Chapter 6 Mishkin (6)

Macreconomics: Policy and Practice (Mishkin) Chapter 6 The Sources of Growth and the Solow Model 6.1 Sources of Economic Growth: Growth Accounting 1) The economic growth of the United States over the last century ________. A) is best understood as the result of high levels of saving and investment B) is quite unlike the experience of most other economies. C) was driven by rising import purchases. D) was the result of reducing government intervention in the economy. Answer: B Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking 2) National output is a function of ________. A) capital and saving B) technology, employment and demand C) labor and depreciation D) labor, technology and capital Answer: D Topic: 6.1 Sources of Economic Growth 3) The growth accounting equation suggests that the growth rate of output is equal to the growth rate of ________. A) total factor productivity plus the contributions of both capital and labor B) total factor productivity minus the rate of depreciation C) capital and labor D) the overall population Answer: A Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills 4) Capital and labor are distinct from productivity in that ________. A) productivity is independent of technology changes B) productivity can only increase over time C) productivity is subject to diminishing returns D) capital and labor are subject to diminishing marginal returns Answer: D Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking

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5) Which of the following is the most difficult to measure? Changes in ________. A) the size of the labor force B) population C) the quantity of labor D) productivity Answer: D Topic: 6.1 Sources of Economic Growth 6) Productivity growth can be measured ________. A) by dividing output by Kt0.3 Lt0.7 B) by adding the contributions from capital growth and labor growth C) by subtracting the contributions from capital growth and labor growth from the growth of output D) by dividing the growth of output by the contributions from capital growth and labor growth Answer: C Topic: 6.1 Sources of Economic Growth 7) Productivity is ________. A) determined by central bank policy B) the combined effect of monetary and fiscal policy C) the residual component of the production function D) driven by changes in the rate of growth of output Answer: C Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking 8) If productivity growth equals 3.0 percent, the contribution from capital growth 1.2 percent and the contribution from labor growth 2.0 percent, then output growth must equal ________. A) 2.2 percent. B) 4.2 percent. C) 6.2 percent. D) 7.2 percent. Answer: C Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills 9) If the contribution from capital and labor growth in a given economy equals 4.0 percent and output growth equals 6.4 percent over that same period of time, then productivity growth must equal ________. A) 25.6 percent. B) 10.4 percent. C) 2.4 percent. D) 1.6 percent. Answer: C Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills 2 Copyright © 2012 Pearson Education, Inc.

10) The slowdown in U.S. economic growth in the period 1974-95 was primarily caused by ________. A) falling labor growth. B) falling capital growth. C) falling productivity growth. D) none of the above Answer: C Topic: 6.1 Sources of Economic Growth 11) The highest rate of U.S. growth was recorded in which of the following periods? A) 1948-73. B) 1967-83. C) 1974-95. D) 1996-2008. Answer: A Topic: 6.1 Sources of Economic Growth 12) Economic growth ________. A) is driven by different elements in different economies. B) is driven primarily by digital technology. C) is driven primarily by labor growth. D) cannot be explained using economic models. Answer: A Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking

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Figure 6.1

13) According to Figure 6.1, the average annual rate of growth of the U.S. economy in the period 1948-73 equalled ________. A) 1.8 percent. B) 4.0 percent. C) 39 percent. D) 697 percent. Answer: B Topic: 6.1 Sources of Economic Growth 14) According to Figure 6.1, the average annual rate of growth of the U.S. economy in the period 1996-2008 equalled ________. A) 0.3 percent. B) 3.0 percent. C) 30 percent. D) 300 percent. Answer: B Topic: 6.1 Sources of Economic Growth

