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foundations of microeconomics

Questions and Answers of Foundations Of Microeconomics

One immediate exceeds the margin.:ice VL > 0, V., >71, AFL(L, -
In words, the cont-:;.:lions for which contract curve, then.t simultaneously%presents all tange t. 7-yes.
combining (8.1( 1– A 7- =
The first-order conditions for this problem are:aw v—x7 71- - w 02 —( A )17 =o w+( 1—A )3T aL – ) V + 1 7rL = 0. v——V 7r(8.18)(8.19)
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
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
Figure 8.4. Wage setting in the right-to-manage model I Figure 8.5.point where there is a tangency between the iso-profit curve .7R and an indifference curve for the union. This occurs at point ER ,
The Foundation of Modern Macroeconomics
8.15)w wEB w FE BL
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
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
for the monopoly solution. It is indicated by point R where the profit level of the firm is 7r R > 7rm . Compared to the competitive solution (at point C), there is still too little employment, and
The RTM solution lies on the labour demand curve, but at a wage level below that
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.
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 =
where (Di, wL/Y is the share of labour income in total income, and can -= it/YY is the share of the minimum profit level in total income.
wuw ED + X(1 - (or, - 0)70 8.16)
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,
wuw - ED [u(w) - u(B)] = A(1/ _ fr. ) )(1 - A[u(w) - u(B)],)wL
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)
1.12) can be simplified to:(8.13)
: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)
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
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 Leontief (1946). The firm unilaterally determine the), but there
Chapter 8: Trade Unions and the Labour Market, •ested in high real wages,
A major problem outcome is Pareto-iin the bargain better with the aid of 1 the firm has a profit along the iso-profit the labour demand 192 193
The exact locati, as represented by ti., M. On the other han is close to the corn'of A., R can be any‘%
where (DI, wL/Y 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
(8.13)wN[wuw - ED PA aWUw - E where we have us:(L/N)(u(w) - u(B))u(w) - u(B)= —wuw
The numerator of the first term on the right-hand side of (8.12) can be simplified to:Vw + VLLD = i' wN ) [wuw - ED [u(w) - u(B)]]
By substituting the labour demand function (8.3) into (8.10), the problem is simplified substantially:m{awx} C2 log [ V(w, LD(w, A, K)) - V] + (1 -A) log [7 (w, LD (w, A, 1)) - , (8.11)for which the
where V U(B) is the fall-back position of the union, 71- is the fall-back position of the firm, and A represents the relative bargaining strength of the union (0 < A < 1).Obviously, the monopoly
subject to 7rL(w, A, L, k) = 0, (8.10)
max C2 log [V (w, L) - V] + (1 - A) log [7(w, L) - Fr]tui
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
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
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
translated into higher wages.In the monopoly union model the trade union unilaterally picks the wage and since the solution 1,, the firm unilaterally chooses the level of employment it wants at that
greater than employment ecause the firm would make too _foes not hold with equality. We 191 The Foundation of Modern Macroeconomics
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
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,
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),
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 = ( u,, + 1 [u(w) - u(B)]
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
)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)
LI (via (8.1)) equal i 190 FE Chapter 8: Trade Unions and the Labour Market rmined in the usual way:F u(B)] dL 0 1ping. Furthermore, union(L/ > 0 and VL(8.5)LM LC N model developed by Dunlop Tolistic
mand elasticity ori), then a prow, monopoly union. 1.....ced predicts a Obviously, as fa:lion is fully t:
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
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.
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
so that the first-order condition is:dV dw= 0 : V„, + VLLD = 0, (8.8)Vw + VL L,1;. ==
"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,
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
(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
8.1.1 The monopoly model of the trade union Perhaps the oldest trade union model is the monopoly model developed by Dunlop
Hence, the union's indifference curves are downward sloping. Furthermore, union utility rises in a north-easterly direction (because V i4, (L/N)u,, > 0 and VL— u(B))/N > 0), i.e. V2 > Vl > V0 in
Foundation of Modern Macroeconomics the slope of an indifference curve of the union is determined in the usual way:dV Vwdw + VLdL = 0 (Tv-) uu,dw + —1 [u(w) — u(B)] dL = 0(dw L)(u(w) — u(B))Lu<
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
function in that it depends on v linked, however. Indeed, the ntity choices of the household Figure 8.2. Indifference curves of the union level of employment L, the level of profit is increased if
curve is downward sloping-oft curve. It represents the n level. It can be interpreted curve can be determined N L (8.4)the slope of an iso-profit line;LL < 0, so that 7ri, is positive)fit-maximizing
-- hically. In order to do so, red. First, the labour demand which profit is maximized ch yields:(8.3)
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 no nz LD Chapter 8: Trade Unions and
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
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
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
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
The representative firm is modelled in the standard fashion. The production function is Y = AF(L, R), where Y is output, K is the fixed capital stock, A is a productivity index, and F(., .) features
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 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)
Suppose that the representative trade union has a utility function V(w, L) with the following form:V(w,L) Nu(w) ± [1 — Cd --)]u(B), (8.1)where N is the (fixed) number of union members, L is the
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
8.1 Some 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
5. How do trade unions affect investment by firms?F
4. How does taxation affect unemployment in trade union models?
3. How can so-called insider-outsider models be used to explain hysteresis?
2. What do we mean by corporatism and how can it explain some of the stylized facts about the labour market?
1. What models of trade union behaviour exist, and what do they predict about unemployment?
Figure 7.8. The economy is initially at E0 and stays there. The reduction in unemployment is represented by the horizontal segment BA. The students are advised to work through the entries of Table
Equation (7.27) can be used to determine what happens to the gross real wage.Consider what happens if the marginal tax rate on labour is increased, leaving all other taxes unchanged. For the given
Equations (7.28)-(7.30) determine employment, labour supply, and the unemployment rate as a function of the tax rates and the exogenous real consumer wage.
The Foundation of Modern Macroeconomics We We Figure 7.8. The effects of taxation with a fixed consumer Figure 7.9.wage macroeconc we have for the change in unemployment:clU = (7.30)
nsumer wage dU pSW + ED IED CD ESW + ED w
In view of this definition, equations (7.16) and (7.26) can be rewritten in terms of the exogenous real consumer wage:By assumption the real consumer wage is too high for full employment, so that the
Tax effects with rigid consumer wages and unemployment Assume now that (for whatever reason) the real consumer wage is exogenously fixed above the level consistent with full employment. The real
ad to stability in that case.a result of the higher average tax, households feel poorer and start to supply more labour. This shifts the labour supply curve to the right, the equilibrium moves from
hey have to pay higher wages is on the elasticities of the average income tax, keeping cts on the labour market are Iso depicted in Figure 7.7. As condition ESW + ED > 0 is satisfied.oping but it
x system more progressive, ms of Table 7.5(a), this means tA = tE = tc = 0). Due to the ar at the same gross real wage f Figure 7.7, the equilibrium Part of the tax is shifted
Chapter 7: A Closer Look at the Labour Market Figure 7.7. The effects of taxation when wages are flexible's and assumes continuous to discuss the effect of differ-4.-rpretation requires the real
4-4! labour (see Cl= ■- 1) . Unemplc 174(7.28)(7.29)= --EDPVC NS = Eswfvc + [tA — tm •
There is no plausible real wage adjustment mechanism that would lead to stability in that case.of the I._ ..:. TiLis to E2 so that ti 4‘Jjects with n,some now tiLi'.ed above the k _aed as the rea
8 This holds regardless of the sign of ESN., provided the stability condition csw + ED > 0 is satisfied.In terms of Figure 7.5, the labour supply curve can be downward sloping but it must be steeper
If, on the other hand, the policy maker increases the average income tax, keeping the marginal tax and all other taxes unchanged, the effects on the labour market are completely different. The
Tax effects with flexible wages and a clearing labour market Suppose that the policy maker wishes to make the tax system more progressive, without however, changing the average tax rate. In terms of
The Foundation of Modern Macroeconomics Table 7.5. Taxes and the competitive labour market F ggu the equilibrium interpretation postulates flexible wages and assumes continuous market clearing (N =
ESW + ED ESW + ED ED EDESW 0 0 —ED ED ESW ED ESW + ED ESW EDESW 0 1 —ED ED ESW + ED ESW + ED—ED ESW + ED tM to 1A4 = IA tE tC
ESW ± ED ESW + ED ESI EDESI 0 1 —ED ESW+ ED ESW + ED ESW + ED ESW EDESW—ED
7 This does not imply that this household is kinky. It just means that the household is very reluctant to deviate from a fixed proportion between consumption and leisure. In case acm = 0, the
The demand and supply equations of the standard model of the labour market(expanded with various tax rates) are given in linearized form by, respectively, equations (7.16) and (7.26). There are
consumption (crcM) exceeds unity, the substitution effect dominates the income effect and thus labour supply is an increasing function of the real wage. Otherwise, the income effect dominates the
where E-sw acm(1 — Ns) is the compensated wage elasticity, and Es/ (1 — Ns) is the income elasticity. The compensated wage elasticity corresponds to the substitution effect and is always

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