Considering Solow Model with technological change. The initial aggregate production Y(0) = 160 and the initial capital K(0) = 64. Also, we know the initial state of technology T(0) = 1.6 and the number of workers L(0) = 100. Given the exogenous parameter s = 0.1, n = 0.01, θ= 0.05, d = 0: what is Δ k e ( 0 ), the change of capital per effective worker?
Considering Solow Model with technological change. The initial aggregate production Y(0) = 160 and the initial...
Not sure if the answer above is correct. Please show work. Thank you! Question 4 2 pts Considering Solow Model with technological change. The initial aggregate production Y(O) = 160 and the initial capital K(0) = 64. Also, we know the initial state of technology TO) = 1.6 and the number of workers L(O) = 100. Given the exogenous parameter s = 0.1, n = 0.01, 0= 0.05, d = 0: what is Ak® (0), the change of capital per...
Considering Solow Model with technological change. The steady-state level of income per effective labor ye = 5. The economy reaches the steady state in Year 99. The initial technology T(0) = 1 and T grows constantly at rate θ = 0.05. What is the income per capita, y, in Year 100? (Round to 1 decimal place)
The Solow model with technological progress.In the lecture, we talked about the Solow model with technological progress and populationgrowth. Now consider a simpler model with only technological progress. Denote thetechnology level at time \(\mathrm{t}\) by \(\mathrm{A}_{\mathrm{t}}\), and the growth rate of technology by \(\mathrm{g}_{\mathrm{A}}\). The number ofworker is constant, \(\mathrm{N}\). The production function is given by$$ Y_{t}=K_{t}^{\alpha}\left(A_{t} N\right)^{1-\alpha} $$where \(\alpha\) is a constant.(a) Define \(x_{t}=X_{t} / A_{t} N\), where \(X_{t}\) stands for all relevant aggregate variables in the model.Write down...
Consider the Solow model with population growth and technological progress. The population grows at rate of d and the technology grows at rate of g. The depreciation rate of capital is λ. The aggregate production function is given as Y=100 ?![(1-u) ?]" where Y, K, L, ?, ? and u refers to aggregate output, aggregate capital stock, aggregate labor, output elasticity with respect to capital, output elasticity with respect to labor, and natural rate of unemployment, respectively. Draw a well-labeled...
3) Consider the Solow model with population growth and labor-augmenting technological progress. Suppose that the aggregate production function is Cobb- Douglas, i.e. Y = AK"(E · L)1-a, where A is a constant, while E denotes technological progress and grows at rate g. Labor grows at an exogenous rate n, and capital depreciates at rate d. As usual, people consume a fraction (1 – s) of their income. a. Use a graph similar to what we have seen in class to...
Consider the Solow growth model. The production function is given by Y = K αN1−α , with α = 1/3. Depreciation rate δ = 0.05, and saving rate s = 0.25. Labor force grows at the rate n = 0.01. (a) Write down the law of motion for capital per worker. (b) Compute steady state capital per worker. (c) Suppose the economy has initial capital per worker k0 = 4. Describe the dynamics of this economy, i.e., how does capital...
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...
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...
Question #3: Solow Model with Technological Progress Suppose than the economy's per effective worker production function is given by y=Ros. Assume that the savings rate (8) is equal to 16 percent, the depreciation rate (8) is equal to 10 percent, the population growth rate (n) is equal to 2 percent and the rate of technological growth (g) is equal to 4 percent. (a) Find the steady-state value of capital per effective worker (K). (b) Find the steady-state value of output...
3) [20 points] Consider the Solow growth model without population growth or technological change. The parameters of the model are given by s = 0.2 (savings rate) and d=0.05 (depreciation rate). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. a. Rewrite production function below in per worker terms: 1 2 Y = K3L3 b. Find the steady-state level of the capital stock, c. What is the golden rule level of...