Production function is given by Y=(1/2)K^a(AN)^(1-a), where a=2/3. The rate ofdepreciation of capital is equal to 15 percent, therate of technological progress is equal to 3percent, and the rate of population growth isequal to 2 percent. The economy was in the steadystate at time tand the level of technology wasequal to A=80. Use the Solow growth model toanswer the following questions.1. If the saving rate s=80 percent, the steadystate level of output per unit of effectivelabor at time tis equal to ...2. If the saving rate s=80 percent, the steadystate level of consumption per unit ofeffective labor at time tis equal to ...3. If the saving rate s=80 percent, the steadystate level of consumption per worker at timetis equal to ..

In economics, a production function gives the technological relation between quantities of physical…

1. If the saving rate s=80 percent, the steady state level of output per unit of effective labor at time tis equal to ... 2. If the saving rate s=80 percent, the steady state level of consumption per unit of effective labor at time tis equal to ...

1. If the saving rate s=80 percent, the steady state level of output per unit of effective labor at time tis equal to ... 2. If the saving rate s=80 percent, the steady state level of consumption per unit of effective labor at time tis equal to ...

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter20: Economic Growth In The Global Economy

Section: Chapter Questions

Problem 4P

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an economy is given by y=k^( 1/3). The depreciation rate is 16%, the saving rate is 26%, the growth rate of the labor force is 4%, and the growth rate of labor-augmenting technological change is 4%. Given these features, this economy's steady-state level of capital per effective worker is (Enter your response rounded to two decimal places.)
Consider the following (made-up) statistics for some econ-omies. Assume the exponent on capital is 1/3 and that the labor composition is unchanged. For each economy, compute the growth rate of TFP.(a) A European economy: gY/L = 0.03, gK/L = 0.03.(b) A Latin American economy: gY/L = 0.02, gK/L = 0.01.(c) An Asian economy: gY/L = 0.06, gK/L = 0.15.
Assume there is a second economy ( country B ) with everything identical to country A except for the rate of population growth , which is 2 percent . Answer the following questions for country B. Assume both countries start a k = 0 , which country grows more in the short run ( before steady state is reached ) , as given by the rate of growth of output per worker ? ( hint : the further away from steady state , the faster the growth towards it ). O. Country A O. Same for both O. Country B
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
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 the growth rate of the capital stock in each period is determined by the level of output in the previous period. 1) An economy of 80 million people has ten percent of them engaged in research and development, where their productivity is 0.0035. The economy is on a balanced growth path, when suddenly 2.88 million people move from goods production into R&D, raising the fraction there to 13.6 percent. In the one period that begins with this labor reallocation, the growth rate of output is ________. [Refer to the instruction above.] A) 2.8% B) 0.0% C) 3.8% D) 2.2%
Consider an economy in which the labour force grows by 2.7 percent per annum, physical capital grows by 4 percent per annum and human capital grows by 1.8 percent per annum. Suppose 45 percent of national income goes to labour and 40 percent to capital. Use a constant returns to scale production function to answer the following growth accounting questions: (a) If the Solow residual were zero what rate of growth would the economy achieve? (b) The country's actual rate of growth has been 4.5 percent per annum, which is faster than the growth rate generated by the accumulation of capital and labour stocks. Calculate the value of the residual.
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.
A country produces output using a production function: Y = F(K, L) = AxK0.5 L0.5 where L is labour, K is capital and A is total factor productivity. Prove that this function exhibits constant returns to scale. Assume that A = 3 and its growth rate is zero. The country has a population growth of 1.5% per year (0.015) and capital depreciates at a rate of 10% (0.10) per year. If the country saves 30% (0.3) of national income, find the steady state levels of capital per worker, as well as consumption and income per worker in the Solow growth model corresponding to this country. What would be the rate of growth of GDP per capita in steady state? Calculate the “Golden Rule” level of capital stock in steady state. Is this economy dynamically efficient?
Country Has Cobb-Douglas production function: Y(it) = A(it) x K(it)1/3L(it)2/3 Where: Y(it) = realGDP K(it) = Capital L(it) = No. workers employed in country (i) on date (t) Suppose multiple countries share the same alpha = 1/3 but different levels of totalfactorproductivity (A(it)). How would one calculate the average annual growth rate of totalfactorprodctivity of each country
How does a fall in the growth rate of technology (g) affect equilibrium capital and consumption in the Ramsey model
Using logarithmic form of this GDP production function compute the TFP contribution to GDP growth rate assumingalpha=0.4, beta=0.50 while GDP growth rate is 4.0 percent, capital stock growth rate is 5percent, labor growth 3percent and human capital growth 2 percent.