Economic growth is a study of the economy in the very long run. What is economic growth?

Transcription

1 Econ 2950 Chapter 7 Economic Growth Theory I Introduction to Economic Growth Economic growth is a study of the economy in the very long run. What is economic growth? Example: Jan 1, 2009 RGDP is $1.2 trillion & Dec 31, 2009 RGDP is $1.3 trillion. The growth rate during 2009 = [(1.3 trillion 1.2 trillion) / 1.2 trillion] x 100 = 8.3% Why is economic growth of interest? To study such questions as: 1. Why has real income increased so much in industrialized countries in the past 100 years? 2. Why has the growth rate of output increased so much in some countries, such that their output per capita has surpassed those of other countries? 3. Why has the growth rate of many countries remained low and constant over the past 100 years? RGDP per capita Consider the GDP of India and of Switzerland: Estimated GDP for India in 2007 is over $8.4 trillion (US) Estimated GDP for Switzerland in 2007 is $293 billion (US) Is not Switzerland known as a much richer country with a higher standard of living than India, explain the difference in GDP? 1

2 When studying the economy in the very long run, per-capita RGDP is considered a superior measure of well-being. The theory of economic growth in per-capita income is called the Solow growth model. 7-1 The Accumulation of Capital The Solow Model Capital is key to growth in the Solow model. We start developing the model with the assumption that. Production function: Y = F(K,L) The Solow model assumes constant returns to scale. i.e. zy = F(zK, zl) This assumption allows us to convert the production function into per capita terms. Set z = 1/L Y/L = f(k/l, 1) We have made an assumption that population = labour force We now introduce some new notation: The per capita production function is Slope of production function = marginal product of capital The production function illustrates diminishing marginal product of capital. Why? Output/person (y) is allocated between consumption per capita and investment per capita. y = c + i.government purchases and exports are ignored. The Solow model assumes that workers save a fraction of their income, s, such that s is a value between 0 & 1 c = example: Suppose s =.20 & y = 30,000 2

3 then c = What is i? y = c + i, y = (1-s) y + i re-arrange to get So, the exogenous savings rate, s, also represents We can draw an investment curve on the graph of our production function. Show output per capita, consumption per capita, & investment per capita for a specific level of k. Per capita capital, k, is the k is the determinant of (RGDP) and Investment: expenditure on new capital goods Deprecation: the reduction in the value of capital stock due to either wear & tear or becoming obsolete. As the population grows, more capital is needed for additional workers. We incorporate depreciation and population growth into our model: 3

4 δ is the depreciation rate n is the population growth rate The amount of investment required to compensate for depreciation & population growth is equal to.we call this. Illustrate this curve on the Solow model graph. So, the amount of per capita capital is affected by: Investment Depreciation Population growth If sf(k) > (δ+n)k, then. (year by year) If sf(k) < (δ+n)k, then. When sf(k) = (δ+n)k, k remains constant and is in a There are steady-state levels of k & y, we call Question: Illustrate a case where k<k*, and show the transition to the steady-state. 4

5 What is the growth rate of y in the steady state? What is the growth rate of Y in the steady state? A numerical example of the Solow Model: Y = K 0.5 L 0.5 Divide both sides by L & convert to a per capita production function: y = k 0.5 Assume s=0.3, δ=0.08, n= 0.02 How do we find the steady stated level of k? Table 7-2 (p225) Approaching the Steady State- numerical example - Explain calculations in the table - Start with given k=4 in year 1 - Use prod n f n to calculate y=2 - sy= 2 (0.3)= 0.6, thus i = c= y s = δk = 0.1(4)= k= sf(k) δk = = 0.2 5

6 In year 2: k = = 4.2.and so on.economy is in steady-state when k=0. Case study (p226) The Miracle of Japanese & German Growth WWII destroyed much of the capital stock in Japan & Germany Assuming the savings rate stayed constant; high levels of growth moved the economies back to the steady-state k* and y*. - Note that the gap between per capita investment & break-even investment is large, thus capital stock grows quickly. - The Solow model predicts that countries that have lost significant amounts of capital due to war will experience rapid growth. There are differences in average savings rates between countries. For instance, many Asian countries including China, South Korea & Singapore have higher savings rates than western countries such as in Western Europe & North America. The case study above fails to mention that both Japan & Germany also had higher saving rates. How do changes in saving rates affect growth? Use Solow Model to examine this question: Draw a Solow model and identify the steady-state levels of k* & y* when the savings rate rises. 6

7 Let s look carefully at the adjustment process to the new SS levels: When s rises: per capita investment, while break-even investment the level of per capita capital into it reaches the new ss levels of. We see that saving is associated with higher levels of k* & y* what is happening to economic growth? Once at the new ss: Y grows at the rate of population growth, n. Illustrate adjustment process of k, y and growth rate of Y. Thus, a higher savings rate is said to have a level effect Figure 7-6 International evidence on Investment rates and Income person As the Solow Model predicts, higher investment is correlated with higher per capita income. Which way is the causation? Solow suggests investment leads to RGDP/person. Could it be the other way around? Consider the question on why saving rates vary among countries? 7

8 Countries have different population growth rates. In some countries, population growth rates change. How do changes in population growth rates affect growth? Use Solow Model to examine this question: Draw a Solow model and identify the steady-state levels of k* & y*. Illustrate an increase in population growth, n: the break-even investment curve, (δ+n)k, shifts up illustrate new lower SS levels of k* & y*. Let s look carefully at the adjustment process to the new ss levels: When n rises: break-even investment, while per capita investment capital until it reaches the of y* & k*. We see that higher population growth is associated with Solow Model predicts countries with high fertility rates will have lower levels of y & k. What happens to the growth rate of y? When the population growth rate rises, until the new ss rate is reached then the growth rate of y is. 8

9 Illustrate adjustment process of y and growth rate of Y. Figure 7-13 International evidence on population growth and income per person The Golden Rule Steady State Level of Capital Is the steady-state level of k optimal? We saw that policy can affect the saving rates and thus the level of k. What steady state levels should government strive for? Assume the goal is to maximize well-being. Individuals in society do not care about the per capita level of capital, they care more about how much they can purchase i.e. consumption spending. We assume the optimal level of k is that level associated with c..this is the. c = y I c* = f(k*) (δ+ n)k* We use break-even investment because it equals investment at the steady-state. 9

10 The equation above tells us that steady-state consumption is the portion of steady-state income not saved. As k rises y rises c rises but As k rises break-even investment rises Use the Solow Model graph: graph prod n f n & break-even investment only. Note: consumption = output/income break-even investment The Golden Rule level of Capital, k* gold, is such that c is maximized..at This occurs at the level of k, such that the. The economy does not gravitate toward the Golden Rule ss, it gravitates toward the ss. Policy would be required to influence savings such that the Golden Rule ss equals the ss. Case Study on Canada s Aging Population Let β be the portion of the population that is working Let LS be the living standard of the average person. LS = consumption/population = consumption per worker/population per worker= c β This means that that growth rate of LS equals the growth rate of the portion of the population that is working. 10

11 According to the Solow Model, sf(k*) = (δ+n)k* determines k* c* = f(k*) (δ + n)k* determines c* thus the. We are told that Canada s β will fall by 10% over the next 30 years. The Solow Model predicts that LS will be 10% less than what it would have been if β had remained constant. Although, some theories suggest people are forward looking, and thus will save more in anticipation of the expected labour shortage. There are other theories about the effects of population growth: 1. The Malthusian Model (late 18 th, early 19 th c) Thomas Malthus contended that the passion between the sexes is necessary and will remain nearly in its present state. He saw a strong link between passion and population growth that could not be controlled. He also contended that the ability of the planet to provide enough food for the population is limited. Thus, he predicted that population growth will only be reduced when people experience misery from insufficient levels of food. He saw a strong inverse relationship between population growth and standard of living. Government s attempts to alleviate poverty do not work, because they make the poor better off and thus encourage larger families. Since Malthus, the population has increased 6 fold and average living standards are higher. What Malthus failed to predict was the improvement in technologies providing a rise in agricultural productivity (fertilizers, pesticides, drought and pest resistant seeds, etc). In addition, modern birth control has curbed the link between passion & population growth. Malthus-like thinking has made a come back recently, but instead of food shortages, the issue is a non-renewable resources. Some expect technological progress to save the day, like it has done for food. Pessimists are not so sure. 11

12 2. The Kremerian Model Michael Kremer sees population growth as leading to economic prosperity. More people provide us more scientists, inventors, etc. to contribute to innovation and technological progress. Evidence: 1. world economic growth has risen with the world population (over a period of close to 2000 years); 2. In comparing regions of the world, more populous regions experience more technological progress and faster growth than smaller more isolated regions. His conclusion: a large population is needed for technological change. 12