difference between this paper and Weitzman (1987). Unions care about employment because higher employment is assumed to increase the probability that any of their members will be in work.3 To be specific, the union is assumed to wish to maximise the one-period expected income of its members. The implicit underlying assumptions of employment by random draw may be regarded as a highly simplified representation of a situation where a firm is subject to a large number of different types of risks each carrying different implications for which workers will be employed and which laid off. If the union in firm i has fi members, its objective function is written Ui=niwi+(Ii-ni)[(l
-U)W+&]
= ni[wi - (1 - u)w - ub] + constants.
(5)
w is the average real wage in the economy as a whole, Z.Jthe unemployment rate in the economy as a whole and b real unemployment benefits. 2.4. Partial equilibrium The union sets the wage by maximising this objective function subject to the firm’s demand for labour [eq. (4)]. The first order condition is (6) The second-order condition requires
a2t+/aw: = Differentiation
D < 0.
of (6) gives
3The counter argument is that, by establishing a ‘last in first out’ convention for redundancies, the majority of senior and established workers in an industry are fully protected from any risk of job loss. Thus a union run by these workers should care only about wages. But this argument is itself based on a number of special assumptions (e.g., that all workers are the same except for seniority). Given the scale of plant closures in the U.K. in recent years it also seems scarcely credible to think that the bulk of workers believe themselves immune from any risk of losing their job.
R. Jackman, Projt-sharing in a unionised economy
51
Hence dwi/du
(7)
However, for the equilibrium of the system as a whole, real aggregate demand per firm is endogenous. For example, from a starting point of above equilibrium unemployment, each union will cut its money wage in an attempt to cut the relative price of its product. Since all unions are doing the same, wages and prices fall generally throughout the ecomony. On the standard assumption of a downward-sloping aggregate demand curve, the fall in the general price level raises real aggregate demand, shifts outwards the demand curves facing individual firms and hence raises employment and restores unemployment to its equilibrium level. In equilibrium, ni=f+yi=f+a=l(l-U), where 1 is the labour force divided by the number of firms. Making use of this expression in (7) gives an approximation for the equilibrium unemployment rate (i.e., neglecting the term in u2),
where C$= f/l, the proportion of overhead to total labour. The above expression holds true for any arbitrary number of firms, though the number of firms will affect the ratio f/l and hence the equilibrium unemployment rate. In the long run, however, firms can enter or leave the economy. If there is free entry in long-run equilibrium firms make zero profits so that 7Li= _Diyi -
Wini =
Wi(clyi
-
= wi[(p - 1)a - f] = 0,
i.e., a = f(q - 1).
f
-
yi)
52
R. Jackman, Profit-sharing in a unionised economy
Hence, from (7), u=l/(q-1)(1-p).
(10)
3. Profit-sharing Now let us assume a change in regime. Specifically, let us consider a law introduced that each firm must pay a given proportion L of its profits to its workers. This proportion il is thus taken as an exogenous policy variable. There is in addition a ‘base wage’, 8, which we assume will be determined by the trade unions, just as was the wage in the wage economy. Total remuneration per worker in firm i is then Zi =
8j +
~(71i/ni).
The union is still interested in its members’ expected incomes, so that its objective function is now written zli= ni[zi - (1 - u)z - ub] + constants,
(5’)
where z is the expected remuneration per worker (taking into account both base wage and profit share) elsewhere in the economy. The firm faces the same production and demand conditions as before [eqs. (2) and (3)], but its retained profits are now
The firm maximises its retained profits taking d and 19,as given, and subject to the constraints (1) and (2), to give Pi =
Mi7
nj = f + a(/&) -4.
(3’)
(4’)
As in the elementary textbook models, the firm ignores the profit-sharing element of remuneration in setting its price and its levels of production and employment. 3.1.
Partial
equilibrium
The union sets the base wages by maximising (5’) subject to (4’). We first require an expression for the impact of changes in the base wage on total remuneration per worker,
R. Jackman, Pro$t-sharing in a unionised economy
53
zi = Bi + /2(7+li) = @i+ ACPi(Yilnil -
eil
= (1 - A)Bi+ ;Ipi(yJni).