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15) According to Figure 6.1, in postwar U.S history ________. A) productivity growth was always exceeded by labor growth. B) labor growth has always exceeded capital growth. C) productivity growth has always exceeded capital growth. D) output growth has always exceeded productivity growth. Answer: D Topic: 6.1 Sources of Economic Growth 16) According to Figure 6.1, the period from 1974 to 1995 is particularly remarkable for the slow growth of ________. A) output per worker B) labor input C) output D) capital input Answer: A Topic: 6.1 Sources of Economic Growth 17) According to Figure 6.1, the period from 1996 to 2008 is particularly remarkable for the rapid growth of ________. A) productivity B) labor input C) output D) capital input Answer: A Topic: 6.1 Sources of Economic Growth 18) According to Figure 6.1, fluctuations in the rate of output growth are due mostly to changes in the growth of ________. A) productivity B) labor input C) output D) capital input Answer: A Topic: 6.1 Sources of Economic Growth 19) In Figure 6.1, the post-World War II "baby boom" is reflected in the growth of ________. A) labor input from 1974 - 1995 B) labor input from 1948 - 1973 C) output from 1948 - 1973 D) capital input from 1996 - 2008 Answer: A Topic: 6.1 Sources of Economic Growth

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20) Across national economies which of the following is the most important source of variation in growth rates? A) labor growth. B) capital growth. C) productivity growth. D) government regulation. Answer: C Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking 21) The label 'Asian Tigers' describes the following economies ________. A) China, South Korea, Singapore and Taiwan. B) Hong Kong, Taiwan, South Korea and Singapore. C) Singapore, Taiwan, Hong Kong, and China. D) South Korea, Singapore, China and Hong Kong. Answer: B Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills 22) The growth rate of which of the following is not a component of the growth accounting equation? A) the capital stock. B) labor. C) depreciation. D) available technology. Answer: C Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking 23) If the contribution from capital growth equals 3 percent and the contribution from productivity growth equals 1.6 percent, GDP will grow by ________. A) 1.6 percent. B) 4.6 percent. C) 4.8 percent. D) an unknown value. Answer: D Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills

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24) If the contribution from capital growth equals 2 percent and the contribution from labor growth equals 4 percent, then GDP ________. A) will grow by 6 percent. B) will grow by 8 percent. C) will grow by 2 percent. D) will change by an unknown percentage. Answer: D Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills 25) Given the production function Y = A K0.3L0.7 if output grows by five percent, the capital input grows by five percent, and the labor input grows by two percent, calculate the Solow residual. Calculate the growth rates of output per worker and capital per worker. Answer: The Solow residual gA = 0.05 - 0.3 ∗ 0.05 - 0.7 ∗ 0.02 = 0.021. The growth rate of output per worker is 0.05 - 0.02 = 0.03, which is also the growth rate of capital per worker. Topic: 6.1 Sources of Economic Growth AACSB: Analytical Skills 26) Output growth in the United States in the period 1996 to 2008 averaged three percent per year. Though this was an improvement on the 2.9% average annual growth of output over the preceding 20 years, an increase of one-tenth of a percentage point seems hardly to justify the popularity of the label "new economy." Comment. Answer: Output growth is the result of growth of the three components, productivity, capital, and labor. Though output growth after 1995 was barely higher than it had been previously, the composition of growth had changed substantially. The growth rates of both capital and labor fell, while the growth rate of productivity nearly doubled, from 0.7% to 1.3%. Topic: 6.1 Sources of Economic Growth AACSB: Reflective Thinking

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6.2 The Solow Growth Model 1) The per-worker production function is ________. A) upward-sloping. B) downward-sloping C) vertical. D) horizontal. Answer: A Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 2) The Solow model is ________. A) the basic model of how technology changes over time B) the foundation for the classical economic thought of Adam Smith. C) one of the dominant explanations of the business cycle. D) based on the notion of diminishing marginal product of capital and labor Answer: D Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 3) In the Solow model, which of the following is an exogenous variable? A) productivity B) the capital-labor ratio C) consumption per worker D) investment per worker Answer: A Topic: 6.2 The Solow Growth Model 4) In the Solow model, which of the following is an endogenous variable? A) output per worker B) government spending C) the saving rate D) the depreciation rate Answer: A Topic: 6.2 The Solow Growth Model 5) The positive slope of the per-worker production function illustrates the relationship between per-worker output and ________. A) diminishing marginal returns. B) the capital-labor ratio. C) the rate of inflation. D) the rate of unemployment. Answer: B Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills

