Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

(7.49)

7.50)

- tA ), and 3 ds/s we also have that:

(7.51)

age, so that workers bear the rates are both increased, the and the net wage rate falls by orkers bear more than 100%

ts about the labour market es, unemployment shows a t ( more so than the business s due to a rise in long-term find it hard to exit the pool ig data sets reveals that there unemployment rate differs

• 1 anatory role for dissimilar flow into unemployment) is Finally, the unemployment ices, and sexes.

early chapters of this book lized facts. For example, the vis-a-vis white collar workers Ts, skilled and unskilled, and is binding for the latter type market for unskilled workers.

binding minimum wage.

—Es) so that 1471'r — WR = (1 — tm)E W

Chapter 7: A Closer Look at the Labour Market

Abolishing the minimum wage would solve the unemployment problem because the unskilled wage rate would fall to clear the market.

The standard model is also quite useful to study the impact of a variety of taxes on the aggregate labour market. We consider a wide array of taxes, namely a progressive system of (labour) income taxes, a payroll tax, as well as a tax on consumption. In the standard model with flexible wages, taxes affect equilibrium wages and employment but do not give rise to unemployment. Ceteris paribus the average income tax rate, an increase in the marginal income tax chokes off labour supply and leads to lower employment, a higher producer wage, and a lower consumer wage. On the other hand, if the marginal tax is kept unchanged and the average tax is increased then labour supply increases (because leisure is a normal good), both producer and consumer wages fall, and employment rises. Simple expressions can be derived which show which side of the labour market ends up paying the tax (so-called tax incidence).

If the consumer wage is assumed to be fixed above the market clearing level then employment is demand determined and unemployment emerges. Now, the effects of the tax system on employment and the unemployment rate can be traced. Raising the marginal income tax or lowering the average tax both lead to a reduction in the unemployment rate. In the former case labour demand (and hence employment) is unchanged but labour supply drops off. In the latter case labour demand (and employment) is boosted and labour supply falls.

Although the standard labour demand model is thus quite flexible there is one stylized fact for which it cannot easily furnish a credible explanation, namely the fact that the real wage appears to be rather rigid in the face of productivity and demand shocks. The standard model can be made consistent with this rigidity by assuming a highly elastic labour supply curve but that assumption is grossly at odds with microeconometric evidence. For that reason, a number of economists have started to look for alternative reasons for real wage rigidity.

A highly influential answer is provided by the theory of efficiency wages. The basic hypothesis underlying this theory is that the net productivity of workers is a function of the wage rate they are paid. A famous example of efficiency wages is provided by the case of Henry Ford, who paid very high wages and achieved a very high level of productivity as a result. The implications of the efficiency—wage hypothesis are quite far-reaching. First, the law of demand and supply is no longer relevant. Even if there is excess supply of labour, the firm may not lower its wage rate because the adverse effect on its workers' productivity may outweigh the beneficial reduction in the wage bill. Furthermore, the law of one price is also repealed. Since the effort—wage relationship may differ across industries, wages may also differ for otherwise identical workers.

In the final part of this chapter we develop a simple model in which efficiency wages lead to real wage rigidity and a positive equilibrium unemployment rate. Crucial determinants of the equilibrium unemployment rate are the replacement rate (the ratio of unemployment benefits and the after-tax wage rate), the so-called

185

The Foundation of Modern Macroeconomics

leap-frogging coefficient (summarizing the productivity-enhancing effect of high wages), and the degree of progressivity of the income tax system.

Further Reading

All serious students of the macroeconomic labour market should take notice of Layard, Nickell, and Jackman (1991) and Bean (1994). Key readings on the efficiency wage theory are collected in Akerlof and Yellen (1986). Katz (1986), Stiglitz (1986), and Weiss (1991) present very good surveys. Hoel (1990) studies the impact of progressive income taxes in an efficiency wage model. On dual labour markets, see Saint-Paul (1992) and Bulow and Summers (1986). Good surveys on the implicit contract literature are Azariadis (1981), Azariadis and Stiglitz (1983), and Rosen (1985). For a good survey article on tax incidence in macro models, see Kotlikoff and Summers (1987).