Then, Vi = (l - A)n,Bi + lpiyi - ni[( 1 -
U)Z +
=(l -A)niei+n~LBi(ni-f)-ni[(l
ni[[1+
/?(,/A - l)Bi - (1 - u)z - ub] -
ub]
-U)Z+ub]
npj-e,.
The first-order condition is
where we assume the replacement ratio remains the same proportion of worker remuneration as it previously was of wages. Comparison of (6) and (6’) reveals that the two first-order conditions are essentially similar in form. Again we require the second-order condition d2vi/&9~= D’< 0. The impact of a marginal increase in profit-sharing on the base wage is given by total differentiation of (67, ae,lan = n,/D’ < 0.
The economic intuition underlying this result is shown in fig. 1, which depicts the average and marginal revenue product curves facing an imperfectly competitive firm. The firm takes aggregate demand and the prices charged by other firms as given, and the expressions for average and marginal revenue are thus found using eqs. (1) and (2). Assume initially the economy is at a long-run free entry zero profit equilibrium, so that the individual firm is at point E in the figure with wage w, and the employment n,. Under profit-sharing, the marginal revenue curve describes the relationship between the base wage and employment set by the firm. The total remuneration per worker corresponding to any level of employment is now given by a weighted average of marginal and average revenue, the weight given by the degree of profit-sharing. The curve PS describes the locus of employmentremuneration combinations facing the union under some prescribed degree of profit-sharing. The union can then attain its optimal point on this locus, say point A with total remuneration zA and employment nA, by setting the appropriate base wage (0,) from the point on the marginal revenue curve (point A’) directly below point A.
R. Jackman, Profit-sharing in a unionised economy
54 Remuneration
MR
f
n
e
“A
Employment
n. 1
Fig. 1. Wages and employment in the firm.
Note that, in this particular example, both union and firm are better off under profit-sharing. In the absence of profit-sharing, the union’s indifference curve is tangent to the marginal revenue curve at point E. Since the PS locus is flatter than the marginal revenue curve, the union must be able to improve its position by moving to the right of point E. But at all levels of employment to the right of point E the firm makes positive profits. In this example, profit-sharing is a Pareto improving device, which raises the question [Wadhwani (1988)] of why in such a model profit-sharing would not arise spontaneously. I return to this point in the conclusion to the paper, but meanwhile note two qualifications of the result. First, and more obviously, if the original equilibrium is one with positive profits the direct transfer of income from firms to workers at the existing level of employment could well outweigh any gains to firms from higher employment. Second, profit-sharing only has an effect because the PS locus is flatter than the marginal revenue curve. This will generally be the case in a model where firms have (at least initially) increasing returns to scale [as in Weitzman (1985)], but there are many standard models which do not have this feature.4 4The most obvious case, where firms have fixed capital and CobbDouglas production functions is analysed by Holmlund (1986). The importance of fixed costs is also emphasised by Nickel1 (1987).
R. Jackman, ProjZt-sharing in a unionised economy
55
3.2. General equilibrium
While each union attempts to increase employment by cutting its relative wage, in the outcome wages and prices fall in each firm and both real and relative base wages are unaffected. But a lower price level raises aggregate demand which raises employment at any given base wage. Hence unemployment falls until the lower level of unemployment offsets the pressure to cut wages. The general equilibrium solution with profit-sharing is thus established in the same way as with the wage economy described above. Again we can impose the conditions for symmetric equilibrium, which are now Bi= B, clei = pi = 1 (and so 8 = l/p) and hence z = (l-2)/~ + la/(a + f). The first-order condition becomes (7’) This is a complicated expression, but it turns out that some insight can be obtained from examining the special case of 100 percent profit-sharing (A= 1). The economically interesting case of partial profit-sharing can be regarded as a move in the direction of the 100 percent profit-sharing special case.5 For this reason I continue to assume that firms continue to pursue profitmaximisation in determining their employment levels. With 100 percent profit-sharing, eqs. (7’) and (8), together with the assumption I= 1, allow a solution for the equilibrium unemployment rate. Again we approximate (by neglecting terms in u2) and obtain
u-(l-r~)/(l+r(l-~)(l-P)).
