Macroeconomics and Economic PolicyGregory de Walque

Chapter 13: exercises

13.1 .

(a) False. The theory points no particular relationship between tech-nological progress and employment, especially in the long run(which is the dimension considered in the question as is clear fromthe expression "steady increase in employment"). In the short run,an increase in technological progress can have either a positive ora negative eect on employment, depending of the direction ofthe shift in the aggregate demand (aggregate supply always shiftsright). If AD shifts right also (case of a technological progressthat makes existing capital stock obsolescent and gives the rmsan incentive to invest in new capital goods that embeds the newtechnology), employment will clearly be pushed upwards in theshort run. If AD shifts to the left su ciently strongly (case of atechnological progress that does not take the form of an invest-ment in a new technology, but rather of a more e cient use of theexisting technology), the short run eect on employment can beeven negative, as there is no further investment and the more e -cient use of the new technology allows to get rid of some workers.In the medium run, the natural unemployment rate can only beaected by technological progress if the latter is badly forecastedby the workers when setting the WS curve. If Ae 6= A, the PSshifts up by +A while the WS curve shifts up only by +Ae A, the natural unemployment ratewill increase, as the PS curve increases less than the WS curve.

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(b) If P e = P but Ae = A then the PS and WS curves crosses when

W

P=

A

1 + = A(1 u)

, u = 1 11 +

=

1 + =

0:08

1 + 0:08= 0:074 = 7:4%

...

(c) ...and we see that the natural rate does not depend on productivitysince A cancels out in the rst line of the computation above. Asseen in point (a) above, the natural rate of unemployment will onlybe aected if Ae 6= A, i.e. for unexpected changes in productivity.

13.4 .

(a) One can hope that increasing spending on computers at publicschool should benet to those for who that will only attend publicschool and no else further education. They will be relatively moreskilled than in the absence of this spending. Therefore it shouldbenet to low skilled workers, but only in the medium to long run,when these pupils will enter the labour force.

(b) limiting the number of foreign temporary farm workers will pro-voke an articial scarcity in low skilled workers. This should alsobenet to the wage of this segment of the labour force.

(c) An increase in the number of public colleges should help reducethe private cost of education. Students who otherwise would havestopped their cursus sooner will continue to study somewhat more,increasing the number of skilled workers versus the number of lowskilled worker. This could decrease the scarcity in skilled workers,decreasing their wage and increase the relative scarcity in unskilledworkers, increasing their relative wage.

(d) Central America countries workers are, on average, less skilledthan US workers and they work for a lower wage than unskilledUS workers. If Central America countries oer tax credits to USrms, those rms will benet from an articial (scal) advantageto install there for they activities necessitating low skilled workers.Doing this, their demand for unskilled workers in US will decrease,pushing downwards the unskilled workers wages.

13.5 It is true that technological progress in the agricultural sector has al-lowed to dramatically increase the production of agriculture while em-ployment in this sector decreased even more dramatically. However, at

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the aggregate level, one cannot say that employment has been destroyedin the United States. The overall number of workers is much bigger nowthan it was at the start of the last century. This means that the workerswho are not needed anymore in the primary sector have found a placeto work in another sector that started to grow at the same time thatless farmers were needed: industry. Later on the productivity gain inindustry (and competition from emerging countries) have pushed thelabour force towards the service sector. Note that the service sector isnow becoming much more heterogenous than it was previously, withsome services requiring relatively few skills (e.g. haircut) while oth-ers require on the contrary very high skill (e.g. consultancy servicesfor rms regarding IT implementation, tax optimization, marketing,production organization, ...).

We thus conclude that technological progress may indeed kill jobswithin a particular sector, but in the medium and long run this willbe compensated by a stronger labour demand in other segments ofthe economy. However, higher technological progress go along with astronger demand for skill labour.

13.6 Lets consider the following equations describing production function,PS andWS curve together with the relationship between employmentand unemployment rate:

Y = ANW

P=

A

1 + (PS curve)

W

P e= Ae(1 u) (WS curve)

N = (1 u)L

(a) Referring to chapter 7, we obtain the aggregate supply curve byequating the WS and the PS curve in order to get a relationshipbetween the aggregate price level on the one hand (P ) and GDP(Y ) and expected price level (P e) on the other hand:

PA

1 + = P eAe(1 u)

, P = P e(1 + )Ae

A(1 u)

, P = P e(1 + )Ae

A

Y

AL(AS curve)

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where the last step is obtained from the production function andthe relationship between employment and unemployment rate

N =Y

A= (1 u)L

, (1 u) = YAL

.

