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- Consider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.Population 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 =Can you show me the solution for part d)
- 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: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…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 output
- 1. Consider a Cobb-Douglas production function that features capital-augmenting technology: Y(t) = [A(t) K(t)]aL(t)¹-a. Assume that technology A(t) grows at rate u: A(t) = μA(t). Show that the economy converges to a balanced growth path, and find the growth rates of Y and K on the balanced growth path. 2. Let the production function be Y(t) = J(t)aL(t)1-a, where J(t) is the effective capital stock. The dynamics of J(t) are given by j (t) = sA(t)Y (t) — 8(t). The presence of the A(t) term in this expression means that the productivity of investment at t depends on the technology at t. Show that the economy converges to a balanced growth path. What are the growth rates of Y and J on the balanced growth path? dy* S as y* 3. Find the elasticity of output on the balanced growth path with respect to s: Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls. 1. What…n the endogenous growth model, suppose that there are three possible uses of time. Let u = the fraction of time spent working s = fraction of time spent neither working nor accumulating human capital (unemployment) 1 – u – s = fraction of time spent accumulating human capital If z = 1, b = 5, and the economy begins in period 1 with 100 units of human capital, find the values of Y, H, and Y’ for each of the scenarios below. In this model, does the scenario with the greater human capital accumulation lead to the highest per capita income (Yes/No)? u s H Y H' Y' .7 .05 100 .6 .15 100 .6 .05 100 .5 .10 100 Does the scenario with the greater human capital accumulation lead to the highest per capita income (Yes/No)?How would I answer this?
