Suppose you were given a production function for the nation of Pluto, Y = A(K.6)(L.4), where Y is GDP per capita, A is Total Factor Productivity, K is physical capital per worker, and L is human capital per worker. Which of the following is true about this production function?
A.)There are diminishing returns to increases in Total Factor Productivity
B.)Pluto only needs human capital per labor to be above zero to have production in its economy
C.)There are diminishing returns to labor and capital
D.)All of the above are true.
Suppose you were given a production function for the nation of Pluto, Y = A(K.6)(L.4), where...
Consider an economy described by the following Cobb-Douglas, constant-returns-to-scale, aggregate production function: Y (K, L) = ?.??.? i.) Derive the per-capita/worker production function. ii.) Assume the depreciation rate (ɖ) is 1.5 percent, the population growth (n) is 4 percent, and the savings rate (s) is 8 percent; derive the discrete fundamental Solow Growth equation, and finally find the steady-state capital stock per-capita/worker (k*) and output per-capita/worker (y*). iii.) Assume the savings rate (s) rises to 16 percent, all else...
12. Suppose an economy's production function is specified by y = A(√K,√L), where A represents the productivity of resources, K the quantity of capital resources, and L the quantity of labor resources. A. Find potential output when A = 10, K = 49, and L =9. B. Find potential output when A = 10, K = 49, and labor resources are 3, 6, and 12. C. Plot the levels of output associated with 3, 6, 9, and...
8. Consider the following production function Y = AK0.3(NH)0.7 where Y is GDP, A is total factor productivity, K is capital, N is employment and H is human capital. Denote by P the population of the country. Thus, Y/P is per-capita GDP and N/P is the fraction of the population employed. What is the contribution of the fraction of the population employed (N/P) to the growth rate of per-capita GDP (Y/P)? (a) Growth rate of N/P. (b) Growth rate of...
15. Consider an economy, with a production function given by Y-AK03L07. This economy's annual GDP growth rate is 5%. Also assume that L and Kare both growing at annual rates of 2%. Calculate the growth rate of total factor productivity for this economy. a. 2.0% b. 3.0% 4.0% c. d. 5.0% 16. Suppose output is determined by a Cobb-Douglas production function Y=AK L1 Where 0ca<1. If total factor productivity (A) remains constant, but labour (L) and capital (K) inputs both...
Suppose the per-capita production function is given by y=\k, where kis capital per person and y is output per person. Suppose that the savings rate in this economy is 50% and capital depreciates at the rate of 25% a year. The steady-state capital-to-labor ratio is: k-1 k 2 k-4 cannot be determined from the above information.
Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor input. Let K>0, L>0. 1. What are the marginal products of capital and labor re- spectively? 2. Please compute the technical rate of substitution (we as- sume K is on the horizontal axis). 3. Dose this production function show diminishing technical rate of substitution (in absolute value) when K increases? Please give a brief proof. 4. Please prove that this production function features increas-...
4. A country is described by the Solow Model, with production function y - Aki where y is Output per Worker (Y/L) and k is Capital per Worker (K/L). Suppose k- 400. The fraction of output invested is 50% (s-05) and the depreciation rate is 5% (6-0.05). A, the overall productivity parameter equals 1. Is the country at its steady state level of output per worker, above the steady state or below the steady state? Show how you reached your...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
Consider the Solow growth model without labor force or technology growth. Suppose y = k^1/4, total factor productivity is constant and equal to 1, s = 0.40, and d = 0.05. Find the steady-state capital––labor ratio for this economy. Find the steady-state real GDP per worker for this economy. Find the steady-state level of investment per worker for this economy. Find the steady-state level of consumption per worker for this economy.
1.(4 pt) Suppose the economy has the following production function: F(K,H,L)=KαHβLγ where K, H, L denotes as the amount of physical capital, the amount of human capital (e.g. experiences, knowledge, the amount of school years), and the amount of labor, respectively. In terms of ∝, β and γ, under what condition such that this production function exhibit constant return to scale (2 pt)? Under what condition such that this production function exhibit increasing return to scale? (2pt)?