Question

In: Economics

1. Given the production function Y = zK1/5N4/5, using the Solow growth model: b) Suppose z=1,...

1. Given the production function Y = zK1/5N4/5, using the Solow growth model:

b) Suppose z=1, n = 0.01 and d = 0.10. Using the Golden Rule of Capital Accumulation, what is the steady-state capital per worker, output per worker, and consumption per worker?

c) Suppose z = 1, n = 0.01 and d = 0.14. Using the Golden Rule of Capital Accumulation, what is the steady state capital per worker, output per worker, and consumption per worker?

d) Show graphically the differences in the steady-state capital per worker between the situations characterized in (b) and (c).

e) Using the generic steady-state equilibrium condition, what is the expression for the derivative of steady-state capital with respect to the depreciation rate (dk*/ dd)? What is the sign of this derivative?

Solutions

Expert Solution


Related Solutions

Solow Growth Model a. Assume the production function is y = f(k) = 5 ∗ √?....
Solow Growth Model a. Assume the production function is y = f(k) = 5 ∗ √?. That is for a given level of the capital-labor ratio, k, output, y, is five times the square-root of k. Assume n, the rate of population growth, is 0.02 and d, the rate of depreciation is 0.03. Assume the savings rate, s, is 0.10. Calculate the steady state levels of output, y*, and the capital-labor ratio, k* for the Solow Growth Model with no...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale...
2. Consider the Solow growth model. Suppose that the production function is constant returns to scale and it is explicitly given by: Y = KaL1-a a. What is the level of output per capita, y, where y = Y/L? b. Individuals in this economy save s fraction of their income. If there is population growth, denoted by n, and capital depreciates at the rate of d over time, write down an equation for the evolution of capital per capita, k,...
In the Solow​ model, suppose the per worker production function is y = 3 k^0.5. Suppose...
In the Solow​ model, suppose the per worker production function is y = 3 k^0.5. Suppose s ​=0.11​,n ​=0.03​,and d​ =0.10. Calculate the​ steady-state equilibrium​ capital-labor ratio. k​ = ​(Round to two decimal places​.)
Consider the Solow Growth model, and assume there is no technological change. The production function is...
Consider the Solow Growth model, and assume there is no technological change. The production function is F(K,L) = K^aN^1−α, α = 1/3. Population growth rate n = 0.01. Capital depreciation δ = 0.09. Savings rate s = 0.4. (a) Write down the law of motion for capital per worker. (b) Compute the steady state capital per worker and output per worker. (c) Suppose a book called Let’s Party Like There is No Tomorrow reduces the nation’s savings rate to 0.35....
Consider the Solow model economic production function, Y = A * K^a * L^(1-a) Assume the...
Consider the Solow model economic production function, Y = A * K^a * L^(1-a) Assume the following initial conditions: A = 1.2 a = 0.27 K = 16 L = 112 Additionally, you know that depreciation rate is 11 % and the savings rate is 12 %. Assuming no changes in any of the parameters, besides the change in K over time, what is the long-run equilibrium level of output?
Suppose that you have a standard Solow model with production given by Cobb-Douglas function. Assume A...
Suppose that you have a standard Solow model with production given by Cobb-Douglas function. Assume A = 1, s = 0.1, α = 1/3, and δ = 0.1. Solve for the steady-state level of capital per worker, k* (Hint: use dynamic formula for capital stock.). Create an Excel spreadsheet to compute the dynamics of the capital stock. Plot the evolution of capital stock for 10 periods (i.e., t = 1, 2, … , 10) using your result in part (a)....
1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a....
1. Using the solow growth model, given y(K) = k^0.4, S=0.20, depreciation rate=0.04 and n=1%, a. What is the steady-state level of capital per worker? b. What is the steady-state of output per worker? c. What is the steady-state level of consumption per worker? 2. Now assume population growth is instead-0.5% (approximately the growth rate when every couple has 1.7 children), but that all other parameters stay the same. a. What is the new steady-state output per worker? Is it...
Let us consider a Solow growth model in which the aggregate production function at time t...
Let us consider a Solow growth model in which the aggregate production function at time t for country i is given by: Yit =Ai(Kit)1-βi(ei Lit) βi Where Yit is the aggregate real GDP in country i, Kit   is the aggregate physical capital in country i, Lit     is the aggregate number of workers in country i, ei is the average working time of a worker parameter in country i, Ai >0 is the total factor productivity parameter in country i and...
Q1. Solow Growth Model. (10 marks) Consider the production function for a closed economy ? =2...
Q1. Solow Growth Model. Consider the production function for a closed economy ? =2 ∙ K1/2(AN)1/2 Assume that the savings rate s equals 20% and the depreciation rate ? equals 5%. Further, assume the growth rate of the labor force gN is 3% and the growth rate of technological progress gA is 2% per year. a. Find the steady-state values of (i) capital per effective worker, (ii) output per effective worker, (iii) the growth rate of output per effective worker,...
Let us consider a Solow growth model in which the aggregate production function at time t...
Let us consider a Solow growth model in which the aggregate production function at time t for country i is given by: Yit =Ai(Kit)1-βi(ei Lit) βi Where Yit is the aggregate real GDP in country i, Kit   is the aggregate physical capital in country i, Lit     is the aggregate number of workers in country i, ei is the average working time of a worker parameter in country i, Ai >0 is the total factor productivity parameter in country i and...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT