Consider an aggregate production function of the form Y= K⅓(AL)⅔ Assume that the labor force is a constant fraction of the population. capital per worker grows at 3% population grows at 1% and labor productivity grows at 6% then GDP per capita grows at_____%
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Question9
Consider an aggregate production function of the form Y= K⅓(AL)⅔
Assume that the labor force is a constant fraction of the population. capital per worker grows at 3% population grows at 1% and labor productivity grows at 6% then
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- Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].QUESTION 6 The table below represents national macroeconomic data for Year 1 and Year 2. Year Y K N 1 4000 1500 X 2 4200 1500 y Where x = 109 and y=196. Suppose that the production function is given by y- AK0.3N0.7. What is the value of TFP in year 1?J 7 Given a production function Yt = AKt1 /3L2 /3 , if K0=8, A = 2, L = 4, s = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K1 , I 1 , Y1 and C1 .
- 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…The production function for an economy is Y; = 1.5 Kª L(1«), where Y; is total output, K; is total capital, and L; is total labor. Total savings for the economy is given by S; = 0.2 Y. The rate of population growth, n, is 5% and the rate of depreciation, 8, is 10%. Write down the per capita production function. (a) (b) Write down the fundamental equation of Solow-Swan. (c) Imagine that a=0.7. In the long run, what is the growth rate of per capita output, y?? In the long run, what is the growth rate of total output, Y;? (d) In the long run, is there a constant level of capital per person, output per person and consumption per person? If so what are they? If not, why not? (e) Imagine that the depreciation rate increases from 10% to 12%. If the economy is initially in steady state, what are the effects on the levels and growth rates of k, y, and c? () Imagine that a=1. In the long run, what is the growth rate of per capita output, y.? In the long run, what is the growth rate of total…Why do large differences in capital per worker lead to relatively small differences in predicted GDP across countries? Workers exert more effort when they have less capital Capital has a high depreciation rate 4 O The exponent on capital in the production function is much lower than one O Capital is not an input in production
- QUESTION 2 Assume we have a Cobb-Douglas production function of Y-KO505 Assume K-160, L-40, a-025, 6-0.10, and initial k-4.0. Derive the steady-state level of capital (k) (calculate unt Ak is at a level where the first 2 decimal points are 0. 1024In a Malthusian model the production function is described in the following form: Y-6LN00 where Lis the quantity of land and N is the quantity it labour employed. Population growth depends on per capita consumption as N/N-04(C/Nya.1, Calculate the steady state value of consumption.7 Assume a Cobb-Douglas production function, where © =0.5 and A = 1. If AN/N = 0.06, d = 0.04, and s = 0.2, what is the steady state value of capital per capita ??
- Depreciation, investment, and output per worker juts Depreciation, ök Ass Output, (k) Investment, (k) Capital per worker (K) The aggregate production function of capital states that output is determined by:Assume that the per-worker production function is yt = 2kt^(0.3). The saving, depreciation and population growth rates are estimated at 0.3, 0.05 and 0.02, respectively. (a) Calculate the capital-labour ratio steady state for this economy. (b) Calculate consumption per worker at the steady state.How is the concept of technology, as defined with the aggregate production function, different from our everyday use of the word?