Answers to Textbook Questions and Problems
CHAPTER 9 Economic Growth II: Technology, Empirics, and Policy
Questions for Review
1. In the Solow model, we find that only technological progress can affect the steady-state rate of growth in income per worker. Growth in the capital stock (through high saving) has no effect on the steady-state growth rate of income per worker; neither does population growth. But technological progress can lead to sustained growth.
2. In the steady state, output per person in the Solow model grows at the rate of technological progress g. Capital per person also grows at rate g. Note that this implies that output and capital per effective worker are constant in steady state. In the U.S. data, output and capital per worker have both grown at about 2 percent per year for the past half-century.
3. To decide whether an economy has more or less capital than the Golden Rule, we need to compare the marginal product of capital net of depreciation (MPK – δ) with the growth rate of total output (n + g). The growth rate of GDP is readily available. Estimating the net marginal product of capit
al requires a little more work but, as shown in the text, can be backed out of available data on the capital stock relative to GDP, the total amount of depreciation relative to GDP, and capital’s share in GDP.
4. Economic policy can influence the saving rate by either increasing public saving or providing incentives to stimulate private saving. Public saving is the difference between government revenue and government spending. If spending exceeds revenue, the government runs a budget deficit, which is negative saving. Policies that decrea the deficit (such as reductions in government purchas or increas in taxes) increa public saving, whereas policies that increa the deficit decrea saving. A variety of government policies affect private saving. The decision by a houhold to save may depend on the rate of return; the greater the return to saving, the more attractive saving becomes. Tax incentives such as tax-exempt retirement accounts for individuals and investment tax credits for corporations increa the rate of return and encourage private saving.
5. The legal system is an example of an institutional difference between countries that might explain differences in income per person. Countries that have adopted the English style common law system tend to have better developed capital markets, and this leads to more rapid growth becau it is easier for business to obtain financing. The quality of government is also important. Countries
with more government corruption tend to have lower levels of income per person.
6. Endogenous growth theories attempt to explain the rate of technological progress by explaining the decisions that determine the creation of knowledge through rearch and development. By contrast, the Solow model simply took this rate as exogenous. In the Solow model, the saving rate affects growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, many endogenous growth models in esnce assume that there are constant (rather than diminishing) returns to capital, interpreted to include knowledge. Hence, changes in the saving rate can lead to persistent growth.
Problems and Applications
1. a. In the Solow model with technological progress, y is defined as output per effective worker, and k is defined as capital per effective worker. The number of effective workers is defined as 酒糟鸡的做法L E (or LE), where 小型水库L is the number of workers, and E measures the efficiency of each worker. To find output per effective worker y, divide total output by the number of effective workers:
爱综合 b. To solve for the steady-state value of y as a function of s, n, g牛仔舞曲, and δ, we begin with the equation for the change in the capital stock in the steady state:
Δk = sf(k) – (δ + n + g)k = 0.
The production function can also be rewritten as y2 = k. Plugging this production function into the equation for the change in the capital stock, we find that in the steady state:
sy laurier– (δ + n + g)y掩耳盗铃近义词2 = 0.
Solving this, we find the steady-state value of y:
y* = s/(δ + n + g).
c. The question provides us with the following information about each country:
Atlantis: s = 0.28 Xanadu: s = 0.10
n = 0.01 n = 0.04
g = 0.02 g = 0.02
δ = 0.04 δ = 0.04
Using the equation for y* that we derived in part (a), we can calculate the steady-state values of y for each country.
Developed country: y*五四运动的性质 = 0.28/(0.04 + 0.01 + 0.02) = 4
Less-developed country: y* = 0.10/(0.04 + 0.04 + 0.02) = 1
2. a. In the steady state, capital per effective worker is constant, and this leads to a constant level of output per effective worker. Given that the growth rate of output per effective worker is zero, this means the growth rate of output is equal to the growth rate of effective workers (LE). We know la
bor grows at the rate of population growth n and the efficiency of labor (E) grows at rate g. Therefore, output grows at rate n+g. Given output grows at rate n+g and labor grows at rate n, output per worker must grow at rate g. This follows from the rule that the growth rate of 和平画Y/L is equal to the growth rate of Y minus the growth rate of L.
