CHAPTER 4 GROWTH AND POLICY
Solutions to the Problems in the Textbook Conceptual Problems:
1. Endogenou Endogenouss or self-sustain self-sustained ed growth suppos supposedly edly can be achieved achieved by policies policies that affect a nation's nation's savings rate and therefore the proportion of GDP that goes towards investment. The neoclassical growth growth model model of Chapte Chapterr 3 predic predicted ted that that long-t long-term erm growth growth can only only be achiev achieved ed throu through gh techno technolog logica icall progre progress ss and that that change changess in the saving savingss rate rate have have only only transi transitor tory y effect effects. s. The endogenous growth model, however, predicts that countries with a higher savings rate can achieve higher long-term growth and that a nation's government can affect the long-term growth rate by implementing policies that affect the savings rate. 2. A simple simple model with constant constant returns returns to scale to capital alone alone implies increasing returns to scale to all factors taken together, which could cause a single large firm to dominate the economy. However, such a model ignores the possibility that external returns to capital exist, in addition to the internal (private) returns. In other words, more investment not only leads to a higher and more efficient capital stock but also to new ideas and new ways of doing things, which can then be copied by others. Therefore, a single firm does not necessarily reap all of the benefits of increased output.
3. In the neoclass neoclassical ical growth growth model, model, an increase increase in the the savings savings rate does not not increase increase the long-t long-term erm growth growth rate rate of output output.. Howeve However, r, becaus becausee of the shortshort-run run adjust adjustme ment nt proces process, s, there there is some some transitional gain that will lead to a higher level of output per capita. In the endogenous growth model, however, the savings rate does affect the long-term growth rate of output.
4.a. Chapter Chapter 4 suggests suggests that the key to long-term long-term economic economic growth is investmen investmentt in human and physical physical capital with particular emphasis on research and development. 4.b. (i) Investment Investment tax credits credits may potentiall potentially y affect economic economic growth in the long run by achieving achieving a higher rate of technological progress. (ii) R&D subsidies and grants lead to technological advances that will have private and social returns. They are very effective in stimulating long-term economic growth. (iii) According to the endogenous growth model, policies designed to increase the savings rate will increase the long-term growth rate of output. However, empirical evidence does not lend much support to that notion. (iv) Increased funding for primary education has large private and social returns and is therefore an excellent means to stimulate long-term growth, even though it may take a long time until these policies have their full effect. effect.
5. The notion notion of absolu absolute te converg convergenc encee state statess that that econom economies ies with the same savings savings rate and rate of population growth will reach the same steady-state equilibrium if they have access to the same
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technology. The notion of conditional convergence states that economies that have access to the same technology and the same rate of population growth but different savings rates will reach steady-state equili equilibri briaa at a diffe differen rentt level level of output output but the same econom economic ic growth growth rate. There There is empiri empirical cal evidence to support the notion of conditional convergence across countries.
6. Endogenous growth growth theory assumes assumes that the steady-state growth growth rate of output output is affected by the rate at which the factors of production are accumulated. Therefore, an increase in the savings rate would increase the rate at which the capital stock is accumulated and this would increase the growth rate of output. While this notion may be important in explaining the growth rates of highly developed countries at the leading edge of technology, it cannot explain the differences in growth rates across poorer countries. For these countries, countries, the notion of conditional conditional convergence seems to hold. hold.
7.
Investing in physical capital capital will lead to a higher capital stock and to a higher higher level of of output in the short run, but often to the detriment of long-term growth unless there are significant external returns to capital. Therefore, investing in human capital is a better strategy, since it has high returns and leads to an increase in long-term growth.
8.a. A country that is able to choose its rate of population growth through population control policies can shift the investment requirement down, thereby increasing the level of steady-state output. With a lower rate of population growth it is possible to achieve a higher level of income per capita with a lower level of investment spending. Therefore, implementing population control policies may be an effective way to escape the so-called poverty trap. 8.b. In an endogenous growth model, a lower population growth rate (n) will increase a nation's long-term growth rate ( ∆y/y). We can see this since, in the second optional section, the per-capita growth rate was derived, as follows: ∆y/y
= sa - (n + d).
9. The Asian Asian Tigers Tigers (Hong Kong, Kong, Singapor Singapore, e, South Korea, Korea, and Taiwan) Taiwan) experie experience nced d a high high rate of economic economic growth between 1966 and 1990 by concentra concentrating ting on improvin improving g the education education of the population and increasing the savings rate, as suggested by the endogenous growth model. However, increases in the labor forces of these countries suggested by the neoclassical growth model, were also at work.
