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foundations of microeconomics

Questions and Answers of Foundations Of Microeconomics

The problem with the c, not believe that the union impossible, the union %N
Comparing the optimal it is clear that the wage is wages in the second period
e.g. (8.8)). A point of tangency is found between a union's indifference curve and the labour demand curve. Assuming that the utility function of the representative
(8.50)-(8.51). The necessary conditions for this optimization problem are:ac = av av =0, (8.56) awl awl 8L1 awl as.2 av av (aLy av2) ail 0g ) = + + 0. (8.57) aw2 awe awe aq aw2 Equation (8.56) has a
which indicates that membership of the union is fixed at N, and the unemployment benefit is constant over time. The optimal plan for the union consists of choosing w1 and w2 such that (8.54) is
where p is the pure rate of time preference (see Chapter 6), and V (wt , Lt ) is the instantaneous utility of the union, that is defined as follows:Lt V (wt, Lt) Lt(—N) u(wt) + [1 - (-Au(B), (8.55)
Equation (8.57) is slightly chooses for the second pt., the wage in the second pet pared to the static case vthe second period is more I Specifically, we can easily d V(wi,Li) -1- 1+ P )V(w2,L2),
where ED 1/(1 - a), Lp is the firm's demand for labour in period t, and q is Tobin's q-ratio discussed extensively in Chapter 4. Equations (8.50)-(8.51) show that the elasticity of labour demand is
(8.53)
Douglas, i.e. Yt = 41g -a , with 0 < a < 1 and Yt representing output. By using these specific functions, (8.47)-(8.49) can be written as:ED 1,113 = (°-) Kl, Wi A, ED LD =W2[Ki + 11= -b 2 1 FK(142,
The Foundation of Modern Macroeconomics In order to keep the model as simple as possible, we work with specific functional forms for the firm's production and adjustment cost functions, and the
ED + 0 w2Uw(w2)log w2 = log B + 1 ED - -where 0 is defined as:
where r is the real interest rate. The first-order conditions for the optimization problem are:an, ir = aL i aIi =a II aL2 an,-14,1= 0, 8.47)( 1 + = 0, (8.48)+1-[FL(L2,Ki 0 — w21 = r) 0. (8.49)207
investment levels in order to maximize the present value of its stream of profits, which is defined as:n= 7r2 + 1 + r F(Li ,Ki ) — wiLi —(pal) (F(L2,Ki + — w2L2 )1 + r(8.46)
the firm does not invest in the second period because our stylized world comes to a close at the end of that period. Furthermore, we have assumed for convenience that the capital stock does not
this function captures the existence of internal adjustment costs that are rising (at an increasing rate) in the rate of investment, i.e. (1)1 > 0 and (1)ll > 0. Obviously
where Trt is real profit in period t (= 1, 2), Lt is employment, It is investment, wt is the real wage rate, F(., .) is a constant returns to scale production function, and(I)(.) is the installation
The remainder of this section serves to demonstrate the underinvestment result in a simple two-period model of the interaction between a monopoly trade union and a firm. This example is a
however, the firm is a "sitting duck" for the union. The capital stock cannot be shifted easily so the union can renege on its promise of moderate wages and skim off a large part of the firm's
Aire will be comparable. A Ia credibility problem assothat investment is largely 1• 1 follow a smooth (and nce the firm has invested,
(8.43)unemployment U) rises if ressivity falls (s rises), and similar to those that were. -ould think the latter. The ble production factor, the conflict between what is un. Take, for example, the
tv of the tax system. For from Chapter 7 that an by a decrease in s.i member's indirect utility ation (8.42) is simplified to:
Chapter 8: Trade Unions and the Labour Márket(8.40)w dtA =0— dw . (8.41)at wdtA /dw = tM — to and 0):(8.42)
T4/ = [14(wa tA» -(8.40)8.41)(8.43)206
firm will not invest too much, so that the wage in the future will be comparable. A kind of wage smoothing behaviour may emerge.This is not the end of the story, however, since there is a credibility
short-sighted union will push for high wages and suffer the consequences in the future as firms accumulate capital and labour demand becomes more elastic. Farsighted unions, on the other hand, will
Are unions good or bad for investment? Intuitively one would think the latter. The argument might go as follows. When capital is a variable production factor, the demand for labour becomes more
8.5.2 Unions and investment
the average tax rate (tA ) rises. These conclusions are very similar to those that were obtained for the efficiency wage model in Chapter 7.
