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- 7. Assume an economy without population growth or technological progress. Their production function is given by ? = 35?0.5. Their currency capital stock is 100, and the depreciation rate is 17.5%. Give a savings rate such that: Income per worker will grow over the current period Income per worker stay the same over the current period Income per worker will fall over the current period (Hint: First, find how the capital stock will change with the savings rate you choose, then how will this change in capital stock affect income per worker?)Countries X and Y are identical, except that the depreciation rate in country X is10%, and the depreciation rate in country Y is 20%. Then, _____ in the long run. the capital-labor ratio (K/N) will be greater in X than in Y the capital-labor ratio (K/N) in X will be the same as that in Y the capital-labor ratio (K/N) will be less in X than in YConsider the Solow model (Y-AK1/4L3/4). Suppose that the productivity parameter is A=500, the depreciation rate is d=1/10, the savings (investment) rate is s=0.30, and the labor force is constant and equal to 2 million. ÊÊWhat is the steady state capital stock (K)? Please choose the closest answer." a. b. 48200 million C. 34341 million d. 15930 million 18340 million
- Y2 Assume that neither country experiences population growth or technological progress and that 4 percent of capital depreciates each year. Assume further that country A saves 14 percent of output each year and country B saves 26 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 (?∗)(k∗), income per worker (?∗)(y∗), and consumption per worker (?∗)(c∗) for each country. For Country A and For Country B ?∗k∗ for Country A: ?∗k∗ for Country B: ?∗y∗ for Country A: ?∗y∗ for Country B: ?∗c∗ for Country A: ?∗c∗ for Country B:Why do large differences in capital per worker lead to relatively small differences in predicted GDP across countries? Workers exert more effort when they have less capital Capital has a high depreciation rate 4 O The exponent on capital in the production function is much lower than one O Capital is not an input in production1 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.)
- Consider a country with production function unction ? = 5? 1/2, where y is the output per worker and kis capital per worker. Suppose the investment in capital occurs at a rate of 35% of income perworker every period, the depreciation rate is 1.5% and the population growth rate is 2%. Use excel toplot the production function, investment line and capital depletion line with k on the x-axis (usethe attached spreadsheet to draw your graphs).a. What is the steady state level of y and k.b. Suppose TFP increases by 20%. What happens to the steady state y and k?c. Suppose the investment rate increases to 40%. What happens to the steady state y and k?Assume an economy without population growth or technological progress. Their production function is given by ? = 35?0.5. Their currency capital stock is 100, and the depreciation rate is 17.5%. Give a savings rate such that: Income per worker will grow over the current period Income per worker stay the same over the current period Income per worker will fall over the current period15.Consider a Solow-Swan model with saving rate s = 0.4, labour force growth gL = 0.05, constant productivity A = 1, and depreciation 86 = 0.05. If output per worker is y = Y/L = 200 and capital per worker is k = K/L = 800, which of the following is %3D %3D true? Group of answer choices 1.Effective depreciation per worker is 80, saving per worker is 60 and k will decrease towards the steady state 2.Effective depreciation per worker is 80, saving per worker is 80 and k is at the steady state 3.Effective depreciation per worker is 60, saving per worker is 80 and k will decrease towards the steady state 4.Effective depreciation per worker is 60, saving per worker is 80 and k will increase towards the steady state
- Population Growth and Technological Progress – Work It Out In the nation of Winknam, the capital share of GDP is 35 percent, the average growth in output is 3.0 percent per year, the depreciation rate is 5.5 percent per year, and the capital-output ratio is 3.0. Suppose that the production function is Cobb- Douglas and that Winknam has been in a steady state. Round answers to two places after the decimal when necessary. b. In the initial steady state, what is the marginal product of capital (MPK)? MPK =./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.QUESTION 6 The table below represents national macroeconomic data for Year 1 and Year 2. Year Y K N 1 4000 1500 X 2 4200 1500 y Where x = 109 and y=196. Suppose that the production function is given by y- AK0.3N0.7. What is the value of TFP in year 1?