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6) The per-worker production function flattens out due to ________. A) the negative relationship between price and quantity demanded. B) the positive relationship between price and quantity demanded. C) the diminishing marginal product of capital D) an increase in the general level of prices. Answer: C Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 7) With a closed economy and no government spending, the total demand for output is equal to ________. A) consumption per-worker plus investment per-worker. B) consumption per-worker minus investment per-worker. C) consumption per-worker times investment per-worker. D) consumption per worker divided by investment per-worker. Answer: A Topic: 6.2 The Solow Growth Model 8) In a closed economy ________. A) investment equals consumption. B) investment equals savings. C) saving equals consumption. D) exports are greater than imports. Answer: B Topic: 6.2 The Solow Growth Model 9) If depreciation is equal to investment ________. A) capital per-worker rises over time. B) capital per-worker is stable. C) captial per-worker falls over time. D) capital per worker equals saving Answer: B Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 10) If capital per-worker is rising, then ________. A) depreciation is equal to investment. B) depreciation is greater than investment. C) depreciation is less than investment. D) depreciation is less than consumption. Answer: C Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills

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11) If depreciation is less than investment ________. A) capital per-worker is falling. B) capital per-worker is rising. C) capital per-worker is constant. D) capital per worker is greater than saving Answer: B Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 12) Changes in the capital stock are caused by changes in ________. A) the quantity of labor. B) depreciaton and investment. C) depreciation and entrepreneurship. D) depreciation and the quantity of labor. Answer: B Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 13) If investment per-worker equals some value X, and depreciation per-worker equals some value Z, then the change in the capital stock per-worker is equal to ________. A) X+Z. B) X-Z. C) X times Z. D) X divided by Z. Answer: B Topic: 6.2 The Solow Growth Model AACSB: Reflective Thinking 14) In the bathtub analogy, which of the following is a stock variable? A) the amount of investment. B) the rate of depreciation. C) the amount of capital-per worker. D) the Cobb-Douglass value. Answer: C Topic: 6.2 The Solow Growth Model AACSB: Reflective Thinking 15) If an economy invests more than it loses through depreciation ________. A) the saving rate will fall. B) the saving rate will rise C) the quantity of labor will fall. D) the capital stock will expand. Answer: D Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills

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16) The loss of capital due to the wearing out of machines is known as ________. A) saving. B) investment. C) consumption. D) depreciation. Answer: D Topic: 6.2 The Solow Growth Model 17) If an economy initially starts away from the steady state ________. A) output will gradually fall over time. B) the economy will converge to the steady state in the long-run. C) consumption spending must be greater than investment spending. D) consumption spending must rise. Answer: B Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 18) The Solow model suggests that economies with the same aggregate production function, ratio of workers to the total population and saving rates will ________. A) trade with one another. B) start with different initial levels of per capita income. C) possess the same rate of depreciation. D) experience convergence. Answer: D Topic: 6.2 The Solow Growth Model AACSB: Reflective Thinking 19) Strong evidence of convergence exists for ________. A) wealthy nations that belong to the Organization for Economic Cooperation and Development. B) both rich and poor nations. C) sub-Saharan African economies and the economies of North America. D) European and Caribbean economies. Answer: A Topic: 6.2 The Solow Growth Model AACSB: Reflective Thinking 20) Which of the following had the highest rate of growth during the period 1948-72? A) West Germany. B) Vietnam C) Japan. D) The United States of America. Answer: C Topic: 6.2 The Solow Growth Model