(9’)
A comparison of (9’) and (9) offers the unambiguous conclusion that the equilibrium unemployment rate under profit-sharing is bound to be lower than in the wage economy. Eq. (9’) again demonstrates the crucial importance of Weitzman’s technology assumption (4 > 0) to the effectiveness of profit-sharing. It may also be confirmed that, as long as profits are positive, so is the equilibrium unemployment ratea The model provides no support for Weitzman’s claim that a profit-sharing economy will be characterized by a permanent excess demand for labour. Finally, the free entry zero profit condition again allows the computation of an exact solution. Following the same procedure as in section 2, we obtain u=(l -A)/(r-
l)(l -p).
(lo’)
‘Recall LW$aAi 0 for all 1. 6Profits q=l$[(pl)a-f]. Making use of (8) gives xi=@- l)&(l -u--t]# so that, with positive profits, 1 -~Q~Bu. Since the denominator of (9’) is greater than one, the solution value of u must be positive.
56
R. Jackman,
Projt-sharing
in a unionised economy
Comparing (10’) with (lo), the equilibrium unempioyment rate falls in exact proportion to the degree of profit-sharing. In the zero profit case the equilibrium size of firms is determined by technology and the degree of competition (i.e., at point E in fig. 1) and neither of these is changed by profit-sharing. In this case, therefore, profit-sharing increases the number of firms in the new equilibrium. By increasing the number of firms, aggregate unemployment falls and hence the union indifference curves become flatter, thus achieving a tangency with the flatter PS curves. In the extreme case of 100 percent profit-sharing the PS curve becomes identical to the average revenue curve and hence horizontal at point E. Thus the union indifference curve also has to be horizontal which is achieved when the unemployment rate reaches zero. 4. Conclusion In the models discussed in this paper, profit-sharing has both private and social benefits. The private benefits arise because the ‘monopoly union’ assumption of no bargaining over employment leads to an inefficient equilibrium. The social benefit may exceed the private benefit, for example in the free entry case where the private benefits are transitory while the social benefits are permanent. The existence of private benefits nonetheless raises the question why such benefits have not already been exploited by private agreements between firms and unions. To some extent, of course, they have. Blanchflower and Oswald (1987), for example, have found a high incidence of various forms of prolitsharing amongst British firms. Many of these schemes are quite recent, and it seems interesting to ask whether there are features of the contemporary economy that might make profit-sharing more advantageous now than it would have been twenty or a hundred years ago. One conjecture is that in a stable commercial and technological environment even in the absence of bargaining over employment firms and unions are able to use agreements on manning levels and other restrictive practices to grope their way towards an efhcient bargain and to avoid the inefficient underemployment outcome of the monopoly union model. In times of more rapid technical change and greater exposure to competition, these practices entail high efficiency costs because of their inflexibility. Competitive pressures have forced unions to abandon restrictive practices and as a result employment levels are inefficiently low. Profit-sharing offers a way of moving towards a more efficient employment outcome without the inflexibilities and inefficiencies associated with manning agreements and the like. It may perhaps be regarded as an appropriate institutional response to the farreaching technological changes sweeping the world economy some of the implications of which are perhaps not fully recognised even by business or trade union leaders.