Trade Ur

Labour 11

The purpose of this c;.‘

1.What models of unemployment'

2.What do we mear about the labour

3.How can so-calle(

4.How does taxi: , 01

5.How do trade uni

8.1 Some Mode

The typical layman's 4,11 trade unions are wages, and hence are : this section we eval corium models of tra,

- esentative union

.oppose that the re the following form:

L

V(w, L) —= (—

where N is the (fixt..., r..,L.mbers of the union

186

rity-enhancing effect of h i tax system.

should take notice of Layard, p on the efficiency wage theon- tiglitz (1986), and Weiss (1991) t of progressive income taxes in t-Paul (1992) and Bulow and literature are Azariadis (1981), I survey article on tax incidence

I

F

Trade Unions and the

Labour Market

ne purpose of this chapter is to discuss the following issues:

1.What models of trade union behaviour exist, and what do they predict about unemployment?

2.What do we mean by corporatism and how can it explain some of the stylized facts about the labour market?

3.How can so-called insider-outsider models be used to explain hysteresis?

4.How does taxation affect unemployment in trade union models?

5.How do trade unions affect investment by firms?

8.1Some Models of Trade Union Behaviour

The typical layman's sentiment about trade unions probably runs as follows. Powerful trade unions are just like monopolists. They sell labour dearly, cause high real wages, and hence are really to blame for low employment and high unemployment. In this section we evaluate this sentiment within the context of several partial equilibrium models of trade union behaviour. The typical setting is one where a single representative union interacts with a single representative firm.

Suppose that the representative trade union has a utility function V(w, L) with the following form:

V(w,L) Nu(w) ± [1 — C--d )]u(B),

(8.1)

where N is the (fixed) number of union members, L is the number of employed members of the union (L < N), w is the real wage rate, B is the pecuniary value

AF(L, R),

The Foundation of Modern Macroeconomics

of being unemployed (referred to as the unemployment benefit), and u(.) is the indirect utility function of the representative union member. 1 Equation (8.1) can be interpreted in two ways. First, L/N can be interpreted as the probability that a union member will be employed, in which case the union cares about the expected utility of its representative member. This is the probabilistic interpretation. The second, utilitarian, interpretation runs as follows. The union calculates the average utility attained by its employed and unemployed members, and takes that as its index of performance.

The representative firm is modelled in the standard fashion. The production function is Y = where Y is output, K is the fixed capital stock, A is a productivity index, and F(., .) features constant returns to scale and positive but diminishing marginal labour productivity (FL > 0 > FLL ). The (short-run) real profit function is defined as:

(w, L) AF(L, R) – wL. (8.2)

All models discussed in this section can be solved graphically. In order to do so, however, a number of graphical schedules must be derived. First, the labour demand schedule is obtained by finding all (w, L) combinations for which profit is maximized by choice of L. Formally, we have irL 07r /81, = 0, which yields:

ITL = AFL (L, i() – w = 0 LD = LD (w, A, k), (8.3)

where Ow < 0, LA > 0, and LRD 0. The labour demand curve is downward sloping in (w, L) space.

The second graphical device that is needed is the iso-profit curve. It represents the combinations of w and L for which profits attain a given level. It can be interpreted as the firm's indifference curve. The slope of an iso-profit curve can be determined in the usual fashion:

thr = 0:	7r,vdw + irLdL = 0	(—dw)	= _ 71,	(8.4)
		dL chr =0	7r w

We know from equation (8.2) that 7rw = –L < 0, so that the slope of an iso-profit line is determined by the sign of irL. But 71, AFL – w, and FLL < 0, so that 771 is positive for a low employment level, becomes zero (at the profit-maximizing point), and then turns negative as employment increases further. Hence, in terms of Figure 8.1, the iso-profit curves are upward sloping to the left of the labour demand schedule, downward sloping to the right of labour demand, and attain a maximum for points on the labour demand schedule. In Figure 8.1 a number of iso-profit curves have been drawn, each associated with a different level of profit. Obviously, for a given

