an economy with a production function, Consider Y = K (AN), saving rate s, depreciation rate 8, population growth gn and rate of technological progress gå, capital per effective worker in the steady state (K/AN)* is given by:
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- 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: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…
- If the production function is given by Yt=Kt 2/3Lt 1/3 and the saving rate (s) equals the depreciation rate (õ). Find the numerical values of the steady-state capital and output?An economy has production function Y = K¹/2L¹/2, a savings rate of 60 percent. There is no technological progress or labour force growth. The depreciation rate initially 10 percent, increases to 40 percent. There are 400 workers in this economy. When the depreciation rate is 40 percent, output will be equal to dollars.In an economy with population growth rate at gn, technology growth rate at gå and depreciation rate at 8. The change in capital per effective worker k is given by the equation: O sf(k)(8 + 9A + 9N)k Of(k) - (8 + 9N)k ○ f(k) - (8 + 9A + 9N)k f(k) + (8 + 9A +9N)k O sf (k) + (8 + 9A + 9N)k
- 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.4. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?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].
- Suppose 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.12. Consider an economy without technological progress and population growth. The production function is given as Y = K²/³N\/3. Both the saving rate and the capital depreciation rate are assumed to be 0.1. Which of the following saving rate delivers the highest consumption per worker in the steady-state: (a) 1/3 (Ь) 1/2 (c) 2/3 (d) none of above is correctQ4) 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?