宏观经济学 教案Chapter04.docx

CHAPTER 4GROWTH AND POLICYChapter Outline Endogenous growth theory Constant and increasing returns to scale Private and social returns to capital Absolute and conditional convergence Stable and unstable equilibria The poverty trap Growth in Asia The role of human capital Limits to growthChanges from the Previous EditionThe material in Chapter 4 has been modified only slightly. All data have been updated, most notably in Table 1 in History Speaks Box 4-1 and in Figure 1 in History Speaks Box 4-3.Introduction to the MaterialThere is no easy explanation for the fact that different countries experience wide variations in their economic growth rates. Chapter 4 sets out to explain what policy options countries have to affect their growth in per-capita income. Industrial countries may fare best if they devote resources to research and development that will lead to technological improvements. Developing countries, on the other hand, may achieve better results by investing in human capital and getting new technology either through direct foreign investment or by borrowing funds to pay for new physical capital. Poor countries with a high population growth may also want to consider population control policies. Investment in human capital in the form of education also plays a crucial role; however, this is a long-run strategy and it takes a very long time to reap its benefits.The neoclassical theory discussed in Chapter 3 makes it clear that technological progress is essential for long-term growth. It does not, however, completely clarify what factors can affect technological advances and in what ways. Therefore the neoclassical growth model, which treats the growth rate as exogenous, needs to be expanded to take into consideration the ways in which endogenous (self-sustained) growth can be enhanced. The endogenous growth model uses a framework that attempts to explain how government policies and economic behavior can contribute to technological advances. In order to do this, the model assumes that the proportion of an economy's resources that is devoted to research and development determines the rate of technological progress and that the steady-state growth rate is affected by the rate at which the factors of production are accumulated. The major conclusion of endogenous growth theory (in contrast to that of exogenous growth theory) is that countries with different savings and investment rates should have persistent differences in their economic growth rates.1 .c. A model like the one in this question can be used to explain how some countries find themselves in situations with no growth and low income while others have ongoing growth and a high level of income. In the first case, a country may have invested mostly in physical capital, leading to some short-term growth at the expense of long-term growth. In the second case, a country may have invested not only in physical capital but also in human capital (education, skills, and training), reaping significant social returns.2 .a. If population growth is endogenous, that is, if a country can influence the rate of population growth through government policies, then the investment requirement is no longer a straight line. Instead it is curved as depicted below.b. The first equilibrium (Point A) is a stable steady-state equilibrium. This is a situation of low income and high population growth, indicating that the country is in a poverty trap. The second equilibrium (Point B) is an unstable steady-state equilibrium. This is a situation of medium income and low population growth. The third equilibrium (Point C) is again a stable steady-state equilibrium. This is a situation of high income and low population growth. In none of these three cases do we have ongoing growth. For any capital stock k < ku, the economy will adjust to kz, but for any capital stock k > k« or k > ke, the economy will adjust to kc. During the adjustment process to any of these two steady-state equilibria, the change in output per capita only will be transitory.3 .c. To escape the poverty trap (Point A), a country has several possibilities: First, it can somehow find the means to increase the capital-labor ratio above a level consistent with Point B (perhaps by borrowing funds or seeking direct foreign investment). Second, it can increase the savings rate such that the savings function no longer intersects the investment requirement curve at either Point A or Point B. Third, it can decrease the rate of population growth through specifically designed policies, such that the investment requirement shifts down and no longer intersects with the savings function at Points A or B.3a If we incorporate endogenous population growth into a two-sector model of growth, we get a curved investment requirement line and a production function with first a diminishing and then a constant marginal product of capital as depicted below. (Note that the savings and production functions have similar shapes.).b. Here we should have four intersections of the savings function sf(k) and the investment requirement |n(y)+dk. The first equilibrium (al Point A) is a stable low-income steady-state equilibrium. Any deviation from that point will cause the economy to eventually adjust again at the same steady-state income level (and capital-output ratio). The second equilibrium (at Point B) is an unstable low-income equilibrium. Any deviation from that point will lead to either a lower income steady-state equilibrium at Point A (if the capital-labor ratio declines) or a higher income steady-state equilibrium at Point C (if the capital-labor ratio increases). Since Point C is a stable equilibrium, the economy will settle back at that point whether the capital-labor ratio is below or above kc. Point D is again an unstable equilibrium but at a high level of income. Any deviation from that point will lead to either a lower income steady-state equilibrium at Point C (if the capital-labor ratio declines) or ongoing growth (if the capitallabor ratio increases).4 .c. This model is more inclusive than either of the two models discussed previously and thus has greater explanatory power. While the graphical analysis is far more complicated, wc can now see much more clearly that a poor country cannot escape the poverty trap at Point A unless it somehow succeeds in increasing the capital-labor ratio (and thus per-capita income) beyond the level at Point B. The model can also explain why a high-income country can experience ongoing growth.5 .a. The production function is of the formY = "(AN 严=K1/2(4K/NN)1/2 = Ki/2(4K)1/2= 2K.From this we can see that a = 2 sinceY = Y/N = 2(K/N) =>y = 2k.4.b. Since a = y/k = 2, it follows that the growth rate of output and capital isAy/y = Ak/k = g = sa - (n + d) = (0.1)2 - (0.02 + 0.03) = 0.15= 15%.4.c. The term "a" in the equation above stands for the marginal product of capital. By assuming that the level of labor-augmenting technology (A) is proportional to the capital-labor ratio (k), it is implied that the level of technology depends on the amount of capital per worker that we have, which may not be realistic.4.d. In this model, we have a constant marginal product of capital and therefore we have an endogenous growth model.Empirical ProblemsThe first graph depicted below indicates that manufacturing output in the United Kingdom increased over the period from 1950 to 