Y=10.K0.5 L0.5 K starts at 500, L at 50, Investment = 0.10Y, Depreciation = 0.05K %3D What is the steady state level of consumption ? (The steady state formula for capital is Labour*(Savings rate*Technology/depreciation rate)^(1/(1-a)) )
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- 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 ?C I G NX Price Yr1 1000 156 560 52 4 Yr2 1300 159 600 52 5 Yr3 2000 169 690 53 6 Yr4 2900 180 880 53 7 -What will the percent rate of change in real GDP be from year 1 to year 2, from year 2 to year 3, and from year 3 to year 4. (round to the whole number for all calculations and final answers) -State how long it will take for real GDP to double in size.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.
- Question 3Consider an economy described by the production function:Y = F(K, L) = K0.3 L0.7 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.c. Assume that the depreciation rate is 10 percent per year. Make a table showing steadystate capital per worker, output per worker, and consumption per worker for saving ratesof 0 percent, 10 percent, 20 percent, 30 percent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?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 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?
- suppose the production formula is given by yt= kt ^1/3 where y is the output per worker and k is the capital per worker. futhermore assume that the saving rate is exogenous and the capital deprecitates at delta rate. if the sum of both deprectiation rate and saving rate equals 1, answer the questions below 1. find the steady state values of capital, output, investments and consumption as functions of the saving rate only? 2. in a diagram show the steady state value values in a part (a)?Country A and country B both have the production function Y = F(K, L) = K^0,5L^0,5 A. Does this production function have constant returns to scale? Explain. B. What is the per-worker production function, y = f(k)? C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Theen find the steady-state levels of income per worker and consumption per worker. D. 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 a computer spreadsheet…Suppose that 10 workers were required in 2010 to produce 40,000 bushels of wheat on a 1,000-acre farm. a. What is the average output per acre? Per worker? b. If in 2020 only 8 workers produce 44,000 bushels of wheat on that same 1,000-acre farm, what will be the average output per acre? Per worker? c. By what percentage does productivity (output per worker) increase over those 10 years? Over those 10 years, what is the average annual percentage increase in productivity?
- 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 production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Explain how the economy goes from one steady state to another.A mathematical approximation called t he rule of 70 tells us that the number of years that it will take something that is growing to double in size is approximately equal to the number 70 divided by its percentage rate of growth. Thus, if Mexico’s real GDP per person is growing at 7 percent per year, it will take about 10 years (= 70 / 7) to double. Apply the rule of 70 to solve the following problem. Real GDP per person in Mexico in 2005 was about $11,000 per person, while it was about $44,000 per person in the United States. If real GDP per person in Mexico grows at the rate of 5 percent per year, about how long will it take Mexico’s real GDP per person to reach the level that the United States was at in 2005? (Hint: How many times would Mexico’s 2005 real GDP per person have to double to reach the United States’ 2005 real GDP per person?)