10. The decline in living standards experienced by Eastern European countries in transition from centrally planned economies to free market economies cannot easily be explained by neoclassical or endogenous growth theory. The decline in GDP in these countries was largely due to disorganized markets that lacked properly assigned property rights or liability rules and an insufficiently developed banking system. In addition, the need for large-scale replacement of outdated production technology caused further disruption.
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11. In is unclear whether countries can actually experience indefinite indefinite increases in their growth growth potential. However, if technological advances occur continuously and if intelligent resource management is practiced, it is conceivable that that economic growth will continue for a very, very long time. time.
Technical Problems:
1.a. A production function that displays both a diminishing and a constant marginal product of capital can be displayed by b y drawing a curved line (as in an exogenous growth model), followed by a upwardsloping line (as in an endogenous growth model). Such a graph is depicted below. 1.b. The first equilibrium (Point A in the graph below) is a stable low-income steady-state equilibrium. Any deviation from that point will cause the economy to eventually adjust again at the same steadystate income level (and capital-output ratio). The second equilibrium (Point B) is an unstable highincome steady-state equilibrium. Any deviation from that point will lead to either a lower income steady-state equilibrium (if the capital-labor ratio declines) or ongoing growth (if the capital-labor ratio increases).
y y = f(k) yB sy
B
(n + d)k
yA
A
0 k A
k B
k
1.c. A model like the one in this question can be used to explain how some countries can find themselves in a situation 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 in physical capital, leading to some short-term growth at the expense of long-term growth, whereas in the second case, a country may have invested heavily in human capital, 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.
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y y
C
y
B
y = f(k) [n(y) + d)]k sf(k)
C y
B
A
A
0 k A k B k C k 2.b. The first equilibrium (Point A) is a stable steady-state equilibrium. equilibrium. It 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. It is a situation of medium income and low population growth. The third equilibrium (Point C) is a stable steady-state equilibrium. It is a situation of high income and low population growth. None of these three equilibria have ongoing growth. 2.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 Point A or Point B.
3.a. If we incorporate endogenous population growth into a two-sector model in Problem 2, then we get a curved line for the 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 function has the same shape as the production function.) y y = f(k)
y
D
sf(k)
D
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[n+d [n+d)] )]k k
y y y
C B
C
A
B A
0 k
A
k
B
k
k
C
D
k
3.b. There should be four intersections of the savings function and the investment requirement. The first equilibrium (at 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 c apital-labor ratio increases). 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 capitallabor ratio declines) or ongoing growth (if the capital-labor ratio increases). 3.c. This model is more inclusive than either of the two models discussed previously, and therefore has greater explanatory power. But now the graphical analysis is far more complicated. It may not be worth the effort to introduce such complications.
4.a. The production function function is of the form Y = K 1/2(AN)1/2 = K 1/2(4[K/N]N)1/2 = K 1/2(4K)1/2 = 2K 4.b. Since a = y/k = 2, it follows that the growth rate of output is 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. If we assume that the level of labor-augmenting technology (A) is proportional to the capital-labor ratio (k), we imply 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.
5.a. The production function is of the form Y = K 1/2 N1/2 ==> Y/N = (K/N) 1/2 ==> y = k 1/2.
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From k = sy/(n + d) = sk 1/2/(n +d) ==> k 1/2 = s/(n + d) ==> y* = s/(n + d) = (0.1)/(0.02 + 0.03) = 2 ==> k * = sy*/(n + d) = (0.1)(2)/(0.02 + 0.03) = 4 5.b. Steady-state consumption equals steady-state income minus steady-state investment, that is, c* = f(k *) - (n + d)k * . The The gold golden en rule rule capit capital al stoc stock k corr corres espo pond ndss to the the high highes estt perm perman anen entl tly y sust sustai aina nabl blee leve levell of consumption. Steady-state consumption is maximized when the marginal increase in capital produces just enough extra output output to cover the increased investment investment requirement. From c = k 1/2 - (n + d)k ==> ( ∆c/∆k) = (1/2)k -1/2 - (n + d) = 0 ==> k -1/2 = 2(n + d) = 2(.02 + . 03) = .1==> k 1/2 = 10 ==> k = 100 Since k * = 4 < 100, we have less capital at the steady state than the golden rule suggests. 5.c. From k = sy/(n + d) = sk 1/2/(n + d) ==> s = k 1/2(n + d) = 10(0.05) = .5 5.d. If we have more capital than the golden rule suggests, then we are saving too much and we do not have the optimal amount of consumption.
Additional Problems 1. "Increasing "Increasing returns returns to scale scale imply imply that the level level of output increas increases es only if the the level of all inputs inputs are increased by the same amount." Comment on this statement.