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21) Within rich economies, there is strong evidence of convergence ________. A) for regions within a country. B) with developing economies. C) leading to military conflict. D) of capital stocks, rather than output Answer: A Topic: 6.2 The Solow Growth Model 22) Evidence that convergence occurs within economies is drawn in part from the example of ________. A) Hiroshima and Nagasaki Japan. B) North and South Korea. C) West and East Germany during the Cold War. D) Hong Kong and Singapore. Answer: A Topic: 6.2 The Solow Growth Model 23) In the typical bathtub, the flow of water into the tub is controlled by a faucet independently of the quantity of water in the tub. How is the bathtub analogy of the steady state in the Solow model different? How does this difference relate to the phenomenon of convergence? Answer: In the Solow model, the flow of investment is determined by the fixed rate of saving and the variable level of output, which depends on the stock of capital, the labor input, and the available technology. It is as if the faucet on the tub were controlled by the level of water in the tub. The convergence phenomenon is that economies with low per capita income have relatively high growth rates. But for economies to converge, all of the determinants of output must be similar. Thus, it is not surprising that convergence is not found among large groups of countries. Among suitably similar economies, evidence of convergence is striking testimony of the importance of diminishing returns. Despite the low level of investment that is feasible in a lowincome economy, the growth impact of new capital there is greater than occurs in an otherwise similar high-income economy in which the level of investment is higher. Topic: 6.2 The Solow Growth Model AACSB: Reflective Thinking Solow Diagram

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24) On the diagram above, show the quantity of consumption per worker in equilibrium. If the actual capital per worker were greater than k*, would consumption be higher or lower than it is in equilibrium? Describe what would happen in an economy with such a high level of capital per worker. Answer: When capital per worker is above its equilibrium value, output per worker is higher, so each worker has more to consume. Total saving/investment is higher, as well, but not enough to replace the capital lost to depreciation. As a result, capital per worker is falling, which brings output and consumption down to their equilibrium levels. Topic: 6.2 The Solow Growth Model AACSB: Reflective Thinking 25) Output per worker yt = 4kt1/3, the saving rate is 30 percent, and the depreciation rate is 0.133. Calculate the steady-state values of capital per worker and consumption per worker. 1.5 Answer: The steady-state capital-labor ratio k* =  sA  = 27. Consumption per worker is (1   

s) ∗ 4∗271/3 = 8.4. Topic: 6.2 The Solow Growth Model AACSB: Analytical Skills 6.3 Saving Rate Changes in the Solow Model 1) A higher rate of saving at the national level will, in the long-run ________. A) cause a decrease in levels of capital and output. B) have no effect on levels of capital and output. C) lead to an increase in population growth. D) cause an increase in levels of capital and output. Answer: D Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills 2) On the Solow Diagram, an increase in the saving rate is shown by ________. A) an upward shift of the depreciation line B) an upward shift of the investment function C) an upward shift of the per-worker production function D) a downward shift of the investment function Answer: B Topic: 6.3 Saving Rate Changes in the Solow Model 3) An increase in the saving rate results in a higher steady state ________. A) growth rate of capital B) growth rate of output per worker C) level of consumption per worker D) level of capital per worker Answer: D Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills 4) In the Solow model, the faster growth of output that results from an increase in the saving rate 13 Copyright © 2012 Pearson Education, Inc.

is temporary, because ________. A) of diminishing marginal product of capital B) with a larger stock of capital, consumption is encouraged more than investment C) the rising capital stock depreciates at a faster rate D) the economy settles into a steady state in which saving no longer rises Answer: A Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Reflective Thinking 5) Following an increase in the saving rate, consumption per worker ________. A) increases B) decreases C) is unaffected D) may either rise or fall Answer: D Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills 6) Suppose an economy is in a steady state, then its saving rate falls, once and permanently. As the economy approaches its new long-run steady state, consumption per worker is ________. A) falling B) rising C) unaffected D) either rising or falling Answer: A Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills 7) International evidence on the relationship of per capita income and the saving rate suggests that ________. A) a high level of income per person requires a high saving rate B) a high saving rate guarantees a high level of income per person C) a high saving rate might result in a high level of income per person D) a high saving rate requires a high level of income per person Answer: C Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills

