Questions and Answers of Economic Growth

Energy’s share in a CES production function. Consider the following production function: Y = F(K,E,L) = (Kr + (BE) r ) a>p(AL) 1-a. (a) What are the returns to scale in this production function?
Robustness of the growth-drag calculations. In the Nordhaus-style calculation of the growth drag, we assumed a land share of 10 percent and an energy share of 10 percent. As some of the discussion
Solving for t. Show how to derive the solution for t in equation (10.10). Calculate the values for t that correspond to interest rates of 4 percent and 8 percent.
Optimal extraction rate. Suppose that the capital-output ratio is constant and that the real interest rate takes the constant value r. Using the energy model in Section 10.1, solve for the constant
A model with land and energy. Derive the steady-state growth rate of output per worker in a model with both land and energy. In particular, assume the production function for output is given by Y =
Transition dynamics in the natural resources model. For the Solow model with natural resources in Section 10.1, show that K>Y does indeed converge to a constant. Calculate the value of this constant.
The idea production function. What is the economic justifi cation for thinking that the production function for new ideas takes the form given in equation (9.6)? In particular, why might this
Growth over the very long run. Historical evidence suggests that growth rates have increased over the very long run. For example, growth was slow and intermittent prior to the Industrial Revolution.
Market structure in the Lucas model. Think about the market structure that underlies the Lucas model. Do we need perfect or imperfect competition? Do we need externalities? Discuss.
Physical investments in the Lucas model. Does a permanent increase in sK have a growth effect or a level effect in the Lucas model? Why?
Population growth in the AK model. Consider the AK model in which we do not normalize the size of the labor force to one. (a) Using the production function in equation (9.5) and the standard capital
A changing land share. 12 In Section 8.3.3 we mentioned the role of structural transformation in contributing to sustained growth. Consider an economy that produces two goods, an agricultural good
Changes in basic education. Assume there is an increase in the basic skills, u, that each child receives. This may be because of the introduction of universal primary schooling, for example. In the
The importance of growth rates versus productivity levels. Consider two economies, A and B. Both economies are described by the model in Section 8.3, having a population growth function similar in
The Black Death. In Section 8.2.1 we discussed how a major drop in the size of the population could actually raise living standards. Consider an economy that is described by the model in that section
Discuss the meaning of the quotation that began this chapter.
Social infrastructure and the investment rate. Suppose that rates of return to capital are equalized across countries because the world is an open economy, and suppose that all countries are on their
Can differences in the utilization of factors of production explain differences in TFP? Consider a production function of the form Y = IKa(hL)1-a, where I denotes total factor productivity and the
Cost-benefi t analysis. Suppose an investment project yields a profi t of $100 every year, starting one year after the investment takes place. Assume the interest rate for computing present values is
in Chapter 5.) (a) Construct a graph with h . >h on the vertical axis and A>h on the horizontal axis. In the graph, plot two lines: h . h = mecua A h b and h . >h = g. (Note that we’ve assumed g =
Openness to technology transfer. This problem considers the effect on an economy’s technological sophistication of an increase in the openness of the economy to technology transfer. Specifi cally,
The role of m. Provide some economic intuition for the role played by the parameter m. What values of m guarantee that h>A is less than one?
Understanding growth rates. How does the model explain the differences in growth rates that we observe across countries?
Understanding levels of income. This model explains differences in the level of income across countries by appealing to differences in sK and u. What is unsatisfying about this explanation?
The importance of A versus h in producing human capital. How might one pick a value of g to be used in the empirical analysis of the model (as in Chapter 3)? Other things equal, use this value to
The share of the surplus appropriated by inventors (from Kremer 1998). In Figure 5.5, fi nd the ratio of the profi t captured by the monopolist to the total potential consumer surplus available if
and the discussion surrounding this fi gure in Chapter 4 that the number of scientists and engineers engaged in R&D has been growing faster than the rate of population growth in the advanced
The future of economic growth (from Jones 2002). Recall from Figure
Too much of a good thing? Consider the level of per capita income along a balanced growth path given by equation (5.11). Find the value for sR that maximizes output per worker along a balanced growth
An increase in the productivity of research. Suppose there is a onetime increase in the productivity of research, represented by an increase in u in Figure 5.1. What happens to the growth rate and
Pricing with increasing returns to scale. Consider the following production function (similar to that used earlier for ColdAway): Y = 100 * (L - F), where Y is output, L is labor input, and F is a
Provision of goods. Explain the role of the market and the government in providing each of the goods in the previous question.
Classifying goods. Place the following goods on a chart like that in Figure 4.1—that is, classify them as rivalrous or nonrivalrous and by the extent to which they are excludable: a chicken, the
The Mankiw-Romer-Weil (1992) model. As mentioned in this chapter, the extended Solow model that we have considered differs slightly from that in Mankiw, Romer, and Weil (1992). This problem asks you
Reconsidering the Baumol results. J. Bradford DeLong (1988), in a comment on Baumol’s convergence result for the industrialized countries over the last century, pointed out that the result could be
Galton’s fallacy (based on Quah 1993). During the late 1800s, Sir Francis Galton, a famous statistician in England, studied the distribution of heights in the British population and how the
What are state variables? The basic idea of solving dynamic models that contain a differential equation is to fi rst write the model so that along a balanced growth path, some state variable is
Policy reforms and growth. Suppose an economy, starting from an initial steady state, undertakes new policy reforms that raise its steady-state level of output per worker. For each of the following
0.028 0.234 Assume that g + d = .075, a = 1>3 and c = .10 for all countries. Using equation (3.9), estimate the steady-state incomes of these economies, relative to the United States. Consider two
0.102
Cameroon
0.015
0.213
Thailand
0.014
0.144
Argentina
0.012
0.246
Canada
0.010
0.204
Where are these economies headed? Consider the following data: yˆ97 sK u n Aˆ 90 United States
Solow (1956) versus Solow (1957). In the Solow model with technological progress, consider an economy that begins in steady state with a rate of technological progress, g, of 2 percent. Suppose g
Can we save too much? Consumption is equal to output minus investment: c = (1 - s)y. In the context of the Solow model with no technological progress, what is the savings rate that maximizes
Manna falls faster. Suppose that there is a permanent increase in the rate of technological progress, so that g rises to g$. Sketch a graph of the growth rate of output per worker over time. Be sure
An income tax. Suppose the U.S. Congress decides to levy an income tax on both wage income and capital income. Instead of receiving wL + rK = Y, consumers receive (1 - t)wL + (1 - t)rK = (1 - t)Y.
An increase in the labor force. Shocks to an economy, such as wars, famines, or the unifi cation of two economies, often generate large fl ows of workers across borders. What are the short-run and
A decrease in the investment rate. Suppose the U.S. Congress enacts legislation that discourages saving and investment, such as the elimination of the investment tax credit that occurred in 1990. As