1 An indirect utility function differs from the usual, direct, utility function in that it depends on prices and income rather than on quantities. The two are intricately linked, however. Indeed, the indirect utility function is obtained by substituting the optimal quantity choices of the household back into the direct utility function.

w

Figure

w

Figure

4,vel of employment d:r I dw = 71-‘,„ < 0. Hen

• 7 labour curve the Trade union behavi

be derived concerns 1

.pply any workers Hence, in terms of I le BB. Furthermor,, current membership. f :1 employment I. e

188

189

tent benefit), and u(.) is the nember. 1 Equation (8.1) can :d as the probability that a don cares about the expected ebilistic interpretation. The union calculates the average 'milers, and takes that as its

ishion. The production func- - tal stock, A is a productivity rid positive but diminishing rt-run) real profit function is

(8.2)

-- hically. In order to do so, red. First, the labour demand which profit is maximized

ch yields:

(8.3)

curve is downward sloping

-oft curve. It represents the n level. It can be interpreted curve can be determined

(8.4)

the slope of an iso-profit line ;LL < 0, so that 7ri, is positive )fit-maximizing point), and ce, in terms of Figure 8.1, le labour demand schedule, —:yin a maximum for points Per of iso-profit curves have rofit. Obviously, for a given

ly function in that it depends on v linked, however. Indeed, the ntity choices of the household

Chapter 8: Trade Unions and the Labour Market

w

no

nz

LD

L

Figure 8.1. The iso-profit locus and labour demand

w

N L

Figure 8.2. Indifference curves of the union

level of employment L, the level of profit is increased if the wage rate falls, i.e. thr/dw = 7rw < 0. Hence, the level of profit increases the further down the demand for labour curve the firm operates, i.e. 70 < Trl < 72.

Trade union behaviour can also be represented graphically. The third schedule to be derived concerns the union's indifference curve. Obviously, the union will not supply any workers to the firm at a wage rate below the unemployment benefit. Hence, in terms of Figure 8.2, the restriction w > B, translates into the horizontal line BB. Furthermore, the union is unable to supply any more workers than its current membership. Hence, there is an additional restriction L < N, which is the full employment line FE in Figure 8.2. Within the feasible region (w > B and L < N),

(L/N)u,, >

The Foundation of Modern Macroeconomics

the slope of an indifference curve of the union is determined in the usual way:

		1	[u(w) — u(B)] dL = 0
dV Vwdw + VLdL = 0 (Tv-) uu,dw + —
(dw	(u(w)— u(B))	< O.	(8.5)
L)	Lu

Hence, the union's indifference curves are downward sloping. Furthermore, union utility rises in a north-easterly direction (because V i4, 0 and VL

—u(B))/N > 0), i.e. V2 > Vl > V0 in Figure 8.2.

8.1.1The monopoly model of the trade union

Perhaps the oldest trade union model is the monopoly model developed by Dunlop (1944). The trade union is assumed to behave like a monopolistic seller of labour. It faces the firm's demand for labour (defined implicitly in (8.3)) and sets the real wage such that its utility (8.1) is maximized. Formally, the problem facing a monopoly union is as follows:

max V(w, L) subject to n-L(w, A, L, K) = 0,	(8.6)
0,1

where the restriction 34 = 0 ensures (by (8.3)) that the monopolistic union chooses a point on the labour demand function. In words, the demand for labour acts like the "budget restriction" for the monopolistic union. By substituting the labour demand function (given in (8.3)) into the union's utility function, the optimization problem becomes even easier:

max V [w, L (w, A, R)],	(8.7)
{w}
so that the first-order condition is:
dV = 0 : V„, + VLLD = 0,	(8.8)
dw

which implies that V,„/VL = —Ow . The slope of the union's indifference curve should be equated to the slope of the demand for labour. 2