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8) In a steady-state economy with no population growth, output per worker is 35, the saving rate is 20 percent, and the depreciation rate is 11 percent. The level of capital per worker is ________. A) 64 B) 19 C) 39 D) 28 Answer: A Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills 9) In a steady-state economy with no population growth, capital per worker is 86, the saving rate is 25 percent, and the depreciation rate is 11 percent. The level of output per worker is ________. A) 195 B) 38 C) 35 D) 47 Answer: B Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills 10) In a steady-state economy with no population growth, consumption per worker is 45, the saving rate is 25 percent, and the depreciation rate is 15 percent. The level of capital per worker is ________. A) 75 B) 36 C) 100 D) 27 Answer: C Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills

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Solow Diagram

11) On the diagram above, show the new steady-state capital-labor ratio that results from a decrease in the saving rate. Can you say what has happened to the equilibrium level of consumption per worker? Answer: As saving/investment falls, the equilibrium capital-labor ratio declines along the depreciation line. As the capital-labor ratio falls, output-per-worker declines along the production function. Beginning from the original equilibrium k* on the graph, the production function is clearly flatter than the depreciation line, so the decline in output is smaller than the decline in saving/investment, so that consumption per worker must be rising. Consumption per worker can fall only if k* is so low that the slope of the production function (at that level of capital per worker) is steeper than the depreciation line. Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Reflective Thinking 12) Consumption per worker is 72, depreciation is 12.5%, and capital per worker is 64. Given the production function y = 20k1/3, show that this economy is in a steady state. If the saving rate should double, what is the new steady-state level of consumption per worker? 1.5 Answer: The steady-state capital-labor ratio k* =  sA  . Plugging the values above into this   

equation yields s = 0.1. Putting the given value of k into the production function yields y = 80, so the given value of consumption per worker implies s = 0.1. This is a steady state. (As further confirmation, note that 64 ∗ 0.125 = 8 = saving, so the loss of capital due to depreciation is exactly restored by investment.) If s = 0.2, then k* = 181, so y = 113, and consumption per worker is 113 ∗ 0.8 = 90. Topic: 6.3 Saving Rate Changes in the Solow Model AACSB: Analytical Skills

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6.4 Population Growth in the Solow Model 1) Other things the same, in the Solow model in the steady state, a higher rate of population growth ________ the level of output per worker. A) leads to an increase in B) has no long-run effect on C) has an ambiguous effect on D) leads to a decrease in Answer: D Topic: 6.4 Population Growth in the Solow Model AACSB: Analytical Skills 2) Other things the same, in the Solow model in the steady state, a higher rate of population growth ________ growth rate of output. A) leads to a higher B) leads to a lower C) has no long-run effect on the D) has an ambiguous effect on the Answer: A Topic: 6.4 Population Growth in the Solow Model AACSB: Analytical Skills 3) Other things the same, in the Solow model in the steady state, a higher rate of population growth ________ growth rate of output per worker. A) leads to a higher B) leads to a lower C) has no long-run effect on the D) has an ambiguous effect on the Answer: C Topic: 6.4 Population Growth in the Solow Model AACSB: Analytical Skills 4) Population growth is similar to depreciation, in that ________. A) each lowers the capital-labor ratio B) each tends to encourage saving C) capital wears out faster when used by more workers D) each helps to explain how economies can sustain a positive growth rate of output Answer: A Topic: 6.4 Population Growth in the Solow Model AACSB: Reflective Thinking