R. Jackman, Profit-sharing in a unionised economy
51
References Blanchflower, D. and A. Oswald, 1987, Profit-related pay: Prose discovered?, Discussion paper no. 287 (Centre for Labour Economics. London School of Economics. London). Estrin, S., P. Grout and S. Wadhwani, ‘1987, Profit-sharing and employee share ownership, Economic Policy 4, 13-52. Farber, H., 1987, The analysis of union behaviour, in: 0. Ashenfelter and R. Layard, eds., Handbook of labor economics (North-Holland, Amsterdam). Holmlund, B., 1986, Profit-sharing, wage bargaining and unemployment, Working paper no. 23 (FIEF, Stockholm). Jackman, R.A., 1985, Professor Weitzman and the unions, or why profit sharing is just another form of wage tax: A note, Working paper no. 776 (Centre for Labour Economics, London School of Economics, London). Nickell, S., 1987, Discussion, of Estrin, Grout and Wadhwani, Economic Policy 4, 52-55. Oswald, A., 1987, Efficient contracts are on the labour demand curve: Theory and facts, Discussion paper no. 284 (Centre for Labour Economics, London School of Economics, London). Wadhwani, S., 1988, Profit-sharing as a cure for unemployment: Some doubts, International Journal of Industrial Organization, this issue. Weitzman, M.L., 1983, Some macroeconomic implications of alternative compensation systems, Economic Journal 93,763-783. Weitzman, M.L., 1984, The share economy (Harvard University Press, Cambridge, MA). Weitzman, M.L., 1985, The simple macroeconomics of profit sharing, American Economic Review 75, 937-953. Weitzman, M.L., 1987, Steady state unemployment under profit sharing, Economic Journal 97, 86-105.
PROFIT-SHARING IN A UNIONISED ECONOMY IMPERFECT COMPETITION
WITH
Richard JACKMAN London School of Economics and Political Science, London WC2A ZAE, UK
Final version received November 1987 This paper sets up a simple model of a unionised economy and shows that the introduction of profit-sharing unambiguously reduces the unemployment rate. The result arises because unions are assumed to care about the employment of their members but cannot bargain over employment directly. Profit-sharing reduces the perceived cost, in terms of worker income foregone, of increasing employment in the firm. In the economy as a whole, the equilibrium unemployment rate falls.
1. Introduction This paper investigates the effect on the equilibrium rate of unemployment of the introduction of profit-sharing in an economy where wages are determined by trade uni0ns.l The analysis is based on a particular, and perhaps very specific, model but given the assumptions of the model it is shown that profit-sharing unambiguously reduces equilibrium unemployment. The paper has been stimulated by Weitzman’s challenging claim [see Weitzman (1983, 1984, 1985)] that the introduction of profit-sharing is likely to lead to a radical transformation of an economy’s macroeconomic performance. Whereas, he claims, a conventional wage economy (with no profitsharing) is prone to recession and unemployment, a system with protitsharing is likely to enjoy conditions of permanent excess demand for labour. Under profit-sharing, firms ‘will cruise around like vacuum cleaners on wheels, searching in nooks and crannies for extra workers to suck in at existing compensation parameter values’ (1983, p. 777). The basic intuition is quite simple. If workers receive part of their income in the form of a profit share and if, as a result, wages are lower than otherwise the marginal cost of labour to the firm is reduced. Firms would then wish to hire more workers and given a sufficient degree of profitsharing, an excess demand for labour could be generated. These claims for profit-sharing clearly depend on a theory of wage determination which enables one to demonstrate that wages would indeed be ‘By equilibrium, I mean a steady state where expectations are fulfilled and the real variables of the system are in a state of rest, but there is no requirement that markets clear.
48
R. Jackman, Profit-sharing in a unionised economy
lower under profit-sharing than otherwise. In Weitzman’s papers cited above, wages are essentially determined by a competitive labour market modified by ‘the realpolitik of wage capitalism, with its less than perfect labour markets and downward inflexible wages’ (1985, p. 943). To simplify without I think doing injustice to Weitzman, his argument is that in a conventional wage economy, wages are set at the market-clearing level phs a supplement of, say, x percent for realpolitik, etc. The x percent supplement is taken to be unaffected by the introduction of profit-sharing, so that, provided that wages can be reduced by more than x percent the economy moves into an excess demand for labour regime. Since Weitzman believes x percent is quite small [the wage economy operates, he suggests ‘most of the time, hopefully not too far from the full employment boundary’ (1985, p. 943)], a modest degree of profit-sharing could well do the trick. This model of wage determination is widely regarded as insufliciently rigorous. In this paper I develop an earlier note [Jackman (1985)] which modelled the introduction of profit-sharing in long-term equilibrium with wages determined by trade unions. In the meantime, papers by Estrin et al. (1987), Holmlund (1986), Wadhwani (1988), and in particular Weitzman (1987), have addressed similar issues. Section 2 of the paper sets out the assumptions and establishes the equilibrium rate of unemployment in the absence of profit-sharing. Section 3 introduces profit-sharing and establishes the main results. Section 4 offers some concluding thoughts.