The level of output will increase as soon as the level of one input is increased, even if the level of other inputs remains 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 at a increasing rate if the level of one factor input is increased while the levels of all other factor inputs remain the same. Similarly, it follows that if there are increasing returns to scale, and the level of all inputs are doubled, then the level of output will more than double.
2. Assume Assume the aggregate aggregate productio production n function function is of the followin following g form: Y = aK. aK. At what capital 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). There will never be an intersection between the savings function and the investment investment requiremen requirementt and thus a steady-st steady-state ate equilibrium equilibrium cannot be reached.
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3. “The endogenou endogenouss growth growth model predic predicts ts conditiona conditionall convergence convergence.” .” Comment. Comment.
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 longterm 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.
4. What are are social social returns returns to capital capital and why why are they they so importan importantt for economic economic growth? 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 leads to others and therefore knowledge may grow indefinitely. Thus it pays to devote resources to developing human capital, particularly research and development, since this will enhance economic growth.
5. "Highe "Higherr popula populatio tion n growth growth is always always desira desirable ble since since it will lead to higher higher living living standar standards. ds. Ther Th erefo efore re,, nati nation onss shou should ld alwa always ys impl implem emen entt poli polici cies es that that will will lead lead to an incr increa ease se in population." Comment on this statement.
In the neoclassical framework, we learned that 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 capital-labor ratio (k) decreases until a new steady state is reached. In other words, the investment requirement, (the [n + d]kline) gets steeper as population growth (n) decreases, and it 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. If we now assume assume that that popula populatio tion n growth growth is endoge endogenou nous, s, then then the [n(y) [n(y) + d]k-fu d]k-funct nction ion (the (the investment requirement) is no longer straight but instead is curved. 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.
6. "One implication of the endogenous growth model is that countries with a higher savings rate will have a higher economic economic growth rate, but only over a transitio transitional nal period. In the long run, only technological advances can bring about economic growth." Comment on this statement.
Actual Actually ly,, it is the neocla neoclassi ssical cal growth growth model model that that predic predicts ts that that countr countries ies with with access access to the same 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-term growth rate. Endogenous growth models predict that savings rates and growth rates are positively correlated across countries.
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7. "A poor poor country country can escape escape the the poverty poverty trap, trap, if it either either devotes devotes a larger larger share share of GDP to investment or implements a population control program." Comment on this statement.
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 these funds are invested invested wisely. wisely. A better better alternativ alternativee for increasing increasing living standards standards is to control control populatio population n growth. growth. However, such population control policies are not easily implemented and their success is not always guaranteed, since there is often resistance among the people.
8. Can a poor country ever catch up with a rich country if if both have the same population 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 techno technolog logica icall progre progress. ss. In the short run, run, a nation nation's 's growth growth rate can be affect affected ed by invest investme ment nt in machinery, infrastructure, and human capital. It is impossible to predict for sure whether lower-income countr countries ies can ever ever succee succeed d in catchi catching ng up with with the the standa standard rd of living living of highe higher-i r-inco ncome me countr countries ies.. Empirical evidence suggests slow "conditional convergence," that is, that the positive impact of a higher level of investment spending is only transitory, leading to a higher level of income per capita but not a higher growth rate. Countries 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 such convergence is extremely slow.
9. Assume a developing developing country that has barely enough enough resources to feed its people and too little to devote devote resour resources ces to invest investme ment nt to increa increase se per per-ca -capit pita a output output.. How can such such a country country successfully increase the level of investment without reducing current consumption?
To increase the level of investment, a developing country can invite foreign firms to invest directly in its economy. An example of such direct foreign investment is Volkswagen building a manufacturing plant in Mexico. Another possibility is to borrow funds in the world capital market, either from a bank in a foreign country or from the World Bank. A third possibility is to solicit foreign aid from an industrialized country. However, even if countries receive funds from abroad to increase the level of their domestic investment, the efficiency of investment will vary widely from one country to another. A country with very inefficient inefficient resource resource allocation allocation may have difficulty achieving achieving a sufficien sufficientt increase increase in economic economic growth. Pro-growth policies should emphasize investment in machinery, the nation's infrastructure, and human capital as well as efforts e fforts to reduce budget deficits and government regulations.
10. Comment Comment on the following following stateme statement: nt: “The Asian Tigers achieved phenomenal economic growth from 1966-1990 by devoting a large share of GDP to investment and by relying on laissez-faire economics.”
