In the Solow model with production function Y = K3 L0.7 which of the following saving rates minimizes consumption in steady state? O 0.3 0.7 (0.3+0.7)/2
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- Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.Country A and country B both have the production function Y = F(K, L) = K1/3L2/3 Does this production function have constant returns to scale? Explain. Find Solow’s production function, y = f (k)? Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Find the steady-state level of capital per worker for each country, then find the steady-state levels of income per worker and consumption per worker. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator (or, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For…
- Suppose, in a country, the production function is Y = K1/3L2/3.1. National saving rate is 25 percent. Capital depreciates at the rate of 10% and the initial value of capital per labor is 4. Find the steady-state values of capital per worker, output per worker, and consumption per worker.2. Suppose, saving rate decreases to 20 percent. Find the steady-state values of capital per worker, output per worker, and consumption per worker. Show the changes between 1) and 2) on a graph (label your graph)The 2020 Economic Report of the President on your country contained the following statements: "Devoting a large share of national output to investment would help restore rapid productivity growth and rising living standards in this period of COVID-19." Do you agree with this claim? Explain.Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Show the steady state in a graph. In the same graph, show the effect of a decrease in the depreciation rate, say to 2%
- Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) 1. Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ?Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Find the steady-state capital-labor ratio, real GDP per worker, investment per worker and consumption per worker for this economy.Consider an economy described by the production function: Y = F(K, L) = K^0,3L^0,7 A. What is the per-worker production function? B. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.
- 4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:kt+1 = sAkαt + (1 − δ)kt.Consumption per worker is given by:ct = (1 − s)Akαt.(a) Solve for an expression for the steady state capital stock per worker. Indoing so, assume that the level of productivity is fixed at some value A.(b) Use your answer on the previous part to solve for an expression forsteady state consumption per worker.(c) Use calculus to derive an expression for the s which maximizes steadystate consumption per worker.An economy has the per-worker production function yt=f(kt)=4kt)0.4, where yt is the output per worker and kt is the capital-labor ratio. The depreciation rate is 0.15, and the population growth rate is 0.04. Saving is St=0.5Yt, where St is total national saving and Yt is total output. The slope of the per worker production function is given by f' (kt)=1.6kt-0.6 . What is the steady state value of capital-labor ratio, k*? Round your answer to at least 2 decimal places.Suppose that capital expenditure varies with time in such a way that t months from now there will be K(t) thousand dollars of capital expenditure,where K(t) =2t^4 + 3t + 149 /t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be produced at this time?