2. The model of the wage economy 2.1. Production The economy consists of a large number of identical imperfectly competitive firms. I make the assumption of imperfect competition for three reasons. First, it seems the empirically relevant assumption for most sectors of the economy. Second, it sits more easily with the assumption of union power at the level of the individual firm. Imperfectly competitive firms have market power and may make excess profits (at least temporarily); these factors provide scope for the exercise of union power. Third, Weitzman’s papers assume imperfect competition in the product market and one can better focus on the effects of different models of wage determination if one maintains the same product market assumptions throughout. The assumption of imperfect competition is, however, not crucial. One could assume perfect competition in the product market and industry wide unions setting a common wage rate within each industry. The wageemployment trade-offs facing the industrial unions in this model are much
R. Jackman,
Profit-sharing
in a unionised economy
49
the same as those facing the firm-based unions of the imperfect competition model. What is crucial, however, is that firms face (at least initially) increasing returns to scale, for reasons that will become apparent. While imperfect competition sits well with increasing returns, it is not essential. The exact form of the imperfection competition model follows Weitzman (1985) both for simplicity and to facilitate comparisons. Thus, the firm’s production function is written
(1)
Q=f+Yi, where n, is employment, f is fixed overhead output. Its demand curve is
labour
requirements
and yi is
where a is aggregate demand divided by the number of firms in the economy, pi the firm’s relative price and v] the elasticity of demand it faces in the product market. (We assume firms’ production and sales are the same.) Let the real consumption wage in firm i (i.e., the money wage in firm i deflated by the general price level) be wi. Then if firms maximise their profits (pi =piyi- wini) subject to (1) and (2) it follows that (3)
Pi=(Ul(V-ll))wi=Pwi,
and hence
ni = f + a(pwi) where An which firm’s
,u( _=n/q increase in turn demand
(4)
‘,
- 1) is the firm’s mark-up of prices over variable wage costs. in the wage in firm i will cause it to raise its product price, will lower sales and hence production and employment. The for labour is thus a decreasing function of the wage it faces.
2.2. Bargaining I assume a ‘monopoly union’ model where unions set the wage and firms determine employment given the wage. The first of these assumptions is made for simplicity; allowing bargaining over wages does not alter the qualitative nature of the results. 2 The second is made because in practice firms do not appear to bargain over employment [Oswald (1987)] and in part because in the face of continually changing circumstances it is hard for a union to make credible a threat to hold a firm to any particular predetermined level of employment [Farber (1987)]. ‘See Holmlund alters the relative
(1986). A more complex question, not pursued bargaining power of firms and unions.
here, is whether
profit-sharing
R. Jackman, Profit-sharing in a unionisedeconomy
50
2.3.
Union preferences
Unions are assumed to be concerned both about their members’ wages and about the level of employment. The assumption that unions care about employment is crucial to the intuition underlying our results, and the main difference between this paper and Weitzman (1987). Unions care about employment because higher employment is assumed to increase the probability that any of their members will be in work.3 To be specific, the union is assumed to wish to maximise the one-period expected income of its members. The implicit underlying assumptions of employment by random draw may be regarded as a highly simplified representation of a situation where a firm is subject to a large number of different types of risks each carrying different implications for which workers will be employed and which laid off. If the union in firm i has fi members, its objective function is written Ui=niwi+(Ii-ni)[(l
-U)W+&]
= ni[wi - (1 - u)w - ub] + constants.
(5)
w is the average real wage in the economy as a whole, Z.Jthe unemployment rate in the economy as a whole and b real unemployment benefits. 2.4. Partial equilibrium The union sets the wage by maximising this objective function subject to the firm’s demand for labour [eq. (4)]. The first order condition is (6) The second-order condition requires
a2t+/aw: = Differentiation
D < 0.
of (6) gives
3The counter argument is that, by establishing a ‘last in first out’ convention for redundancies, the majority of senior and established workers in an industry are fully protected from any risk of job loss. Thus a union run by these workers should care only about wages. But this argument is itself based on a number of special assumptions (e.g., that all workers are the same except for seniority). Given the scale of plant closures in the U.K. in recent years it also seems scarcely credible to think that the bulk of workers believe themselves immune from any risk of losing their job.
