Chapter 12
Government
Note: Special icons in the margin identify problems requiring calculus .
◼ Solutions to Problems
1. a. Standardization of the length of axles on carts is a form of a public good. Everyone benefits
e. If one assumes that mail delivery services 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
f. The answer is unclear. On 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
g. The failure of African governments to maintain roadways is a government failure. The case for
government intervention in the provision of public goods such as roadways is economically
48 Weil • Economic Growth, Second Edition
2. In the first figure below, we represent two countries with varying quality levels of government and
varying incomes. In this figure, the horizontal axis measures output and the vertical axis measures
the quality of government. A country with a low quality of government will be positioned vertically
below a country with a high quality of government. As such, Country A has both more income and a
better quality government than does Country B.
In the second figure, we graphically depict each channel of causation. Both curves are positively
Chapter 12 Government 49
3. The economist understands that the only way to determine whether more income causes better
government or whether better government causes more income is to find an event in which we know
that one determinant changed, and which cannot plausibly have caused a direct change to the other,
and then see if the other determinant changed. In statistics, this is known as having a valid instrument.
4. a. Denoting
d
Q
as the quantity demanded and
s
Q
as the quantity supplied, at the market-
clearing price or equilibrium price of this model, the quantity supplied must equal the quantity
demanded for a good. That is,
,
ds
QQ
=
b. At a tax rate of
for each good, the quantity demanded for any given price does not change
because the price paid by the consumer remains unaffected. However, the quantity supplied for
50 Weil • Economic Growth, Second Edition
In equilibrium, the price must be set such that the quantity demand meets the quantity supplied.
Setting
,
ds
QQ=
and solving for P, we get:
c. In order to solve for the tax rate that will maximize government revenue, we first must write the
revenue function as a function of the tax rate. Government revenue for each good is
eq .P
Since
the amount of the good sold is
eq ,Q
we know that government revenue is equal to
eq eq.PQ
5. The elasticity of labor supply determines the market response to the income tax. If labor is supplied
Chapter 12 Government 51
6. a. In the steady-state level of output per worker, the quantities of government capital per worker
and physical capital worker will not change over time. Therefore,
52 Weil • Economic Growth, Second Edition
Using the values,
(1/3),
==
we now have two equations with two unknowns. Working
through the algebra and solving for the steady-state values of
ss
x
and
,
ss
k
we get: