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foundations of microeconomics

Questions and Answers of Foundations Of Microeconomics

where to CitA / (1 — tA). Hence, the average income tax rate influences the budget restriction of the household.By solving (7.24)—(7.25) for the change in labour supply, the following expression
C + (1/coL)ks = acm — tM — , (7.24)where tM dtm / (1 — tM), dtc / (1 + tc), and (Di, (1 — Ns)/Ns is the initial ratio of leisure to labour supply. The budget restriction (7.18) can also be
Chapter 7: A Closer Look at the Labour Market happy to substitute consumption for leisure. In graphical terms, the former household has sharp kinks in its indifference curves, 7 whereas the latter
ntiating with respect to Ns we e text.
w. Equation (7.22) drives titution between leisure and e average) tax rate facing Ivne that the utility function i ty between consumption> (7.23).erms) for the household to h a very low value of acM,
t is straightforward to derive be combined to yield the(7.22)
(7.23)budget restriction is:(7.18)it 4imal level of consumption(7.19)(7.20)(7.21)
7 This does not imply that to deviate from a fixed pro., curves are at right angles, ani consumption and leisure.
where acM (1 -income elasticity. The effect and is always n sponds to the income the gross wage is meal(acM - 1)(1 - Ns), N\the magnitude of ac, •consumption (acM ) ex c::ect and thus labour the
where tM dtm / (1 - th of leisure to labour s:.„+ = - 4-where dtA/(1 - tA restriction of the hot.By solving (7.24)-(7_ is obtained: 1= (1 — Ns) [(aa= — LM -= ESW [1'V' —
6 The average tax rate is defined as tA T(WNs)/(WNs). By differentiating with respect to Ns we obtain:happy to substitute col hold has sharp kinks i flat indifference curves of (7.22):d log
(7.17) is homothetic and define the substitution elasticity between consumption and leisure as follows:%ge change in C/(1 - Ns) d log (C/(1 - Ns))acm = %ge change in Lh_N/Uc d log
where we have used the definition of the gross real wage w. Equation (7.22) drives home a very important point: the marginal rate of substitution between leisure and consumption depends on the
. o components. First, as the It benefits falls, thus reducing e previously unemployed find The Foundation of Modern Macroeconomics ac =uc —AP(1 + tc) = 0, aL =-Urrl-N ac + [0. tA) _ Ns ( ca)]
ernment could invest in (re-)rkers. By making unskilled mand for those workers and r 6, a golden rule of financing ublic investment in (re-) train-:hemes may even be financed-king taxation. The
:!led labour because this type this type of labour is simply wage, to be consistent with at the minimum wage causes hour.--e of unemployment. First, Iviously work, but may cause ocial unrest, etc.
U = U(C, 1 — Ns), (7.17)with Uc > 0, > 0, Ucc < 0, < 0. In addition to facing (progressive)income taxes, the household also has to pay an ad valorem tax on consumption-.-orker's skill level) must
Most income tax systems in use in the developed countries are progressive, in the sense that the tax rate rises with the tax base (labour income in this case). Since we wish to investigate the
PF (N , k) — W(1 + tE)N , (7.15)where tE is an ad valorem tax levied on the firm's use of labour (e.g. the employer's contribution to social security). The usual argument leads to the marginal
7.2.2 The effects of taxation Before leaving the standard model of the aggregate labour market, we turn to an analysis of the effects of taxation on employment and the real wage rate. This analysis
In conclusion, even our very simple standard model can be used to derive sensible conclusions about the labour market. If we look at the Dutch situation, for example, the relative wage of unskilled
Chapter 7: A Closer Look at the Labour Market work, they also start to pay taxes, thus further reducing the government's revenue requirement.
facing households coin i.e. tM dr(i4'.\-ices, the average tax.3c. >n is assumed to be t.,= u(c, — Ns),!t1 > 0, > 0, L ale taxes, the househo 170 171
1,,,6unearized:SID = -ED [iv" +w W IP is the gro•abour demand elasticity.,t income tax system:se that the tax rate ri rare h to investigate..1/4,useholds, we specify 1
.2.2 The effects of to Before leaving the standa a lysis of the effects of as was commenced in completed here. Atten t:med to be constant d itcpresentative firm max IFl PF(N ,R) - W (1 -I...re tE is
the government's revenue requirement. Second, as the previously unemployed find work, they also start to I requirement.In conclusion, even ou conclusions about the lal the relative wage of ur.t: _c
A fourth option may be more attractive. The government could invest in (re-)training projects specifically targeted at unskilled workers. By making unskilled labour more productive, it is possible to
Third, the government can directly employ some unskilled workers at the going minimum wage. Again, the demand for unskilled labour shifts to the right, and unemployment is reduced. The problem with
A number of policy options exist to solve this type of unemployment. First, the minimum wage could be abolished. This will obviously work, but may cause politically undesirable income distribution
Classical Unemployment in the market for unskilled labour.
