Problem Set 6
FE411 Spring 2014
Rahman
Some Answers
1) Capital Flows Within Europe
Consider Europe as a whole. Europe’s entire capital stock in the steady state may be
accurately described by the following equation:
 A 
k ss Eur   Eur Eur 
 

1
1
where  Eur and AEur is the European-average investment rate and European-average
productivity, respectively.  is the depreciation rate of capital.
Now consider a small open country within Europe, like Greece. Greece’s capital stock in
the steady state may be accurately described by the following equation:
1
k ss Greece
 AGreece  1

 
r
 Eur 
where AGreece is the productivity of Greece, and rEur is the rental rate of capital for all of
Europe.
a) In a couple of sentences, can you explain why the expression for European capital
differs so much from Greek capital? In particular, why is it that the investment
rate in Greece does not affect the stock of capital in Greece?
If Greeks save more (that is, γGreece increases), Greeks will not get any more
capital than they already have. The reason is that the extra savings will likely
flow abroad to other European countries. Similarly, if Greeks save very little,
they will probably have capital flow into the country. On the other hand, Europe
as a whole can be considered a closed economy – in this case savings in Europe
must equal investment in Europe.
b) Suppose that Greeks save a lot (that is, γGreece is very high). Would you expect
Greece to be a net borrower or a net lender in international capital markets. Why?
We would expect Greece to be a net lender. Those extra savings are allowed to
flow to the most productive places in Europe. When that happens, Greek savers
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Problem Set 6
FE411 Spring 2014
Rahman
lend to other parts of Europe, and those other European countries get to have
more capital.
c) Suppose that AGreece / AEur rises (that is, relative productivity in Greece rises).
How would you expect this to change the flow of capital?
We should expect capital to flow into Greece. Why? Because capital flows to
where it is most productive (i.e., where its marginal product is highest).
d) Finally, suppose that the European rental price of capital, rEur , doubles. By what
factor will the level of GDP per worker change in Greece? For this problem,
assume that the value of α, capital’s share in the production function, is 0.5.
If the European rental price of capital doubles (from rEur with the old steady-state
to 2 rEur with the new steady state), we can write the new steady-state level of
output per worker as:
y new ss  A
1
1
  


2
r
 eur 

1
A
1
1
  


r
 eur 

1


1
 1  1
old  1 
   y ss  
2
2
Assuming α = 0.5, you should find that
1
y new ss   
2
0.5
0.5
1
   y old ss
2
That is, the new steady-state income level in Greece falls by half when the
European rental rate of capital doubles.
2) Government Actions
For each of the following government actions, explain where it fits into the discussion of
the rationales for government policy listed in Section 12.1. What market failure, if any,
does the policy address? Does the policy stimulate economic growth? Is the policy an
example of government failure? Whose interests are served by the policy?
a) In 238 B.C., the Chinese emperor Qin Shi Huang Di enacted a law standardizing the
length of axles on carts so that the wheels of carts could more easily follow in the ruts of
those that had gone before.
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Problem Set 6
FE411 Spring 2014
Rahman
Standardization of the length of axles on carts is a form of a public good. Everyone
benefits from improvements in travel, and improvements in travel are beneficial for
growth.
b) Most countries have central banks that are responsible for controlling the quantity of
money and regulating the price level.
Central banks that control the quantity of money and regulate the price level address
coordination failures. Everyone benefits from economic stability, and the minimization
of idle resources improves the prospects for growth.
c) Many governments subsidize vaccinations against infectious diseases or require that
children be vaccinated before attending school.
This is a public good that also addresses the externality characteristic of the spread of
disease. Everyone benefits through improvements in health, and improvements in health
a component of human capital that leads to higher growth.
d) In many countries, it is illegal to operate a private mail service in competition with the
government post office.
If one assumes that mail delivery is a natural monopoly, as it may be inefficient for
multiple firms to be able to route to all houses, government regulation can address the
market failure present in monopolies. By operating mail delivery services, the
government can insure that an inefficiently high price for mail delivery is not charged.
By preventing competing private mail delivery services, the government insures that mail
delivery will be controlled by the government. Hence everyone benefits.
If the previous assumption is invalid, then government policy restricting competing mail
services would maintain a government monopoly in this sector. Limiting competition in
this manner would reduce productivity in the long run. Everyone would be worse off in
the long run.
e) Many governments impose a minimum wage.
The answer is unclear. On the one hand, the imposition of a minimum wage can be an
example of a government failure. The minimum wage can result in the misallocation of
factors among firms and sectors, and in this case, it serves those who do receive the
minimum wage. Growth may be hindered. On the other hand, the minimum wage may
satisfy normative goals of government, that being equality and general well-being. In
this case, the minimum wage is intended to serve everyone by eliminating low wage
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Problem Set 6
FE411 Spring 2014
Rahman
abuses by firms. Growth may be positive. It depends on the level of the minimum wage
itself. If it is above the “optimal” wage, the first scenario will likely hold.
f) Many governments pay some or all of the costs of college education for their citizens.
The payment for some or all of the costs of college education for their citizens is an
example of government intervention leading to an increase in the positive externalities of
education. In choosing to pursue college education, an individual does not factor the
additional societal benefit that an educated person offers, but only considers one’s direct
benefits compared to one’s direct costs. By allowing college education to be more
affordable, the positive externality effects (provided they exist) increase, benefiting
everyone and inducing further growth.
3) Inequality and Economic Mobility
What is the relationship between a poor person’s perception of economic mobility and
the person’s desire to see a high level of redistributive taxation? How would the degree
of redistributive taxation compare in two countries that had the same distribution of
income but different levels of economic mobility?
The relationship between a poor person’s perception of economic mobility and
that person’s desire to see a high level of redistributive taxation is negatively correlated.
If perceptions of mobility are low, a high level of redistributive taxation will be desired,
and conversely, if perceptions of mobility are high, a low level of redistributive taxation
will be desired. As a result, in a country with the same distribution of income as another,
the country with low mobility would have a higher level of redistributive taxation relative
the other country with high mobility.
4) Culture and Ethnic Fractionalization
In a certain country, there are three ethnic groups: 50% of the population belongs to
Group A, 25% of the population belongs to Group B, and 25% of the population belongs
to Group C. What is the country’s index of ethnic fractionalization?
I
2
A country’s index of ethnic fractionalization is 1   ni , where ni is the fraction of the
i 1
population belonging to group i. Given that there are 3 ethnic populations with
respective fractions of 0.5, 0.25, and 0.25, we substitute and solve.
1-[ (0.5)2 + (0.25)2 + (0.25)2 ] = 1 – [0.375] = 0.625.
That is, the index of ethnic fractionalization is 0.625.
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