The monopoly union solution is illustrated in Figure 8.3. The wage rate is set at wM, the union attains a utility level VM, and employment is LM . The union has (N — LM) of its members unemployed. How does this unemployment level compare to the competitive solution? If there were no unions, the forces of the free market would force the wage rate down to w = B, so that point C in Figure 8.3 represents the competitive point. Employment is equal to Lc which is greater than employment

2 It is possible that the union cannot choose this interior solution because the firm would make too little profit there. In such a case a corner solution is attained, and (8.8) does not hold with equality. We ignore this case here.

Figu

with monopoly ur unemployment t sentiments men ti o Recall that ont.- to investigate thc..

(see Figure 7.9). model? In the cc .. on real wages if tt demand equation similar happens effects of a produce

Vw + VL L,1;. =

=

J

where ED

mand elasticity ori), then a prow, monopoly union. 1

.....ced predicts a

Obviously, as fa

:lion is fully t:

LI (via (8.1)) equal i

190

rmined in the usual way:

F

u(B)] dL 0

(8.5) 1ping. Furthermore, union

(L/	>	0 and V
		L

model developed by Dunlop Tolistic seller of labour. It i (8.3)) and sets the real wage )blem facing a monopoly

(8.6)

,onopolistic union chooses a Ind for labour acts like the stituting the labour demand 1, the optimization problem

(8.7)

(8.8)

I's indifference curve should

8.3. The wage rate is set at nt is LM. The union has employment level compare - forces of the free market in Figure 8.3 represents the greater than employment

ecause the firm would make too _foes not hold with equality. We

Chapter 8: Trade Unions and the Labour Market

FE

LM

LC

N

Figure 8.3. Wage setting by the monopoly union

with monopoly unions, i.e. Lc > LM. Hence, the monopoly union causes more unemployment than would be the case under perfect competition, and the layman's sentiments mentioned in the introduction are confirmed.

Recall that one of the reasons for being interested in models of union behaviour is to investigate their potential in explaining the (near) horizontal real wage equation (see Figure 7.9). What happens if there is a productivity shock in the monopoly model? In the competitive solution (point C in Figure 8.3) there is only an effect on real wages if the productivity shock (dA) is very large, i.e. if the new labour demand equation intersects with the FE line at a wage rate above B. Something similar happens in the monopoly union model. In order to derive the real wage effects of a productivity shock, we first rewrite (8.8) in a more intuitive form:

V„, + VLLD = (	N	u,, + 1	[u(w) - u(B)] LD = 0
		N
= (—wivid ) [wuw + [u(w) - u(B)] wLEP Ll = 0
	u(w) - u(B)		—=1 ,	(8.9)
		WUw

where ED 7- -wLP,„/L is the absolute value of the labour demand elasticity. If this demand elasticity is constant (as is the case for a Cobb-Douglas production function), then a productivity shock has no effect on the real wage rate chosen by the monopoly union. Only employment reacts to a productivity shock, and the model indeed predicts a rigid real wage.

Obviously, as for the competitive case, this conclusion must be qualified if the union is fully employed (L = N). In that case the union's effective utility function is (via (8.1)) equal to V(w, L) = U(w), which no longer depends on the employment

191

(DI, wL/Y

wuw

u(w) - u(B)