Therefore, in the (Y; P ) plane, the AS curve is

- positively sloped (if Y increases, P increases as well);- its position depends positively on the price mark-up , theprice expectation P e and of the expected level of technologicalprogress, i.e. if , P e or Ae increases, the AS curve shifts up;

- its position depends negatively on the price actual level oftechnology A and on the labour force L.

(b) If A and Ae shift by the same amount, then Ae

A= 1 and the AS

curve shifts down because of the increase in labour productivityinduced by the increase in A:

P = P e(1 + )Y

A " L (AS curve)This shifts the AS curve down and to the right, such that forthe same price level corresponds a higher GDP reecting that forthe same labour cost per worker (wage), the economy is able toproduce more. Note that in this case, the potential output (deter-mined by the natural rate of unemployment) is left unchanged.

(c) Assume now that A shifts up but that Ae doesnt. Then we have

P = P e(1 + )Ae

A "Y

A " L (AS curve)

and the AS curve is shifted down and right but much more than in(b) above since A appears now twice in the denominator. Further-more, if A shifts up but not Ae, the natural unemployment ratewill decrease. Therefore the potential output increases, yielding toa permanent increase in real output.

13.7 We assume a dual labour market with high-skill and low-skill labour.

(a) If the labour force is unchanged and that the demand for thehigh-skill segment increases while the demand for the low-skillsegment decreases, the real wage of high-skilled workers will tendto increase and this of low-skilled workers will tend to decrease.

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(b) In a country with minimum wage legislation, the wage cannotdecrease to lower levels than xed by law. If ever the wages forlow-skilled workers was pushed down to the minimum wage limit,any further downward pressure would then translate into moreunemployment in this segment of the labour market. Thereforewe may conclude that limiting the wage exibility usually end upinto more unemployment.

(c) After an increase of demand in the high-skill segment and a de-crease of demand in the low-skill segment, the wage inequalitywill be higher in the country without minimum wage legislation.In the country with minimum wage legislation, from the momentthe limit of the minimum wage is hit, the wage distribution willbe relatively less unequal, but the unemployment will increase,creating another form of inequality.

(d) The labour market is indeed less exible in European countriesthan in the US, not only because of minimum wage legislation,but also because of the higher degree of unionization of the econ-omy and some other practices like wage indexation to price level,longer duration of wage contract or a higher protection of labour(higher ring costs for example). This lack of exibility in thelabour market has indeed led the last two decades to less inequal-ity in labour revenues in European countries, but the other sideof the coin is the structurally higher rate of unemployment. Fur-thermore, changes in unemployment are much more persistent inEurope than in the US, an observation that has led to the namehysteresis.

13.8 We consider the WS curveW

P= F (u

; z+

)

with u = 1 NL

(a) The WS curve can then be rewritten as

W

P= F

0BB@1 NL| {z }

; z+

1CCAand the real wage demanded by the workers increases as employ-ment becomes higher. The WS curve may thus be re-interpreted

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as the supply of labour by the workers, where workers agree towork more (N increases) against higher real wages).

(b) If the PS curve is given by

P = (1 + ) MCwith MC =

W

MPL

(ATTENTION there is a fault in the statement of the exercise!!!,MC = W

MPLand not MC = W MPL!!!)

(c) ...and substituting for MC into the price setting equation we ob-tain

P = (1 + ) WMPL

, WP

=MPL

(1 + )

(d) Note that theMPL (marginal productivity of labour) depends onthe form of the production function. In chapter 6, with

Y = N

the MPL was computed as

@Y

@N= 1

which is constant and independent of labour. For a more generalproduction function of the type used in chapters 11 and 12 as

Y = KN1

MPL @Y@N

= (1 )K

N

which depends negatively on labour (i.e. the higher employmentis, the lower the marginal productivity of labour). Since

@(W=P )

@MPL=

1

(1 + )> 0

and@MPL

@N= ()(1 ) K

N1+< 0

then@(W=P )

@N=

@(W=P )

@MPL @MPL

@N< 0

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and we see that the PS curve can be also interpreted as the labourdemand curve by the rms, which is downward sloping. For agiven real wage, rms will hire workers up to the point wherehiring one more worker will make drop the marginal productivityof labour below the marginal cost (equal to the wage). For protmaximizing rms, this is equivalent to the price setting equation.

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