41. Assume that a country's per-worker production is y = k2, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year and there is no population growth or technological change. a. If the saving rate (s) is 0.2, what are capital per worker, production per worker, and consumption per worker in the steady state? b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.4. c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8. d. Is it possible to save too much? Why?

41. Assume that a country's per-worker production is y = k2, where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year and there is no population growth or technological change. a. If the saving rate (s) is 0.2, what are capital per worker, production per worker, and consumption per worker in the steady state? b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.4. c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8. d. Is it possible to save too much? Why?

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter20: Economic Growth

Section: Chapter Questions

Problem 9SCQ: Would the following events usually lead to capital deepening? Why or why not? A weak economy in...

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Q7 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…
Question 1: 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 product in 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…
Suppose that for a particular country, the savings rate is 20%, the capital–output ratio is 4, the depreciation rate is 1%, and the rate of growth of the population is 2% per year. a) Calculate the rate of growth of overall GDP. b. What is the rate of per capita GDP growth? c. What should the savings rate be to get the growth rate of overall GDP to 8%?
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)