EC108 Macroeconomics 1
Review Class 2 - Suggested Answers∗
Jorge F. Chavez
May 10, 2015
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True or false
Indicate whether the following statements are true, false or uncertain. Explain your answer.
(a) Tax cuts decrease national savings.
Answer. UNCERTAIN. The statement is true under the Keynesian way to model consumption, i.e. that
there is a marginal propensity to consume: public savings decrease by the amount of the tax cut and private
savings increase but by a lower amount due to the mechanical way in which agents decide between consumption and savings. The statement is false if the Ricardian Equivalence holds. Under these assumptions,
private savings might exactly offset the reduction in public savings if people anticipate that the government
will have to increase taxes in the future. They simply save the tax cut, and continue to consume the same
amount as before.
(b) Faster money growth causes inflation to increase.
Answer. UNCERTAIN. We know from the quantity equation that %∆M + %∆V = %∆P + %∆Y . Hence
an increase in %∆M must be matched with some increase of the growth rates of P , Y or a decrease in the
growth rate of V . Empirically, in the long-run, an exogenous increase in the growth rate of M will produce
a matching increase in inflation, so that in that sense the answer is true. However if the growth rate of
Money is rising in combination with an increase in the growth rate of output, which produces an increase
in money demand, then inflation might not be affected at all.
(c) In the Solow model, economies with faster population growth have lower per capita incomes.
Answer. TRUE. Faster population growth rotates the break-even investment line upwards (e.g. the line
[n + δ + g]k in the model with population growth and technological progress), so that it intersects the
savings function at a lower steady state capital/labor ratio, which means steady state per capita income
will be lower when population growth is faster.
∗
Disclaimer: None of these questions are mine, they come from several sources that I collected through the years. In
some cases I adapted those from their original versions to fit the requirements of our module. Please note that as can
be inferred from the title these are only suggested answers.
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EC108
Review May 2014
(d) According to advocates of the Ricardian Equivalence theory, government spending does not affect
saving.
Answer. FALSE. Ricardian Equivalence is concerned with the financing of a given path of government
expenditures e.g., whether its financed by taxes now, or by bonds (taxes later). Temporary, or anticipated,
government spending policies will generally cause private saving to respond, as households attempt to
smooth out their effects over time.
(e) Reducing inflation causes the unemployment rate to rise.
Answer. UNCERTAIN. It depends on whether the policies implemented to bring down inflation are credible
(i.e. expected). Credible disinflations need not increase unemployment.
(f) The growth rate of nominal GDP always exceeds the growth rate of real GDP.
Answer. FALSE. If prices are falling on average (i.e, the country is experiencing deflation), then the growth
rate of real GDP will exceed the growth rate of nominal GDP.
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Unemployment
Indicate whether each of the following people is frictionally unemployed or structurally unemployed
or cyclically unemployed or not officially unemployed. Explain your answer.
(a) A poorly educated former telephone operator, replaced by a machine, looking for work.
Answer. Structural unemployment. From the textbook: The unemployment resulting from wage rigidity
and job rationing is sometimes called structural unemployment. Workers are unemployed not because they
are actively searching for the jobs that best suit their individual skills but because there is a fundamental
mismatch between the number of people who want to work and the number of jobs that are available. At
the going wage, the quantity of labor supplied exceeds the quantity of labor demanded, so many workers
are simply waiting for jobs to open up.
(b) A woman with good job skills who cannot find a job due to a sluggish economy.
Answer. Cyclical unemployment, which is defined as the deviation of unemployment rate from the natural
rate. This is precisely what occurs in recessions.
(c) A 17 year old with good job skills looking for a job.
Answer. Frictional unemployment. The unemployment that results because it takes time for workers to
search for the jobs that best suit their skills and tastes.
(d) A welfare recipient with good job skills who is not looking for work.
Answer. Not officially. The individual is not part of the labor force.
(e) A man with obsolete job skills who has given up trying to find work.
Answer. Not officially. The individual is not part of the labor force.
Jorge F. Chávez
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EC108
3
Review May 2014
Money and inflation
The quantity theory of money (Fisher 1911) asserts that money demand is proportional to nominal
income, i.e. Md = kP Y , with k constant.
(a) What is the velocity of circulation of money according to this specification?
Answer. Velocity is defined as the ratio between nominal income and money, i.e.P Y /M . In this specification
this is equal to 1/k. As k is constant, velocity is also constant.
(b) Modern theory of money demand considers the nominal interest rate as a further determinant of
money demand. Specifically Md = P L(Y, i), with L increasing in Y and decreasing in i. Give
intuition for why L decreases with i.
