Macroeconomics
10th Edition
ISBN: 9781319105990
Author: Mankiw, N. Gregory.
Publisher: Worth Publishers,
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Chapter 8, Problem 7PA
To determine
The steady state growth in the economy.
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Assume the production function takes the general form:
Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.
Country A and country B both have the production function
Y = F(K, L) = K1/3L2/3
Does this production function have constant returns to scale? Explain.
Find Solow’s production function, y = f (k)?
Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Find the steady-state level of capital per worker for each country, then find the steady-state levels of income per worker and consumption per worker.
Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker?
Remembering that the change in the capital stock is investment less depreciation, use a calculator (or, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For…
Please no written by hand and graph
Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…
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- The graph below represents per-worker production functions for the same country. Answer the following questions using this graph. Which 1 concept explains that the area between B and C has a flatter slope than the area between A and B? Answer: Law of Diminishing Marginal Returns What has to happen for a country to move from point E to B to D? Answer: The movement through which 3 points (out of 5 given) would indicate the largest increase in productivity? Answer:arrow_forwardIn the Solow model, population growth leads to steadystate growth in total output, but not in output per worker. Do you think this would still be true if the production function exhibited increasin g or decreasing returns to scale? Explain.arrow_forwardCountry A and country B both have the production function Y = F(K, L) = K^0,5L^0,5 A. Does this production function have constant returns to scale? Explain. B. What is the per-worker production function, y = f(k)? C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Theen find the steady-state levels of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator or a computer spreadsheet…arrow_forward
- Many countries, including Pakistan, import substantial amounts of goods and services from other countries. However, economists claim that a country can enjoy a high standard of living only if it can produce a large quantity of goods and services itself. Can you reconcile these two facts? (Maximum 100 words). Given the production function Y= AF (L, K, H, N), explain the determinants of productivity. ( Maximum100 words). Population growth has a variety of effects on productivity. Explain this statement and justify your answer. (Maximum 200 words).arrow_forwardSuppose that the production function of a company is given by q = qL^2 · qC and that the amount of labour qL and the amount of capital qC are functions of time t. At time t = 2, we know that qL = 9 andqC =8 and that the growth rateof qL is equal to 2 and the growth rate of qC is equal to 8. Find the growth rate of the production q at that moment.arrow_forwardProduction function is given by Y = Ka(AN)'¯ª, where a=2/3. Initially, the saving rate was equal to s and the economy was in the steady state. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a yomma as a decimal separator: 10,5) 1. In order to increase capital per unit of effective labor in the steady state by a factor of 27 (i.e. to make it 27 times larger), the rate of saving needs to increase by a factor of 2. In order to increase output per unit of effective labor in the steady state by a factor of 4 (i.e. to make it 4 times larger), the rate of saving needs to increase by a factor of 3. Suppose that s=25 percent, the rate of depreciation of capital is equal to 5 percent, the rate of technological progress is equal to 1 percent, and the rate of population growth is equal to 0,25 percent, a=2/3. The steady state level of investment per unit of effective labor is equal toarrow_forward
- In Wonderland production per worker (y) depends on capital per worker (3) such the y=10√k. Every year 15% of the capital stock depreciates, while workers in Wonderland save 10% of their income. Every year the population grows at as e of 3% a) How might Wonderland and Neverland achieve economic growth in the long run?arrow_forwardConsider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.arrow_forwardAssume a production function is Cobb - Douglas in capital and labour. Y = ZF(K, N) = zK\alpha N1-\alpha (a) Derive the per worker production function, y = zf (k) where y = Y/N, k = K/N (b) Use the Solow Model to derive the steady state level of capital per worker, for given s, d and n. (c) Show diagrammatically the impact on the steady state solution of i) a rise in z; ii) a rise in s, using both the Solow Model diagram and time path diagrams of Iny and Inc. (d) Showdiagrammatically (ideallysupplementedwithkeyequations)howtode rive the Golden Rule, and explain why this matters for your answer to part c) ii) (e) Show diagrammatically the impact of a fall in n, in the short and long termarrow_forward
- Economies production function is Y = AK0.3N0.7. If K = 2000, N = 100, and A= 1, then Y = ?arrow_forwardAssume the production function takes the general form (as in lecture notes) Y = z xF(K,L, A) Z X where all marginal products are positive. Which 3 of the following statements are correct? Select one or more: O a. If A is fixed, then population growth acts as a drag on growth of output per person. b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that population growth will always reverse the impact of technological improvements. Both rises in z and rises in K/L (capital intensity) will boost output per worker. O d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), or both.arrow_forward1. Consider an economy that operates under competitive markets and meets the assumptions of the Solow model. The production function is given as follows: Y(t) = K (t) 0.3 (A(t)L(t)) ⁰.7 Assume a saving rate of 15%, labor force growth rate of 2% and depreciation rate of 5% and effectiveness of labor growth rate of 8%. a. Show that the production function exhibit constant return to scale? b. Derive the production function for output per capita. c. Derive the production function for output per effective unit of labor. d. Find equilibrium real wage as a function of capital per unit of effective labor and effectiveness of labor. e. Find equilibrium real rental price of capital as a function of capital per unit of effective labor and effectiveness of labor. f. Solve for steady state level of capital per unit of effective labor. g. Find steady state level of output per unit of effective labor. h. Find growth rate of output and output per worker on the balanced growth path. i. Which one would…arrow_forward
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