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 falls
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- Consider an economy described by the production function Y=F(K, L)=?^0.4?^0.6 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.part C and Dplease do it in the table
- Suppose Westeros produces output according to the production function: Y = √K The fraction of output that is saved and invested in new capital is 20%. The depreciation rate is 5%. Use this information to answer the following questions. Macmillan Learning a. What is the steady-state amount of capital (K) in Westeros? b. What is the steady-state amount of output (Y*) in Westeros? c. If Westeros had started out with 25 units of capital, what would the Solow model predict would happen to its output in the long run? O It will decrease, since that is above its steady state level of output of 4 It will decrease, since that is above its steady state level of output of 16 It will increase, since that is below its steady state level of output of 16 It will increase, since that is above its steady state level of output of 41 It will remain at 25, since that is its steady state level of outputPopulation Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =If capital per worker decreases, real GDP per hour of labour Answers: increases because the level of technology increases. decreases because the level of technology decreases. increases for a given level of technology. decreases for a given level of technology. none of the above
- The graph below represents per-worker production functions for the same country. Answer the following questions using this graph. Which 1 concept explains that the area between B and C has a flatter slope than the area between A and B? Answer: Law of Diminishing Marginal Returns What has to happen for a country to move from point E to B to D? Answer: The movement through which 3 points (out of 5 given) would indicate the largest increase in productivity? Answer: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.Question 9. Suppose that an economy has the following production function: Y = F(K, L) = K0.210.7, where Y is output, K is capital stock and L is the labour force. a. What is the per-worker production function? b. Assuming no population growth or technological progress, find steady- state capital stock per worker, steady-state output per worker, and steady-state consumption per worker as a function of the saving rate and the depreciation rate. c. Assuming that the depreciation rate is 10 percent per year. What level of capital stock per worker and saving rate maximize consumption per worker?
- Say an economy begins with an initial level of capital per worker, k0, that is above its steady state level of capital per worker, k*. All else equal, what will happen to output per worker and capital per worker?Why Capital does not Flow from Rich to Emerging Countries? We assume that the production function in country i is 1 1 2 Yi = A ² k², (1) where y, and ki are output and capital per capita, respectively, in country i, and A is a measure of technology in country i. (a) Calculate the marginal product of capital (MPK) denoted by Ri in country i. (b) Express the MPK in terms of output per capita, yi, i.e., eliminate ki from Ri by using the production function (1). (c) We consider two countries, indexed by i 1 and i 2, whose production function is described by (1). Both are assumed to have the same level of productivity, i.e., A₁ A2. We assume y2 50y₁. Calculate the ratio R₁/R₂. (d) We keep assuming that y2 50y1, but now we assume that A2 educational attainment is higher in country 2. Calculate the ratio R₁/R₂ under 10A₁ because these assumptions. FX = - (e) We keep assuming y2 50y₁ but now we consider that technology in country 1 is a function of technology of the more advanced country 2,…Please no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…