From (8.43) we can see that the gross wage w (and thus unemployment U) rises if the unemployment benefit (B) rises, the degree of progressivity falls (s rises), and
function is given by U(.) log (.). Then the markup equation (8.42) is simplified to:log w(1 - tA) = log B+sIED w= B e ED. 1 - tA
where s (1 - tm)I(1 - tA) is the index of progressivity of the tax system. For a progressive tax system, tM > tA, so that s < 1. Recall from Chapter 7 that an increase in progressivity of the tax
This expression can be simplified by using the result that wdtA/dw = tM - to and using the labour demand elasticity ED (defined below (8.9)):u(w(1 - tA)) - u(B) = s w(1 - tA)Uw(1-tA)(8.42)
The Foundation of Modern Macroeconomics(from (8.1)) to include income taxes:v(w, L) (R) u(w(1 - tA)) + [1 - (Ki)]u(B), so that the first-order condition for the optimal wage is:(B)A L dtA 1 = D,v +
=FL(LI,Ko-
where r is the real it problem are:aL1 an all an ( 1 aL2 1 +\an
that the capital stoatinvestment levels in which is defined as:n = Tri + 1+r F(L i ,Ki) -
this function capture!an increasing rate) 1 the firm does not in a close at the end of
where 7rt is real proi is the real wage rate, 4)(.) is the install,:
equal to:7ni 7-- F(1.1, --= F(1,2, K1 +
in a simple two-periol and a firm. This exam(1987b). The firm t
the risk and impact of result, discussed for bility issues in Chapt can overcome (son:behaviour. 1 The remainder of ti
however, the firm is shifted easily so the u off a large part of the has this incentive to cl ment of smooth and n
swing. Labour demand is 205
vi models (see Chapter 7).e modest in his/her wage her job. Second, the threat-eaten current employees nployed workers.
Dr the unemployment rate.process. First, there is the
i quite easily. Following n and the group of insiders
clined to lower wages to get ds after a positive aggregate Dr empirical and theoretical ovment rates in the UK and utoregressive coefficient in ival to unity. Theoretically,,,, rs have all the
he unemployment rate foil('surprises are random, the no tendency for the unem-- ,iition behind this result is)y (8.35)). The unemployed
(8.3 "-ms of the unemployment(8.3(
Suppose that the system of income taxes is progressive, that unemployment benefits are untaxed, and that the tax function is given by T(w), so that the marginal tax rate is tM dT dw and the average
In order not to unduly test the reader's patience, only one tax experiment is conducted.
In this section some of the union models discussed in this chapter are used to study two issues. First, we continue our study of the effects of taxation on employment, wages, and unemployment.
Unemployment is at its worst for intermediate cases. There, unions are large enough to cause some damage (in the form of higher wage claims and lower employment levels), but too small to feel
The reason why countries with a low degree of centralization fare well on the unemployment front is that unions, if they exist at all, are very small, have very little power and are hence rather
Again, large unions are more likely to internalize this external effect than small unions. Third, it is possible that leapfrogging effects (see Chapter 7) are important when there are small unions.
The reason why highly corporatist countries have a good unemployment record may be that highly centralized unions tend to internalize external effects that smaller unions would cause. First, higher
Chapter 8: Trade Unions and the Labour Market of corporatism is found in countries such as Austria, Norway, Sweden, Denmark, and Finland. An intermediate degree of corporatism is found in the
of corporatism is found the US, since these counlrkets.A very high degree
d. We saw that (at least up:ria, Sweden, Norway, and t countries such as Belgium r-Nrs and Driffill (1988) sugg to do with the degree of elationship is parabolic, as sm is hard to define preree of
The basic model. There is pelf Uw 198 Sweden Austria 1 centralized wage bargaining ratism are large differences in the
3kgain, large unions:ions. Third, it Anen there are sma ects will be absc al., 1991, p. 30).The reason why- .employment frc power and are henc do not internalize 4 L4cmselves are smut
rates, union n1,,
is drawn in Figure 8.7. Although the concept of corporatism is hard to define precisely, Calmfors and Driffill intend it to mean the degree of centralization of the wage-setting process. In terms of
Finland are characterized by low unemployment, whilst countries such as Belgium and the Netherlands have high unemployment. Calmfors and Driffill (1988) suggest that the unemployment rate may have
8.2 Corporatism Our fifth stylized fact in Chapter 7 suggests that there are large differences in the unemployment rates of countries of the developed world. We saw that (at least up until the early
The Foundation of Modern Macroeconomics /primary sector (because wages are higher there), but are prevented from getting work there because of the union's wage-setting power.Suppose now, however,