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5) If output per worker in a steady state is $30,000, depreciation is 13%, the population growth rate is two percent, and the saving rate is 20%, what is the steady state capital-labor ratio? A) $10,500 B) $85,714 C) $22,500 D) $40,000 Answer: D Topic: 6.4 Population Growth in the Solow Model AACSB: Analytical Skills 6) Output per worker is 50, the saving rate is 15 percent, the population is growing at one percent, depreciation is 9 percent, and the capital-labor ratio is 80. Consumption per worker is ________. A) 37.5 B) falling C) 75 D) 68 Answer: B Topic: 6.4 Population Growth in the Solow Model AACSB: Analytical Skills 7) "Capital dilution" refers to ________. A) the flow of investment in the "bathtub model" B) the depreciation of capital associated with an increase in the percentage of younger workers C) the decline in the marginal product of capital that results from reliance on new, inexperienced workers D) the decrease in capital per worker that is a direct consequence of an increase in the number of workers Answer: D Topic: 6.4 Population Growth in the Solow Model 8) On the Solow Diagram, an increase in population growth is shown by A) an upward shift of the depreciation plus capital dilution line B) an upward shift of the investment function C) an upward shift of the per-worker production function D) a downward shift of the investment function Answer: A Topic: 6.4 Population Growth in the Solow Model

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9) The impact of immigration on an economy's steady state capital-labor ratio is reduced to the extent that the immigrants tend to ________ than the native population. A) save more B) have higher fertility C) have lower income D) be younger Answer: A Topic: 6.4 Population Growth in the Solow Model AACSB: Reflective Thinking 10) A One-Child Policy was instituted in 1979 in ________. A) Brazil. B) South Africa. C) India. D) China Answer: D Topic: 6.4 Population Growth in the Solow Model 11) According to the Solow model, a benefit of policies to limit population growth might be ________. A) that smaller families are more likely to contribute to technological advances B) that smaller families have better access to birth control methods and devices C) that smaller families might provide each person a larger share of national income D) that smaller families have less need to save, and so enjoy higher consumption Answer: C Topic: 6.4 Population Growth in the Solow Model AACSB: Reflective Thinking 12) Evidence of a negative correlation between income per capita and population growth rates ________. A) implies that birth control is most effective in low-income countries B) has not been found in the available data C) is consistent with the Solow model D) suggests that population growth stimulates technological progress Answer: C Topic: 6.4 Population Growth in the Solow Model AACSB: Reflective Thinking

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Solow Diagram

13) The diagram above shows a steady state with a constant quantity of labor. Show on the graph how the steady state is determined if the labor force is growing at some constant rate. On the graph, show how to measure the change in consumption per worker that results from growth of the labor force. Answer: Graphing answers will vary. Topic: 6.4 Population Growth in the Solow Model AACSB: Analytical Skills 6.5 Productivity Growth in the Solow Model 1) When an economy experiences a one-time increase in productivity, there is an immediate increase in ________. A) the saving rate B) the capital-labor ratio C) the depreciation rate D) consumption per worker Answer: D Topic: 6.5 Productivity Growth in the Solow Model AACSB: Analytical Skills 2) When an economy experiences a one-time increase in productivity, there is an increase in the long-run, steady state value of ________. A) the growth rate of output B) the depreciation rate C) consumption per worker D) the saving rate Answer: C Topic: 6.5 Productivity Growth in the Solow Model AACSB: Analytical Skills

