Consider this statement: “Devoting a larger share of national output to investment would help to restore rapid productivity growth and rising living standards.” Under what conditions is the statement accurate
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14... Consider this statement: “Devoting a larger share of national output to investment would help to restore rapid productivity growth and rising living standards.” Under what conditions is the statement accurate?
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- Question 1Some data at first might seem puzzling: The share of GDP devoted to investment was similar for Country liberty and Country Techno from 1970 - 2001. However, during these same years Country Techno had a 6 percent growth rate of average annual income per person, while Country liberty had only a 2 percent growth rate. If the saving rates were the same, why were the growth rates so different?In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of…
- 2. Suppose that two countries (A and B) are exactly alike in every respect except that thecitizens of country A have a higher saving rate than the citizens of country B.Which country will have the higher level of: i) Capital per worker in the steady state?ii) Output per worker in the steady state?iii) Rate of growth of Output per worker in the steady state?Use one graph to illustrate the answer and explain your answer of i), ii), and iii)In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital-output ratio is about 1.5. Suppose that the production function is Cobb-Douglas and that Ghana has been in a steady state. a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (6 + n+ g)k] b. What is the marginal product of capital in the initial steady state? c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal product in the initial steady state. Explain.Question 1:In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratiois about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has beenin a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-staterelationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the GoldenRule level of capital. What will the marginal product of capital be at the Golden Rule steadystate? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product…
- Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.Economic Growth I – Work It Out Question 1 a. Does this production function have constant returns to Country A and country B both have the production scale? function. yes Y = F(K, L) = KL no b. What is the per-worker production function, y = f(k)? y = 0.5Q7 An economy has a Cobb–Douglas production function: Y = Kα(LE)1−α The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in a steady state. a. At what rates do total output, output per worker, and output per effective worker grow?b. Solve for capital per effective worker, output per effective worker, and the marginal product of capital. c. Does the economy have more or less capital than at the Golden Rule steady state? How do you know? To reach the Golden Rule steady state, does the saving rate need to increase or decrease?d. Suppose the change in the saving rate you described in part (c) occurs. During the transition to the Golden Rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)? After the economy reaches its new steady state, will the growth rate of…
- 1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change = f(k)? b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to What is the per-worker production function y а. make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.) (Ctrl) -The 2020 Economic Report of the President on your country contained the following statements: "Devoting a large share of national output to investment would help restore rapid productivity growth and rising living standards in this period of COVID-19." Do you agree with this claim? Explain.Population Growth and Technological Progress-Work It Out An economy has a Cobb-Douglas production function: Y = K (LE)¹- The economy has a capital share of 0.20, a saving rate of 49 percent, a depreciation rate of 4.00 percent, a rate of population growth of 1.50 percent, and a rate of labor-augmenting technological change of 4.0 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: Output per effective worker is constant in the steady state and does not change. increases in the steady state. declines in the steady state. % Output per worker growth rate: %