R. Jackman, Projt-sharing in a unionised economy
51
Hence dwi/du
(7)
However, for the equilibrium of the system as a whole, real aggregate demand per firm is endogenous. For example, from a starting point of above equilibrium unemployment, each union will cut its money wage in an attempt to cut the relative price of its product. Since all unions are doing the same, wages and prices fall generally throughout the ecomony. On the standard assumption of a downward-sloping aggregate demand curve, the fall in the general price level raises real aggregate demand, shifts outwards the demand curves facing individual firms and hence raises employment and restores unemployment to its equilibrium level. In equilibrium, ni=f+yi=f+a=l(l-U), where 1 is the labour force divided by the number of firms. Making use of this expression in (7) gives an approximation for the equilibrium unemployment rate (i.e., neglecting the term in u2),
where C$= f/l, the proportion of overhead to total labour. The above expression holds true for any arbitrary number of firms, though the number of firms will affect the ratio f/l and hence the equilibrium unemployment rate. In the long run, however, firms can enter or leave the economy. If there is free entry in long-run equilibrium firms make zero profits so that 7Li= _Diyi -
Wini =
Wi(clyi
-
= wi[(p - 1)a - f] = 0,
i.e., a = f(q - 1).
f
-
yi)
52
R. Jackman, Profit-sharing in a unionised economy
Hence, from (7), u=l/(q-1)(1-p).
(10)
3. Profit-sharing Now let us assume a change in regime. Specifically, let us consider a law introduced that each firm must pay a given proportion L of its profits to its workers. This proportion il is thus taken as an exogenous policy variable. There is in addition a ‘base wage’, 8, which we assume will be determined by the trade unions, just as was the wage in the wage economy. Total remuneration per worker in firm i is then Zi =
8j +
~(71i/ni).
The union is still interested in its members’ expected incomes, so that its objective function is now written zli= ni[zi - (1 - u)z - ub] + constants,
(5’)
where z is the expected remuneration per worker (taking into account both base wage and profit share) elsewhere in the economy. The firm faces the same production and demand conditions as before [eqs. (2) and (3)], but its retained profits are now
The firm maximises its retained profits taking d and 19,as given, and subject to the constraints (1) and (2), to give Pi =
Mi7
nj = f + a(/&) -4.
(3’)
(4’)
As in the elementary textbook models, the firm ignores the profit-sharing element of remuneration in setting its price and its levels of production and employment. 3.1.
Partial
equilibrium
The union sets the base wages by maximising (5’) subject to (4’). We first require an expression for the impact of changes in the base wage on total remuneration per worker,
R. Jackman, Pro$t-sharing in a unionised economy
53
zi = Bi + /2(7+li) = @i+ ACPi(Yilnil -
eil
= (1 - A)Bi+ ;Ipi(yJni).
Then, Vi = (l - A)n,Bi + lpiyi - ni[( 1 -
U)Z +
=(l -A)niei+n~LBi(ni-f)-ni[(l
ni[[1+
/?(,/A - l)Bi - (1 - u)z - ub] -
ub]
-U)Z+ub]
npj-e,.
The first-order condition is
where we assume the replacement ratio remains the same proportion of worker remuneration as it previously was of wages. Comparison of (6) and (6’) reveals that the two first-order conditions are essentially similar in form. Again we require the second-order condition d2vi/&9~= D’< 0. The impact of a marginal increase in profit-sharing on the base wage is given by total differentiation of (67, ae,lan = n,/D’ < 0.