rising conclusions.relevance. Although-1t, it is hardly ever( which includes the than the efficient nt case appears to be firm can unilaterally Belgium The Netherlands/ Japan United States Canada
Aution (WEB > B) but The intuition behind the maximum profit s for union members.basis of the efficient at first sight. Wage bour (dk < 0), turns the EE locus down power of the firm is forced closer
CD, the equilibriurprising conclusion mployment is higher g model (LEB >this chapter, is only
(solution lies to the(FL. The equity loafs share of the pie (k)
Figure 8.6. Unemployment in a two-sector model by postulating a st, the union and tht terms of the mode(8.27 n gets 1 - k of ou`termined in the usu,..(8.2 -
= N - L. Hence, with a monopoly union in the primary sector, there is full employment of labour at the aggregate level, but wage disparity between the primary and secondary sectors. Workers in the
in Figure 8.6. In the primary sector, the monopoly union selects the tangency point for a union indifference curve and the demand for labour (point M). The wage rate is wM and employment is L. In the
workers, so that N = L1 + L2 + U. We assume that a monopoly union sets the wage in the primary sector. The demand for labour in the two sectors is given by L if (wi)and LY(w2), respectively, where w
'3.1.4 Trade unions in a two-sector model Before turning to the next issue, it is instructive to study the effects of trade union behaviour in a two-sector setting. This allows us to study the
Chapter 8: Trade Unions and the Labour Market
ll workers that c the secondary sec?1.:;1 = N — L . He employment of labs and secondary 01 Figure 8.6.196 Bw M2 02 Ly Ly
in the primary _ and LY (w2), respei in Figure 8.6. In ti for a union inch.. , is wiivr and employ of labour betwe, clearing competi ti 4. , respectively. I
to N. EmploymL .4 workers, so that
is homogeneous, called the primary has a competitive
Before turning to behaviour in a 1, unions may have
determine the employment level.8.1.4 Trade un
bargaining model. In other words, in the real world the relevant case appears to be that firms and unions negotiate over the wage rate, but that the firm can unilaterally
The problem with the model appears to be its tenuous empirical relevance. Although simultaneous bargaining over wages and employment is efficient, it is hardly ever observed in practice. It therefore
moderation, as modelled by a smaller share of the pie for labour (dk < 0), turns out to be bad for employment! Graphically, a lower k shifts the EE locus down and to the left, shifting the
level (at point C), and instead turns some of this profit into jobs for union members.In that sense the next conclusion that can be drawn on the basis of the efficient bargaining model is perhaps
The layman's sentiment, mentioned in the introduction to this chapter, is only partially correct. Wages are higher than in the competitive solution (wEB > B) but employment is also higher than in the
By combining the equity locus EE and the contract curve CD, the equilibrium wage-employment combination is obtained at Eo . A very surprising conclusion is reached. Compared to the competitive
where the sign follows from the fact that 71-1, AFL — w < 0 (solution lies to the right of the labour demand function) so that a fortiori w > kAFL. The equity locus is downward sloping and shifts
The Foundation of Modern Macroeconomics McDonald and Solow (1981, p. 903) suggest closing the model by postulating a socalled"fair share" rule. After repeated interactions in the past, the union and
wEB vR and an indifference n attains a utility level Put point C is efficient.ns, especially in the two parties bargain-Itly smart to eliminate Adel. For that reason, and Solow (1981).LC LEB N L FE WM
In Figure 8.5, the entire contract curve is drawn as the dashed line connecting points C and D. We assume that full employment is possible in principle. This means that the profit level associated
One immediate implication of the efficient bargaining model is that the real wage exceeds the marginal product of labour. Indeed, (8.20) says that rci, = VLTrw/ Vw < 0(since V', > 0, Vw > 0, and 7rw
contract curve, there is no (w, L) combination that makes one party better off without simultaneously harming the other party. In graphical terms, the contract curve represents all tangency points
Figure 8.5. Wages and employment under efficient bargaining In words, the contract curve (CD in Figure 8.5) represents the locus of (w, L) combinations for which efficient bargaining solutions are
Jr — — (V — ) 7rw V — )7TL Vw n-w
Chapter 8: Trade Unions and the Labour Market(8.20)By combining (8.18)-(8.19), the so-called contract curve is obtained:1 X—Vw=( = L
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
t rice, with the eN on the labour dema:he contract curve.

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