The Foundation of Modern Macroeconomics

level. As a result, the fully employed union is only interested in high real wages, Furthermore, the st, , and its optimal strategy is to set w = AFL (N , k). This is the point of intersection ofII

	the FE line and the labour demand curve. Any productivity shocks are immediately	7tw + ITLLI;', = 7r„
	translated into higher wages.	1
		since the solution 1,,
	In the monopoly union model the trade union unilaterally picks the wage and
		(8.13)-(8.14) into (8.
	the firm unilaterally chooses the level of employment it wants at that wage. In the

next union model this setting is made more realistic by assuming that the firm and the RTM model (the

the union bargain over the wage rate.	(v — f7) -1 [1

8.1.2 The "right to manage" model

The right to manage (RTM) model was first proposed by Leontief (1946). The firm still has "consumer sovereignty" in the sense that it can unilaterally determine the employment level (hence the name "right to manage"), but there is bargaining between the firm and the union over the real wage. The outcome of the bargaining process is modelled as a so-called generalized Nash bargaining solution (see e.g. Binmore and Dasgupta, 1987, and Booth, 1995, pp. 150-151). According to this solution concept, the real wage that is chosen after bargaining maximizes the geometrically weighted average of the gains to the two parties. In logarithmic terms we have:

max C2	log [V (w, L) - V] + (1 - A) log [7(w,	L) - Fr]
tui
	subject to 7rL(w, A, L, k) = 0,	(8.10)

where V U(B) is the fall-back position of the union, 71is the fall-back position of the firm, and A represents the relative bargaining strength of the union (0 < A < 1). Obviously, the monopoly union model is obtained as a special case of the RTM model by setting ), = 1. We have already argued that the union has no incentive to

accept wages lower than the unemployment benefit B, where utility of the union is at its lowest value of V(w, L) = V (B, L) = U(B). This rationalizes the fall-back position of the union. For the firm a similar fall-back position will generally exist. To the extent that the firm has fixed costs, minimum profit must be positive, i.e. n > 0.

By substituting the labour demand function (8.3) into (8.10), the problem is simplified substantially:

max C2 log [ V(w, LD (w, A, K)) - V] + (1 -A) log [7 (w, LD (w, A, 1)) - , (8.11) {w}

	for which the first-order condition is:
	dS2 = x Vw +		± A) (7w + 7LL/f„ = 0.	(8.12)
	dw	V - V )n -n

The numerator of the first term on the right-hand side of (8.12) can be simplified to:

Vw + VLLD = wiN' ) [wuw - ED [u(w) - u(B)]] •

(8.13)

[wuw - ED PA wN a

WUw - E

where we have us:

(L/N)(u(w) - u(B))

= —

where is the share of the mini Equation (8.16) shi

process is lower

the bargaining powe The RTM solution the monopoly solut. The RTM solution lie for the monopoly firm is 7R > 7m. Ca too little employm, solution, however, ui

The exact locati, as represented by ti., M. On the other han is close to the corn' of A., R can be any‘%

A major problem outcome is Pareto-i-

in the bargain better with the aid of 1

the firm has a profit along the iso-profit

the labour demand

192

(w, L)

, •ested in high real wages, he point of intersection of '*v shocks are immediately

terally picks the wage and wants at that wage. In the rssuming that the firm and

(v

Leontief (1946). The firm unilaterally determine the ), but there is bargaining e outcome of the bargaintrgaining solution (see e.g. 0-151). According to this

ling maximizes the geoti es. In logarithmic terms

(8.10)

s the fall-back position of of the union (0 < < 1). special case of the RTM ion has no incentive to there utility of the union rationalizes the fall-back :1 will generally exist. To ist be positive, i.e. n > 0. 0 ( 8.10), the problem is

, LD(w, A, K)) - n], (8.11)

(8.12)

1.12) can be simplified to:

(8.13)

Chapter 8: Trade Unions and the Labour Market

Furthermore, the second term on the right-hand side of (8.12) becomes:

7rw + 7TLLD,, = 7rw = -L, (8.14)

since the solution lies on the labour demand curve, so that 74 = 0. By substituting (8.13)-(8.14) into (8.12), and simplifying, we obtain the real wage expression for the RTM model (the counterpart to (8.9)):