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3) Comparing steady states, which of the following is a result of a permanent increase in the saving rate, but is not a consequence of a one-time increase in productivity? A) an increase in consumption per worker B) a decrease in the marginal product of capital C) an increase in output per worker D) an increase in the growth rate of output Answer: B Topic: 6.5 Productivity Growth in the Solow Model AACSB: Analytical Skills 4) On the Solow Diagram, an increase in productivity is shown by A) an upward shift of the depreciation plus capital dilution line B) an upward shift of the investment function C) a downward shift of the depreciation plus capital dilution line D) a downward shift of the investment function Answer: B Topic: 6.5 Productivity Growth in the Solow Model 5) If productivity is growing at some sustained rate g, then output and capital per worker ________. A) are growing at the same rate g, in a stable steady state B) are growing faster than g, because improving technology encourages a higher rate of saving and investment C) are growing slower than g, because some of the new capital is merely replacing obsolete capital D) are growing faster than g, because productivity does not suffer from diminishing marginal product Answer: D Topic: 6.5 Productivity Growth in the Solow Model AACSB: Analytical Skills 6) The Solow model implies that continuous growth in productivity at a rate of one percent will result in continuous growth of output per worker at a rate of 1.43%. Thus, if at a point in time output per worker is 270 and productivity rises by one percent, the resulting level of output per worker is A) 386 B) 273 C) 274 D) 277 Answer: C Topic: 6.5 Productivity Growth in the Solow Model AACSB: Analytical Skills

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7) A major contribution of the Solow model is its ________. A) insight into what distinguishes rich economies from poor economies B) explanation of why productivity grows over time C) demonstration that the key to sustained growth is a high level of saving D) encouragement of policies to limit population growth Answer: A Topic: 6.5 Productivity Growth in the Solow Model AACSB: Reflective Thinking 8) In theory, differences in output across economies and over time might be the result of differences in either capital input, labor input, or productivity. The evidence points clearly to productivity as a more likely and powerful source of growth differences. Which aspects of the Solow growth model help to explain why the inputs of capital and labor contribute little to growth of output, relative to productivity? Answer: Diminishing marginal product undermines the impact on output of increases in either capital or labor. As long as the labor input grows, and saving is sufficient to compensate for depreciation and capital dilution, output can grow at the same rate as the labor input. Faster growth is possible during recovery from an event that has reduced the capital-labor ratio, or in response to an increase in the saving rate. But such growth episodes end as the capital-labor ratio approaches a steady state. A growing stock of capital has a diminishing effect on output, on the one hand, and a linearly-increasing reliance on saving from output on the other. Productivity is subject neither to diminishing marginal returns nor to depreciation & dilution, so nothing impedes the connection from productivity growth to output growth. Topic: 6.5 Productivity Growth in the Solow Model AACSB: Reflective Thinking

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9) Given the production function Y = A K0.3L0.7 and fixed values for the saving rate and depreciation, if productivity is growing at an average rate of three percent, and the labor input grows at two percent, there is a unique growth rate of capital that is sustainable. That is, if the growth rate of capital is either higher or lower than this steady-state value, then it must eventually change, even if nothing else in the economy changes. Calculate this steady-state growth rate of capital, and explain why it alone is a sustainable rate. [Hint: Use the fact that the growth rates of output and capital per worker are 43% higher than the growth rate of productivity.] Answer: Since productivity is growing at three percent, capital per worker is growing at 4.3% ( = 0.03 ∗ 1.43). Since labor grows at two percent, capital must grow at 4.3% + 2% = 6.3%. Putting this into the growth accounting equation: = 0.03 + 0.3 ∗ 0.063 + 0.7 * 0.02 = 0.063. Thus, capital and output grow at the same rate. If capital were to grow at a faster rate, say eight percent, the growth of output could not keep up: 0.03 + 0.3 ∗ 0.08 + 0.7 ∗ 0.02 = 0.068. A growing capital stock requires enough saving to compensate for depreciation and capital dilution, but saving can increase only as fast as output. If the growth rate of capital were too low, say five percent, output would be growing faster than capital, so saving a constant fraction of output would result in investment that is increasingly large relative to depreciation and capital dilution. The investment needed to keep capital growing at a constant rate can occur only when output grows at the same rate as the capital stock. Topic: 6.5 Productivity Growth in the Solow Model AACSB: Reflective Thinking 6.6 Summing Up the Solow Model 1) There are no questions for this section. Answer:

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