1. Over a period of 10,000 years, the population of Brobdingnag is estimated tohave increased from 4 million to 170 million. Assuming that the level ofincome per worker was constant, there are only two factors of production,Land (X) and Labour (L), and the exponent on land in the production functionis one-third, what was the annual growth rate of productivity, A?a) 0.17%b) 0.42%c) 0.03%d) 0.01%

The correct answer is (c) 0.03%.To solve this problem, we can use the Cobb-Douglas production…

Answered: 1. Over a period of 10,000 years, the…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.8P

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Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor 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 isY? What is labor productivity computed from the per-worker production function? Is thisvalue 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 isnecessary 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 ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?
Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor 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 isY? What is labor productivity computed from the per-worker production function? Is thisvalue 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 isnecessary 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 ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker? Only D, other option answered
What is meant by economies of scale and what is the importance of this concept toeconomic growth?
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Assume the rate of technological progress is constant in a SSGM with Cobb- Douglas production function. Show that a steady-state cannot be identifiede if the technological progress is capital augmented, i.e. F(K, L) = [A(t)K(t)]*L(t)'_ª, where A(t) is the efficiency term growinge with a constant rate g.t
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…
1. Over the period from B.C. 10,000 to A.D. 1, the world population is estimated to have increased from 4 million to 170 million, while the level of income per capita was constant over time. Assuming that the quantities of human and physical capital per worker did not change, and that the exponent on land in the production function is one-third, calculate the growth rate in productivity over this period. What was the annual growth rate of productivity, A?
Which of the following statements about the opportunity cost of economic growth is correct? The opportunity cost of economic growth O A. is human capital O B. is capital consumption O C. is greater the faster we make our production grow O D. is zero
Based on the notations used in class, let y=k06, 6-0.3, 8-0.45, n = 0.015, and k = 2 initially. Then suddenly the saving rate goes up to s' 0.5. Then the growth of steady-state capital per worker will be: O a. 40% O b. None of the other choices are correct. O c. 50% O d. 30 %
Are there key differences between an increase in the capital stock and an improvement in the level of technology?
A key assumption in an endogenous growth model with both labour and capital inputs in the production function is that Multiple Choice O о о о O the share of capital is larger than the share of labour the share of capital and labour have to be equal better technology is a byproduct of more capital investment there are no external returns to capital long-run growth comes solely from technological progress
Write out the equation for output growth with capital, labor and total factor productivityas determinants of growth. Suppose that the shares of capital and labor are respectively0 .3 and 0.7. If labor supply grows by 10% what would be the growth rate of outputassuming that there is no change in the other determinants? What would happen to percapita output if labor supply growth is entirely due to population growth?

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