There is unemployment in the market for unskilled labour because this type of labour is too expensive: the marginal product of this type of labour is simply too low, given the existence of a binding
(7.8) explanation runs as follows. Suppose that there is a minimum wage law, which states The Foundation of Modern Macroeconomics that the real wage of any worker (irrespective of that worker's skill
The equilibrium in the two labour markets can be drawn as in Figure 7.6.If wages are perfectly flexible, full employment is attained in both markets. This is the case at points Eo and Eg,
In order to close the model as simply as possible, we assume that the supply curves of the two types of labour are perfectly inelastic.1\1:Z = Rs, NU = Ru. 7.14)(7.11)(7.12)
In words, if unskilled labour becomes dearer, the demand for skilled labour increases, and similarly if skilled labour becomes more expensive, the demand for unskilled labour increases. This is
The "cross" real wage effects cannot be signed without making further assumptions.Assume that skilled and unskilled labour are gross substitutes. This implies that Fsu is negative, and the cross
Chapter 7: A Closer Look at the Labour Market demand functions for the two types of labour:Ns = Anws,wu), Nu = Nu (ws, wu), where the "own" real wage effects are guaranteed to be negative:NsD aND ND
Figure 7.6. The markets for skilled and unskilled labour 169 Nu Nu
The term in round brackets ell-behaved production func-, arative static results of the ws wNs
pc of labour must be equated(7.9) can be used to derive,y total differentiation of the con:
wages are pei, :se at ry iur t!planation runs ivae 7.6. Tho 168 TrIployment I White Collar 13.2 3.3 4.2 4.0 8.9 8.7 7.7 8.6 8.6 5.3 5.2 5.8 6.3 6.3 5.0 4.7 5.3 4.9 Iwe (7.10)Ins:
ibt .r incre.:pros in order to cl two type,=""le equi., „
where ws Ws/P, wu Wu/P, and Fsu 32F/aNsNu. The term in round brackets on the right-hand side of (7.10) is positive for any well-behaved production function.Equation (7.10) can be used to find all the
which yields the usual marginal productivity conditions:PFu(Nu , Ns) = Wu, PFs(Nu , Ns) = W.In words, the value of the marginal product of each type of labour must be equated to its wage rate.
urce: OECD (1994, p. 15)the choice problem is:max n PF(Nu, NO - WuNu - WsNs, uvu,Ns}
United States 1983 13.5 6.3 1984 9.8 5.0 1991 9.4 4.7 1992 10.1 5.3 1993 9.0 4.9
United Kingdom 1985 9.7 5.3 1986 9.6 5.2 1992 13.2 5.8 1993 13.9 6.3
Canada 1983 15.9 8.9 1984 14.4 8.7 1991 15.0 7.7 1992 15.6 8.6 1993 15.2 8.6
Table 7.4. The skill composition of unemployment Blue Collar White Collar Australia 1986 6.6 3.2 1987 6.5 3.3 1992 9.9 4.2 1993 8.9 4.0
8, a reason for this different r market institutions that exist our Market Theory 167 demand functio NI) =.nere the "own vD SS =CA s-The Foundation of Modern Macroeconomics
The representative firm maximizes profit by choosing the optimal production level. With perfect competition in the output market and both input markets, the output price P and the wage rates Wu and
Y = G(Nu, Ns, k) = G(Nu,Ns,1) _= F(Nu, N5), (7.7)where Y is output, and the capital stock is fixed in the short run at K = 1. Hence, F(Nu, Ns) is the short-run production function that satisfies Fu
Source: Layard, Nickell, and Jackman (1991, p. 7)unemployment rate than white collar workers (see Fact 7). Obviously, this can be done by distinguishing two types of labour. Call the blue collar
Men Women Men Women Belgium 11.0 5.6 15.3 16.0 27.1 Denmark 7.8 5.2 9.4 9.3 11.9 France 10.5 6.4 10.1 19.6 27.9 Germany 6.2 5.1 7.5 6.1 8.5 Greece 7.4 3.8 6.7 15.5 35.1 Ireland 17.5 13.5 18.5 27.2
Chapter 7: A Closer Look at the Labour Market Table 7.3. Sex composition of unemployment All Over 25 Under 25
-* ,.7gregate demand and supply tthough a high level of aggre-)roach flies in the face of the!Ile, suppose that one wishes ar workers experience a higher
so show in which important one of these failures concerns to with respect to demand and o theories that can explain)ter.,et in the same way we would
x explained about the labour standard labour market story
ters experience about double"e collar colleagues.
roups, occupations, regions,- .3 shows the unemployment ries. Women experience much have higher unemployment pain are particularly dramatic lot for occupatiOns as well. In-2rs and white collar workers
Abe representau 4 - h P anc 166 become unemployed Only job in order to become unemit majority of unemployment rmloyer. This fact will prove iour.111
model the market for peanuts, i.e. by looking at the aggregate demand and supply schedules (for labour in this case; see Chapter 1). Although a high level of aggregation is the hallmark of
7.2.1 Flexible wages and clearing markets Up to this point we have modelled the labour market in the same way we would
7.2 The Standard Macroeconomic Labour Market Theory
Table 7.4 the unemployment rates for blue collar workers and white collar workers are shown for a number of countries. Blue collar workers experience about double the unemployment rate of their (more
Fact 7: Unemployment differs a lot between age groups, occupations, regions, races, and sexes Examples are easy to come by. Table 7.3 shows the unemployment rates of workers, by age and by sex, for
Fact 6: Few unemployed have themselves chosen to become unemployed Only a very small minority of the unemployed have quit a job in order to become unemployed(for example, to search for a new job).