The Asian Asian Tigers Tigers (Hong (Hong Kong, Kong, Singap Singapore ore,, South South Korea Korea,, and Taiwan Taiwan)) experi experienc enced ed a high high rate rate of economic growth by increasing their savings rate so more could be invested. In addition, however, they increased their labor forces and concentrated on improving the education of their people. While Hong
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Kong Kong relied relied largel largely y on laisse laissez-f z-fair airee econom economics ics,, there there was signif significa icant nt governm government ent involv involveme ement nt in Singapore, where many investment projects were directed by the government.
11. Assume Assume the governm government ent wants to increa increase se the long-t long-term erm growth growth rate rate of the econom economy y and considers the policy options listed below. In your opinion, which of these policies will be successful in stimulating long-term growth and why? (a) expansionary monetary policy (b) an increase in government spending (c) tax credits to stimulate new research and development (d) policies to improve education (e) policies to control population growth
a. Expansion Expansionary ary monetary monetary policy policy may affect real output output in the short short run and the rate of inflatio inflation n in the long run, however it does not affect the long-term growth rate. By affecting saving and investment, it may affect the level of GDP per capita but not the growth rate of GDP. b. An increase in government spending may have some short-run effects on real output, but it will not affect the long-term growth rate of GDP. Only increases in spending affecting either the level of education (human capital), the level research and development, or investment spending (physical capital) may potentially affect economic growth in the long run. c.
Investmen Investmentt tax credits credits are designed designed to create create incentives incentives to undert undertake ake new research research and and developmen developmentt which may, in turn, lead to a higher rate of technological progress. Such a policy may potentially affect economic growth in the long run.
d. Policies Policies that support support educatio education n will lead to an increase increase in human human capital and this, this, in turn, will will affect the long-term growth rate. However, this is likely to be a very slow process. e.
Policies Policies designed designed to affect affect the populatio population n growth rate rate will affect affect the steady-s steady-state tate level level of growth. growth. For example, in developing countries that have rapid rates of population growth, most of the available resources are needed to feed and educate people. This leaves only limited resources for investment in new capital equipment that would allow for an increase in output per capita and a higher standard of living.
12. Developing Developing countries countries can increase increase productivi productivity ty growth growth more easily than industrial industrial countries. countries. Does this imply that they eventually are able to achieve the same living standards as industrial countries? Why or why not?
Developing countries tend to have lower levels of per-capita income than industrialized countries. If they are able to obtain new technology from industrialized nations, they can increase their productivity growth fairly rapidly. At the start of the process of industrialization, developing countries may have low income levels, but eventually they will begin to catch up with the more industrialized countries. As the income levels levels in the poorer poorer count countrie riess begin begin to grow, grow, howeve however, r, a point point will will eventu eventuall ally y be reache reached d when when productivity growth will fall off. Thus, it is impossible to predict with certainty whether a developing country will ever succeed in catching up with the standard of living of an industrial country. country.
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The econom economic ic growth growth rate rate of a count country ry is largel largely y determ determine ined d by how much much techno technolog logica icall progress is made and how much is invested in human capital. The endogenous growth theory does not predict a convergence of income levels among countries starting from different initial levels of capital stock. The neoclassical growth theory, on the other hand, predicts a conditional convergence, that is, that countries will eventually converge to steady states, which are determined by the share of investment to GDP, the share of government spending to GDP, and the rate of investment in human capital. Empirical evidence tends to support this prediction. The process is likely to be extremely slow and is likely to be much easier for newly industrialized countries than for less developed nations.
13. Many countries countries in Eastern Eastern European are still in the process of transforming transforming their previously previously central cent rally ly planne planned d econom economies ies,, where where virtua virtually lly all proper property ty was owned owned by the state state and unemployment was non-existent, to more market-based economies. What reform strategies do you think these countries should have employed to increase living standards and what are the chances for fast results of such strategies?
Policies that can be implemented by countries undergoing the transformation from a centrally planned system to a free market system include the following measures: • • • • • • • •
Establishing property rights and developing contract and bankruptcy laws Privatizing government-owned firms Removing price controls and price subsidies Providing access to foreign markets for consumers and firms Restoring macroeconomic stability through responsible fiscal and monetary policies Education and training of business managers, bankers, lawyers, etc., to familiarize them with a more competitive business environment Provid Providing ing a social social safety safety net for those those who who experi experienc encee diffic difficult ulties ies survi survivin ving g in a more more competitive marketplace Shaking up the current bureaucracy that is predisposed against economic reform
Implementing these policies is not likely to be easy or to achieve positive results immediately. As we have seen, most of the Eastern European countries that have implemented such policies have experienced a decline in GDP. How long it will take to turn the situation around will vary from country to country. There will also probably be great social costs (increases in unemployment and the crime rate, a widening income gap, etc.).
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