Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
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Question
Chapter 6, Problem 6AP
To determine
To evaluate: Output per woker remains unaffected with an equal increase in perecntage of capital and labor.
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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:
Assume that a country's production function is Y = K/2*L/2 and there is no population growth
or technological change.
a. What is the per-worker production function y = f (k)?
b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is
Y? What is labor productivity computed from the per-worker production function? Is this
value the same as labor productivity computed from the original production function?
c. Assume that 10 percent of capital depreciates each year. What gross saving rate is
necessary to 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.)
Q4:
a; 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).
b: Given the production function Y= AF (L, K, H, N), explain the determinants of productivity. ( Maximum100 words).
c: Population growth has a variety of effects on productivity. Explain this statement and justify your answer. (Maximum 200 words).
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- Consider 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_forward0.5 0.5 Given a production function: Y = AK N If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at % ? (Answer in integer only, no decimal place.) Your Answer: Answer Given a production function: Y = AK0.5 N0.5. If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at %? (Answer in integer only, no decimal place.) Your Answer: Answerarrow_forwardSuppose that total capital and labour both increase by the Suppose that total capital and labour both increase by the same percentage amount so that the amount of capital per worker k does not change. Writing the production function in per-worker terms, y = f(k), requires that this increase in capital and labour must not change the amount of output produced per worker y. Use the growth accounting equation to show that equal percentage increases in capital and labour will leave output per worker unaffected only if aK + aN = 1. Suppose that total capital and labour both increase by thearrow_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 an economy’s production function is Y = AKαL1−α. If the annual rate of economic growth is 3.5 per cent and labour and capital are both growing by 2 per cent annually, what contribution to growth is made by total factor productivity? You can assume that labour receives 75 per cent of the total income generated in this economy.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
- Countries X and Z produce a composite output Y by employing two factors labor (N) and capital (K), when the given state of technology is A. The production function of Y is Y = √(K)(AN) In a particular year, Country X's growth rate of output per worker is 4.2%, growth rate of employment is 3.1%, and growth rate of capital is 3.9%. In the same year, Country Z's growth rate of output per worker is 7%, growth rate of employment is 1%, and growth rate of capital is 8%. What is the growth rate of technological progress for the two countries? (Round your responses to two decimal places.) Country X: gax= Country Z: 9AZ = % Given the above information, which combinations of the following statements are true? a) Country X and Country Z are investing heavily in innovation and R&D. b) Country X has achieved its balanced growth path. c) Country Z could be using a combination of heavy capital formation and import of technology. d) Country Z has a higher standard of living than Country X. O A. a, b…arrow_forwardSuppose the per-worker production function is: y = A(1-ga) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (ga/m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If g, fell to 0.8 the level of output per worker would: Impossible to say fall stay the same O risearrow_forwardIn 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_forward
- Consider an economy described by the production function Y=F(K, L)=?^0.4?^0.6 A) What is the per-worker production function?B) Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.arrow_forward1.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). 2.Given the production function Y= AF (L, K, H, N), explain the determinants of productivity. ( Maximum100 words). 3.Population growth has a variety of effects on productivity. Explain this statement and justify your answer. (Maximum 200 words).arrow_forward[The following scenario applies to the next two questions.] An economy has a Cobb-Douglas production function: Y = AK L(1-a). A is the technology level, K is capital; L is labor; and Y is income. ● In 20X1, the technology level A is 139, capital K = 245, labor L = 458, income Y = 8,155 In 20X2, the technology level A is 144.96, capital K = 259.26, labor L = 474.12, income Y = 8,945.71 In 20X3, the technology level A is 152.02, capital K = 273.31, labor L = 489.20 Question 1.6: Elasticity of income with respect to labor What is the elasticity of income with respect to labor? A. 18% B. 20% C. 22% D. 24% E. 26% Question 1.7: Income What is income in 20X3? A. 9,240.34 B. 9,535.25 C. 9,830.15 D. 10,125.06 E. 10,419.96arrow_forward
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