The economic intuition underlying this result is shown in fig. 1, which depicts the average and marginal revenue product curves facing an imperfectly competitive firm. The firm takes aggregate demand and the prices charged by other firms as given, and the expressions for average and marginal revenue are thus found using eqs. (1) and (2). Assume initially the economy is at a long-run free entry zero profit equilibrium, so that the individual firm is at point E in the figure with wage w, and the employment n,. Under profit-sharing, the marginal revenue curve describes the relationship between the base wage and employment set by the firm. The total remuneration per worker corresponding to any level of employment is now given by a weighted average of marginal and average revenue, the weight given by the degree of profit-sharing. The curve PS describes the locus of employmentremuneration combinations facing the union under some prescribed degree of profit-sharing. The union can then attain its optimal point on this locus, say point A with total remuneration zA and employment nA, by setting the appropriate base wage (0,) from the point on the marginal revenue curve (point A’) directly below point A.
R. Jackman, Profit-sharing in a unionised economy
54 Remuneration
MR
f
n
e
“A
Employment
n. 1
Fig. 1. Wages and employment in the firm.
Note that, in this particular example, both union and firm are better off under profit-sharing. In the absence of profit-sharing, the union’s indifference curve is tangent to the marginal revenue curve at point E. Since the PS locus is flatter than the marginal revenue curve, the union must be able to improve its position by moving to the right of point E. But at all levels of employment to the right of point E the firm makes positive profits. In this example, profit-sharing is a Pareto improving device, which raises the question [Wadhwani (1988)] of why in such a model profit-sharing would not arise spontaneously. I return to this point in the conclusion to the paper, but meanwhile note two qualifications of the result. First, and more obviously, if the original equilibrium is one with positive profits the direct transfer of income from firms to workers at the existing level of employment could well outweigh any gains to firms from higher employment. Second, profit-sharing only has an effect because the PS locus is flatter than the marginal revenue curve. This will generally be the case in a model where firms have (at least initially) increasing returns to scale [as in Weitzman (1985)], but there are many standard models which do not have this feature.4 4The most obvious case, where firms have fixed capital and CobbDouglas production functions is analysed by Holmlund (1986). The importance of fixed costs is also emphasised by Nickel1 (1987).
R. Jackman, ProjZt-sharing in a unionised economy
55
3.2. General equilibrium
While each union attempts to increase employment by cutting its relative wage, in the outcome wages and prices fall in each firm and both real and relative base wages are unaffected. But a lower price level raises aggregate demand which raises employment at any given base wage. Hence unemployment falls until the lower level of unemployment offsets the pressure to cut wages. The general equilibrium solution with profit-sharing is thus established in the same way as with the wage economy described above. Again we can impose the conditions for symmetric equilibrium, which are now Bi= B, clei = pi = 1 (and so 8 = l/p) and hence z = (l-2)/~ + la/(a + f). The first-order condition becomes (7’) This is a complicated expression, but it turns out that some insight can be obtained from examining the special case of 100 percent profit-sharing (A= 1). The economically interesting case of partial profit-sharing can be regarded as a move in the direction of the 100 percent profit-sharing special case.5 For this reason I continue to assume that firms continue to pursue profitmaximisation in determining their employment levels. With 100 percent profit-sharing, eqs. (7’) and (8), together with the assumption I= 1, allow a solution for the equilibrium unemployment rate. Again we approximate (by neglecting terms in u2) and obtain
u-(l-r~)/(l+r(l-~)(l-P)).
(9’)
A comparison of (9’) and (9) offers the unambiguous conclusion that the equilibrium unemployment rate under profit-sharing is bound to be lower than in the wage economy. Eq. (9’) again demonstrates the crucial importance of Weitzman’s technology assumption (4 > 0) to the effectiveness of profit-sharing. It may also be confirmed that, as long as profits are positive, so is the equilibrium unemployment ratea The model provides no support for Weitzman’s claim that a profit-sharing economy will be characterized by a permanent excess demand for labour. Finally, the free entry zero profit condition again allows the computation of an exact solution. Following the same procedure as in section 2, we obtain u=(l -A)/(r-
l)(l -p).
(lo’)
‘Recall LW$aAi 0 for all 1. 6Profits q=l$[(pl)a-f]. Making use of (8) gives xi=@- l)&(l -u--t]# so that, with positive profits, 1 -~Q~Bu. Since the denominator of (9’) is greater than one, the solution value of u must be positive.