2011, although the increase was not consistent. Over the same time period, the average number of hours worked by an employee decreased. Employment in manufacturing initially increased slightly but then decreased after I960. The fact that output increased despite decreases in employment and the number of hours worked can be explained by an increase in the productivity of workers, as illustrated by the last graph that shows an increase in hourly output per employee.OutputEmployment200Output per hour10702010Additional ProblemsComment on the following statement:Increasing returns to scale imply that the level of output increases only if the level of all inputs is increased by the same amount.”The level of output will increase as soon as the level of one input is increased, even if the levels of all other inputs remain the same. This is always true, even under the assumption of decreasing or constant returns to scale. Increasing returns to scale imply that the level of output increases more than proportional to the increase in all levels of inputs. For example, increasing returns to scale exist when the levels of all inputs are doubled and the level of output more than doubles as a result.1. Comment on this statement.“One implication of the endogenous growth model is that countries with a higher savings rate will have a higher economic growth rate, but only during a transitional period. In the long run, only technological advances can bring about economic growth.”Actually, it is the neoclassical growth model that predicts that countries with access to the same technology and the same rate of population growth but a different savings rate will reach a steady-state equilibrium. In other words, the countries will achieve a different level of income per capita but will have the same long-tenn growth rate. The endogenous growth model, on the other hand, predicts that there is a positive correlation between savings rates and growth rates across countries and that those countries that can increase their savings rates will also increase their long-term growth rates.2. Assume the aggregate production function is of the following form: Y = aK. At what capital-labor ratio (k) can a steady-state equilibrium be reached?From the production function: Y = aK, it follows that y = Y/N = a(K/N) = ak. Therefore, the savings function is sy = s(ak) and has a constant slope sa > (n + d). Since the savings function and the investment requirement both have constant slopes, namely sa for the savings function and (n + d) for the investment requirement, these two lines will never intersect. Therefore, a steady-state equilibrium cannot be reached.3. What are social returns to capital and why are they so important for economic growth?Paul Romer suggested that private returns to capital should be separated from social returns to capital. If a country invests in new technology, the result is not only an increase in the capital stock that will produce a higher level of output, but also the development of new ways of doing things. Since new production methods may be applied elsewhere, they create external (social) benefits. In addition, one new idea generally creates other new ideas and knowledge may grow indefinitely. Therefore it pays to devote more resources to enhancing human capital, with particular emphasis on research and development, since this will lead to a higher economic growth rate.4. Comment on the following statement:“The endogenous growth model predicts conditional convergence.”This statement is false. Conditional convergence is the notion that countries with different savings rates but the same rate of population growth and access to the same technology will achieve the same long-term growth rate even though they may achieve a different standard of living. This is contrary to the endogenous growth model, which predicts that there is a positive correlation between savings rates and growth rates across countries. In other words, the endogenous growth model predicts that if a country is able to increase its savings rate, it will be able to achieve a higher long-term growth rate.5. Can a poor country ever catch up with a rich country if both have the same population growth? Explain your answer.Over the long run, the growth rate of output is determined by the rate of population growth and the rate of technological progress. In the short run, a nation's growth rate can be affected by investment in machinery, infrastructure, and human capital. Il is impossible to predict for sure whether countries with low incomes can ever succeed in catching up with the standard of living of countries with much higher incomes. Empirical evidence suggests slow conditional convergence, which means that the positive impact of a higher level of investment spending is only transitory. In other words, by devoting a larger share of GDP to capital investment a country can achieve a higher level of income per capita but most likely not a higher economic growth rate. Countries eventually will converge to steady states, depending on the share of investment to GDP, the share of government spending to GDP, and the rate of investment in human capital. However, the process of convergence is extremely slow.6. “A higher population growth is always desirable since it will lead to higher living standards. Therefore, nations should always implement policies that will lead to an increase in population." Comment on this statement.In the neoclassical framework, if the rate of population growth (n) increases, the capital stock will also grow but at a lower rate. Since a country has to feed its people, not enough can be saved and invested to keep the capital-labor ratio (k) at its original level. Thus, the capitallabor ratio decreases until a new steady state is reached. In other words, the investment requirement, (the n + dk-linc) gets steeper as population growth (n) decreases, and will now intersect the savings function at a lower steady-state capital-labor ratio (k). This implies a lower level of output per capita (y) and therefore a lower living standard.But if we instead assume that population growth is endogenous, then the investment requirement, that is, the n(y) + dk-function, is curved and no longer straight. In this case, a country that has a high rate of population growth but a low income level can find itself in a poverty trap. Such a nation needs to implement population control policies to increase living standards.Therefore we can see that the exogenous growth model and the endogenous growth model both suggest that a lower population growth is desirable and can serve to increase per- capita income.7. Comment on the following statement:“A poor country can escape the poverty trap, if it either devotes a larger share of GDP to investment or implements a population control program.”A poor country may be hard pressed to devote a larger share of its GDP to investment if there are barely enough resources to feed the population. Therefore, attracting direct foreign investment or borrowing foreign funds for capital investment projects may be a more feasible solution, as long as the funds are invested wisely. A better alternative for increasing living standards is to control population growth. However, population control policies can be unpopular and difficult to implement and their success is not always guaranteed.8. If a developing country has barely e