Answer. L decreases with i because the nominal interest rate represents the opportunity cost of holding
money. The higher the interest rate, the higher the loss of financial income that could be earned on assets
that are imperfect substitutes to money.
(c) Consider the further assumption that the L(Y, i) function is separable, i.e. L(Y, i) = Y ℓ(i), with ℓ
decreasing in i. Is money demand still proportional to nominal income as in the original quantity
theory?
Answer. Now Md = P Y ℓ(i). Money demand is no longer proportional to nominal income, as ℓ(i) varies
with the interest rate (is not constant).
(d) Obtain an expression for velocity in this new specification. How would you expect velocity to
change with an increase in i? Provide economic intuition for this effect. How does this result
differ from the original quantity theory?
Answer. V elocity = P Y = M = 1/ℓ(i). As ℓ′ (i) < 0, velocity increases with the interest rate. When the
interest rate is relatively high, the opportunity cost of holding money is high, and thus individuals - other
things equal - tend to get rid of their money holdings faster. This raises velocity.
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Solow and inmigration
Three economists are debating whether an increase in the number of immigrants will increase, decrease
or have no effect on the growth rate of the domestic economy. Use the Solow model to justify each
of their arguments. Hint: Take into account that immigrants could arrive with some endowment of
capital k ≥ 0.
Answer. If immigrants enter the country with an endowment of capital per head that is lower than that of
natives (including the case in which immigrants arrive with no capital), then more intensive migration reduces
the capital/labor ratio in the economy (i.e. to the left of the steady-state), so growth becomes positive in the
short run, until capital per worker goes back to the pre-existing steady-state level.
If immigrants enter the country with an endowment of capital per head that is higher than that of natives
(for example, suppose immigrants arrive with their machines), more intensive migration raises the capital/labor
ratio (i.e. to the right of the steady-state), so growth goes negative in the short run, again until capital per
worker goes back to the pre-existing steady-state level.
Jorge F. Chávez
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EC108
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Finally, if immigrants enter the country with an endowment of capital per head that is the same as that of
natives, the capital/labor ratio does not change, nor the short term growth rate of the economy.
In the long run, growth is unchanged in the three cases (e.g. it will stay at zero in the case of an economy
with no population growth and not tech. progress).
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Solow with technological progress
An economy described by the Solow growth model with technological progress has the following
√
production function yt = (kt ) where yt denotes output per effective worker, yt = Yt /(At Lt ), and kt
denotes capital per effective worker, kt = Kt /(At Lt )
(a) Solve for the steady state value of yt as a function of parameters s, n, g and δ?
Answer. The steady-state condition is:
sf (k) = (δ + n + g) k
And the resulting k is:
(
k=
s
δ+n+g
)1/(1−α)
Solving for y:
y = k 1/α =
s
δ+n+g
where the last equality comes from α = 1/2.
(b) A developed country has a saving rate of 28% and a population growth rate of 1% per year. A
less-developed country has a saving rate of 10% and a population growth rate of 4% per year. In
both countries, g = 0.02 and δ = 0.04. Find the steady-state value of y for each country.
Answer. For the developed country: y = 0.28/(0.04 + 0.01 + 0.02) = 4. For the less developed country
y = 010/(0.04 + 0.04 + 0.02) = 1
(c) What policies might the less-developed country pursue to raise its level of income?
Answer. Two policies are clear:
(a) Lowering the growth rate of population, with birth control campaigns and/or subsidized/free birth
control.
(b) Raising the saving rate, by reducing the government budget deficit and/or with private incentives to
saving (reducing tax on capital gains, estate etc., replacing income with consumption tax, etc.).
When trying to raise the saving rate, it makes sense to wonder what happens to steady state consumption.
The condition that characterizes the golden rule stock of capital per effective worker is f ′ (k) = δ + n + g.
With the given numbers:
• f ′ (k) = 12 k −1/2 = 12 and δ + n + g = 0.1 in the less developed country (recall that k = 1 in steady
state). As the marginal product of capital is above δ + n + g the economy is below the golden rule
Jorge F. Chávez
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EC108
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steady state and an increase in s would temporarily reduce consumption per effective worker but
will yield a permanent increase in the long run (which will be equal to the maximum consumption
attainable by this economy).
• f ′ (k) = 12 k −1/2 = 12 (4)−1/2 = 1/4 and δ + n + g = 0.1 in the developed country (recall that k = 4
here. Same conclusion applies here.
Jorge F. Chávez
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