56
R. Jackman,
Projt-sharing
in a unionised economy
Comparing (10’) with (lo), the equilibrium unempioyment rate falls in exact proportion to the degree of profit-sharing. In the zero profit case the equilibrium size of firms is determined by technology and the degree of competition (i.e., at point E in fig. 1) and neither of these is changed by profit-sharing. In this case, therefore, profit-sharing increases the number of firms in the new equilibrium. By increasing the number of firms, aggregate unemployment falls and hence the union indifference curves become flatter, thus achieving a tangency with the flatter PS curves. In the extreme case of 100 percent profit-sharing the PS curve becomes identical to the average revenue curve and hence horizontal at point E. Thus the union indifference curve also has to be horizontal which is achieved when the unemployment rate reaches zero. 4. Conclusion In the models discussed in this paper, profit-sharing has both private and social benefits. The private benefits arise because the ‘monopoly union’ assumption of no bargaining over employment leads to an inefficient equilibrium. The social benefit may exceed the private benefit, for example in the free entry case where the private benefits are transitory while the social benefits are permanent. The existence of private benefits nonetheless raises the question why such benefits have not already been exploited by private agreements between firms and unions. To some extent, of course, they have. Blanchflower and Oswald (1987), for example, have found a high incidence of various forms of prolitsharing amongst British firms. Many of these schemes are quite recent, and it seems interesting to ask whether there are features of the contemporary economy that might make profit-sharing more advantageous now than it would have been twenty or a hundred years ago. One conjecture is that in a stable commercial and technological environment even in the absence of bargaining over employment firms and unions are able to use agreements on manning levels and other restrictive practices to grope their way towards an efhcient bargain and to avoid the inefficient underemployment outcome of the monopoly union model. In times of more rapid technical change and greater exposure to competition, these practices entail high efficiency costs because of their inflexibility. Competitive pressures have forced unions to abandon restrictive practices and as a result employment levels are inefficiently low. Profit-sharing offers a way of moving towards a more efficient employment outcome without the inflexibilities and inefficiencies associated with manning agreements and the like. It may perhaps be regarded as an appropriate institutional response to the farreaching technological changes sweeping the world economy some of the implications of which are perhaps not fully recognised even by business or trade union leaders.
R. Jackman, Profit-sharing in a unionised economy
51
References Blanchflower, D. and A. Oswald, 1987, Profit-related pay: Prose discovered?, Discussion paper no. 287 (Centre for Labour Economics. London School of Economics. London). Estrin, S., P. Grout and S. Wadhwani, ‘1987, Profit-sharing and employee share ownership, Economic Policy 4, 13-52. Farber, H., 1987, The analysis of union behaviour, in: 0. Ashenfelter and R. Layard, eds., Handbook of labor economics (North-Holland, Amsterdam). Holmlund, B., 1986, Profit-sharing, wage bargaining and unemployment, Working paper no. 23 (FIEF, Stockholm). Jackman, R.A., 1985, Professor Weitzman and the unions, or why profit sharing is just another form of wage tax: A note, Working paper no. 776 (Centre for Labour Economics, London School of Economics, London). Nickell, S., 1987, Discussion, of Estrin, Grout and Wadhwani, Economic Policy 4, 52-55. Oswald, A., 1987, Efficient contracts are on the labour demand curve: Theory and facts, Discussion paper no. 284 (Centre for Labour Economics, London School of Economics, London). Wadhwani, S., 1988, Profit-sharing as a cure for unemployment: Some doubts, International Journal of Industrial Organization, this issue. Weitzman, M.L., 1983, Some macroeconomic implications of alternative compensation systems, Economic Journal 93,763-783. Weitzman, M.L., 1984, The share economy (Harvard University Press, Cambridge, MA). Weitzman, M.L., 1985, The simple macroeconomics of profit sharing, American Economic Review 75, 937-953. Weitzman, M.L., 1987, Steady state unemployment under profit sharing, Economic Journal 97, 86-105.