	—V) -1 [Vw +	= -(1 - (7r - 7- ) -1 7rw
	7,N		(1 - A)(V -		L
			xo.e.
	1 L [wuw — ED [U(W) - u(B)]]=
			(1 - A )wL			8.15)
	wuw - ED [u(w) - u(B)] =		A(1/	_	fr. ) ) [u(w) - u(B)],

where we have used the definition of 7 (in (8.2)) and the fact that V - V = (L/N)(u(w) - u(B)) in the final step. Continuing the derivation, we obtain:

u(w) - u(B) 1 ,	=	(1 - ?)wl, > 0,	8.16)
wuw ED+		X(1 - (or, - 0)70

where (Di, wL/Y is the share of labour income in total income, and can -= it/Y is the share of the minimum profit level in total income.

Equation (8.16) shows that the real wage markup that rolls out of the bargaining process is lower than under the monopoly union model (unless the union has all the bargaining power, in which case A = 1, (1) = 0, and (8.9) and (8.16) coincide). The RTM solution can be illustrated with the aid of Figure 8.4. For ease of reference, the monopoly solution M and associated iso-profit curve 7rm have also been drawn. The RTM solution lies on the labour demand curve, but at a wage level below that for the monopoly solution. It is indicated by point R where the profit level of the firm is 7rR > 7rm . Compared to the competitive solution (at point C), there is still too little employment, and too much unemployment. Compared to the monopoly solution, however, unemployment is lower.

The exact location of point R depends on the bargaining strength of the union, as represented by the parameter A. The higher is A, the closer point R lies to point M. On the other hand, if A is very low, then is very large (see (8.16)) and the wage is close to the competitive solution, i.e. w B. Hence, depending on the magnitude of A, R can be anywhere on the labour demand curve between points M and C.

A major problem with the RTM solution is that the chosen wage-employment outcome is Pareto-inefficient, i.e. it is possible to make one of the parties involved in the bargain better off without harming the other party. This can be demonstrated with the aid of Figure 8.4. At point R, the union attains a utility level of VR and the firm has a profit level of 7 R . The firm is indifferent for all combinations along the iso-profit curve 7TR, but the union's utility strictly increases if a point off the labour demand curve is chosen. Indeed, the efficient solution occurs at the

193

The Foundation of Modern Macroeconomics

w

FE

w

B

L

Figure 8.4. Wage setting in the right-to-manage model

point where there is a tangency between the iso-profit curve .7R and an indifference curve for the union. This occurs at point ER , where the union attains a utility level VRE > VR . (For the same reason, point M is also inefficient, but point C is efficient. Verify these claims.)

Economists are not particularly fond of inefficient solutions, especially in the "small numbers" case—that we are considering here—with only two parties bargaining. One would expect that the two parties would be sufficiently smart to eliminate the type of inefficiency that exists in the RTM and monopoly model. For that reason, the efficient bargaining model was developed by McDonald and Solow (1981).

8.1.3 The efficient bargaining model

McDonald and Solow (1981) analyse the case where the union and the firm bargain simultaneously over wages and employment. Again the bargaining problem can be analysed within a generalized Nash bargaining setup. Now the negotiations lead to the maximization of S2 by choice of the appropriate wage-employment combination:

max S2 )1/4. log [V(w, L) –	(1 – )■) log [7(w, L)	.	(8.17)
{w,L}

The first-order conditions for this problem are:

02 —(		A )17		+( 1—A )3T=o		(8.18)
aw		v—x7	w	71- -	w
aL	–		) V + 1		7rL = 0.	(8.19)
		v——V7r

wEB

I

Figure 8.5.

combining (8.1

( 1– A

7 - =

In words, the cont- :;.:lions for which contract curve, then

.t simultaneously %presents all tange t. 7-yes.

One immediate exceeds the margin

.:ice VL > 0, V., >

71, AFL(L, -

t rice, with the eN on the labour dema :he contract curve.

In Figure 8.5, al, points C and D. We a it the profit level point D) exceeds tt 'he entire line st _ not yet fully si,„. wage-employment

194