4.If population growth rate is 0.03, and the depreciation rate is 0.2, then in order to maintain the steady state capital-labor ratio equal to the amount found in Qs. 2, what would be the investment per worker?
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- Calculate the steady state level of investment in an economy with a savings rate of 15%, population growth of -1%, depreciation of 10%, and a= 2/3If the share of GDP used for capital goods is 0.3, the growth rate of productivity is 0.01, the growth rate of population is 0.04, the depreciation rate is 0.05, the initial capital/output ratio is 0.53, and the elasticity of GDP with respect to capital is 0.1, then what is the growth rate of the GDP per capita? Use three decimal places. Please show worked solution, thank you very muchUse the following table to find the steady-state values of the capital-labor ratio and output if the per-worker production 03 function is y=2k S Saving rate 8 Depreciation rate n Population growth rate A Technology 0.35 0.02 0.06 2 k* = Steady-state capital-labor ratio = y*= Steady-state output = (Round your responses to two decimal places.) CHILD Output, Investment, and Depreciation Capital-Labor Ratio Output Depreciation Investment After plotting the final point of your multipoint curve, press the Esc key on your keyboard to end the line Q
- If the share of GDP used for capital goods is 0.08, the growth rate of productivity is 0.09, the growth rate of population is 0.02, the depreciation rate is 0.02, the initial capital/output ratio is 3.75, and the elasticity of GDP with respect to capital is 0.1, then what is the growth rate of the GDP per capita? Use three decimal places.1. A country has the per-worker production function: Yt = 6k/3 where y, is output per worker and k, is the capital-labor ratio. The depreciation rate is 0.1 and the population growth rate is 0.1. The saving function is S; = 0.1Y, where S, is total national saving and Y, is total output. a) What is the steady-state value of capital-labor ratio? b) What is the steady-state value of output per worker? c) What is the steady-state value of consumption per worker? Answer: 2. What happens in the steady state to the capital-labor ratio, output per worker, and consumption per worker when each of the following events occur? You should assume that the steady-state capital-labor ratio is below the Golden Rule level. k y a) Productivity falls b) Population growth falls c) The saving rate falls d) The depreciation rate fallsSuppose that the per-worker production function for an economy is given by y = 10k°3. The depreciation rate is 14%, the savings rate is 23%, and the growth rate of labour hours is 8%. a. The steady-state capital stock per worker for this economy is (Round to two decimal places as needed.)
- 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 ??Population Growth Population growth in the US has, for a very long time been about 1% per year.Take the production function to be y = k0.5, where y and k are output andcapital per capita. The depreciation rate is about 10% per year and the savingsrate is about 20%. 1. What is the steady state capital per capita rate?2. From one period to the next, at what rate does total capital (not percapita) grow.3. If the population growth rate grew to 1.5%, how much would steady statecapital per capita change? Then how much is total capital changing atthis steady state?9. Suppose there is no population or technological growth. Define k as the capital-to-labor ratio. If the per worker production function is given by y = ¹/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady state capital per worker ratio is (a) 1 (b) 2 (c) 4 (d) 6 9
- 1 1 1. Assume that a country's production function is Y = K2L2. Assume there is no population growth or technological change = f(k)? b. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to What is the per-worker production function y а. 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.) (Ctrl) -If Y = A*(K*L)^.5 a. What is the equation for the steady state capital per worker k* in terms of savings rate deprectation rate population growth rate and technology? b. If technology doubles how much does the steady state of capital increase by?Use the following table to find the steady-state values of the capital-labor ratio and output if the per-worker production function is 03 Yt=2k₁ 3 8 n A Saving rate Depreciation rate Population growth rate Technology 0.47 0.03 0.02 2 k* = Steady-state capital-labor ratio= (Round your response to two decimal places.) y* = Steady-state output = (Round your response to two decimal places.)