Y - K"(LE) The economy has a capital share of 0.20, a saving rate of 45 percent, a depreciation rate of 3.75 percent, a rate of population growth of 5.00 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 elffective worker (y"), and the marginal product of capital. k' - y* = marginal product of capital =

Suppose that the production function is Y = 10 ( K )^1/4 ( L )^3/4 and capital lasts for an average of 50 years . Assume that the rate of growth of population equals 0 and saving rate s = 0.128 . a. Calculate the steady - state level of capital per worker , output per worker , consumption per worker , saving and investment per worker , and depreciation per worker b. Suppose that initial level of capital per worker is 100 , explain the moving process to the steady state . c . Use relevant graph to demonstrate . Plsss provide detailed answers, thank you

Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].

(Long Run) The country of Prosperous has: Production function: Y = 2 K1/2 (AN)1/2, where Y=output;K=capital; A=technology; and N=labor Saving rate (s): 20% per year Depreciation rate (d): 10% per year Labor growth rate (n): 2% per year Rate of technological change (g): 8% per year b. Calculate: The steady state level of capital accumulation per effective worker The steady state level of output, consumption and investment per effective worker Graphically illustrate the above steady state condition.

2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker.     Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…

(Long Run) The country of Prosperous has: Production function: Y = 2K1/2 (AN)1/2 ; where Y=output;K=capital; A=technology; and N=labor Saving rate (s): 20% per year Depreciation rate (d): 10% per year Labor growth rate (n): 2% per year Rate of technological change (g): 8% per year c. Calculate the growth rate of the following variables when the economy achieves its steady-state: Output per effective worker (Y/AN) Output per worker (Y/N) Output (Y)

Parameters     Equations     s =0,20  marginal propensity to save    Y=WKr.L1-r   Production Function  u=0,02  Population growth rate    K.=s.f(k)−aK     Capital Accumulation     b=0,04  Technological growth rate      L./L=  ?     Population Growth            a=0,05  Depreciation rate     W./W=b   Technological Progress          S=s.f(k)   Savings     a.  Find steady-state level of capital per effective labor: k*     b.  Draw a graph and show output function, actual investment and breakeven investment lines.     c.  Assume that in this economy, people start spending more and therefore marginal propensity to save decline permanently. What will happen to variables in the model (steady-state level capital per effective labor; output growth etc.).     d.  Instead of reduction in saving assume this time that we face lower fertility rate in the country. What will happen to variables in…

Suppose that the production function is Y= 10(K)1/4 (L)3/4 and capital lasts for an average of 50 years so that 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate, s =0.128, calculate the steady-state level of capital per worker, output per worker, consumption per worker, saving and investment per worker and depreciation per worker.

The current population of the United States is 327.2 million with 2.2% of the population is engaged in R&D at an efficiency rate of 1/375 per million persons per year. If R&D is the only source of total-factor productivity growth what is the growth rate of total factor productivity in the United States?

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.