Table 7.2, the level of unemployment differs a lot even between the countries of Europe. It is very high for countries of the (original) EC, whilst it is very low (and unchanged over time) for other
The Foundation of Modern Macroeconomics Fact 5: Unemployment differs a lot between countries As we can see from
+ ait-1 =1 l - al By using this result plus the definition of U (given in (7.3), equation (7.5) is obtained.165 Tab'I BF Franc&Grt.cce Ireland Its Nether'Pt SP.. , United AL, ...New A Ca . :13
•
We ignore the fact that we are using estimates for ao and al, and should really be constructing confidence intervals for U.5 The trick is to write the term in square brackets as:— at 1 + al + ai +
For the UK this amounts to tH = 10.15 years (see (7.1)). Hence, it takes slightly more than a decade before even half of the difference between the actual and the long-run unemployment rate is
2), the coefficient of the nity. Ultimately, there are to some average level. The
10 trend This fact has been h there are sharp peaks and nd in the unemployment He in view of the enormous ry and a half. Apparently, ermanently pushing workers
(7.6)
Equation (7.5) can be used to determine how long it takes for any discrepancy between U0 and U to be eliminated. Suppose that the unemployment rate is currently Uo and the long-run unemployment rate
This expression can be rewritten in the following (more elegant) form: 5 Ut - = [Uo - ati . (7.5)
which would equal 6.21% for the UK, for example. 4 From (7.3) we can compute the adjustment speed by solving the difference equation for Ut . Suppose that the unemployment rate at time t = 0 (the
Chapter 7: A Closer Look at the Labour Market convergence to this average level is very slow, however, as can be demonstrated as follows. From equations like (7.1)-(7.2) we can determine the
the UK this amounts to- than a decade before e.....6-run unemployment ra ignore the fact that we ar nce intervals for U.trick is to write the term .-1 -0- a I + ai 1 - = 1 -zing this result plus the
Uo and the long-run 111e, for example, before hL:as z.e indicator for the au,[UtH -U] = [Uo - UJ a A a - 1 tit log ai = - log 2
= ao + ai Uo, U2 = ao + al Ui =- ao + ai Ut = ao [1 + ai + a; +expression can be re% ai Ut - f7/ = [ U0 - a 41 fquation (7.5) can be used een U0 and U to be el
Ut = ao + ai Utwould equal 6.21% 1- he adjustment speed by sol;:employment rate at time can be solved by repeated su
Fact 4: In the very long run unemployment shows no trend This fact has been graphically illustrated in Figures 7.4 and 7.5. Although there are sharp peaks and deep troughs, there does not seem to be
Source: Layard, Nickell, and Jackman (1991, p. 6)rise in long-term unemployment has been much larger than that in short-term unemployment. We shall return to this issue below.
Belgium 8.7 1.9 6.8 8.2 3.4 4.8 Denmark 9.6 6.8 2.8 6.2 - -France 8.9 5.4 3.5 5.9 4.1 1.8 Germany 5.0 2.6 2.4 3.2 2.6 0.6 Ireland 14.0 4.8 9.2 7.1 4.8 2.3 Italy 7.9 2.4 5.5 5.2 3.3 1.9 Netherlands
The Foundation of Modern Macroeconomics Table 7.2. Unemployment duration by country 1990 1979 All Under 1 year Over 1 year All Under 1 year Over 1 year
c Nordic countries only Source: Bean (1994)163
b Percentage of total unemployment
a Percentage of source population
Table 7.1. The nature of unemployment European Community United States Japan Non-EC Europe'Notes:
The same pattern is observed in Table 7.2 which has been taken from Layard, Nickell, and Jackman (1991, ch. 1). Between 1979 and 1990, the total level of unemployment has risen in most countries, but
The striking pattern that can be observed in Table 7.1 is that the inflow rates are relatively similar in the two years, but that the outflow rate in the EC has halved between 1979 and 1988! In
Fact 3: The rise in European unemployment coincides with an enormous increase in long-term unemployment Almost half of Europe's unemployed have been unemployed for more than one year. In Table 7.1,
Chapter 7: A Closer Look at the Labour Market where Ut is the actual unemployment rate at time t and Ch- is the unemployment rate predicted by the regression equation. The numbers in parentheses are
cs▪ pt JAC Oki 'Some: Bean I 162 1980 I 2000-0 1990 10-2000 OP period 1900-1989:(7.1)(7.2)
Milemployment TJble 7.1.1 S• es won hon-EC hoop I
vitireen 1979 and much by probabilay 1 same pat!and
4%. a job express, The striking p,: -. i

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