Y = K (LE) ¹-α. e economy has a capital share of 1/3, a saving rate of 20 percent, a depreciation rate of percent, a rate of population growth of 2 percent, and a rate of labor-augmenting chnological change of 1 percent. In steady state, capital per effective worker is:
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- 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 ??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].Q4) Production Functions and Growth (a) Time is continuous and the production function of the economy is given by (1) Y¢ = ( K¢ )ª( A¿N; )1-« Total factor productivity evolves according to (2) A = egt Ao such that A where the growth rate of technological progress g is exogenous. Population grows at an exogenous rate n according to (3) N{ = ent No with No = 1 such that = n Find an expression for the growth rate of (i) output per capita (Yt / Ni) and (ii) output per effective worker ( Yt/ (A:N:) ). When is the growth rate of (ii) equal to zero?
- Y=√KVAN, where K is capital, N is labor, A is the state of technology, and AN denotes the amount of effective labor in the economy. Suppose that the saving rate, s, is equal to 18%, and that the rate of depreciation, 8, is equal to 12%. Suppose further that the number of workers, gn, grows at 6% per year and that the rate of technological progress, 9A, is 4% per year. Given the values of the economy, compute the following: The steady-state value of the capital stock per effective worker is. (Round your response to two decimal places.) The steady-state value of output per effective worker is. (Round your response to two decimal places.) The steady-state value of the growth rate of output per effective worker is%. (Enter your response as an integer.) The steady-state value of the growth rate of output per worker is%. (Enter your response as an integer.) The steady-state value of the growth rate of output is%. (Enter your response as an integer.) Suppose that the rate of technological…Assume that the saving rate s is equal to 24%, the population growth rate n is 2% and the depreciation rate d is 2%. Assume also that output per worker is given by: y = k0.5. Then, output per worker in steady state is equal to: 05 36 O 100 06Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.
- 1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…Assume the per-worker production function is y = 2k05 The saving and depreciation rates are 0.2 and 0.04 respectively. Calculate the value for output per worker (y) at the steady state, assuming no population growth. Answer:1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change 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 а. b. 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.)
- 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…Suppose that the per-worker production (labour productivity) function in South Korea is Y over L equals A open parentheses K over L close parentheses to the power of 0.4 end exponent open parentheses H over L close parentheses to the power of 0.6 end exponent. South Korea's labor productivity rises 6% per year, capital-labour ratio rises 5% per year, and human capital per worker rises 2% per year. This information suggests that total factor productivity grows at _________ per year../3-2/3 Given a production function Y₁ = ĀKĻ³³Ī²³, if Kô=8, Ā = 2,Ī = 4, 5 = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K₁, 1₁, Y₁ and C₁.