Question

In: Economics

Assume a Solow model that uses Cobb-Douglas production function with and α = 0.5 for a...

  1. Assume a Solow model that uses Cobb-Douglas production function with and α = 0.5 for a society that saves 40% of their income but sees their capital depreciate at a rate of 5%, population grows at a rate or 2% and technology grows at a rate of 3%.
    1. Determine the steady state level of capital per worker.
    2. Now assume that the economy experiences population growth of 5%, what would their savings rate need to be to make sure that the capital per worker amount in “a” is unchanged?

Solutions

Expert Solution


Related Solutions

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)....
2) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters:...
2) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α = 0.4; d = 0.05; A = 1; s = 0.75; n = 0.4 a) Calculate the rate of capital accumulation (law of motion) b) Calculate the steady state level of capital? c) Calculate the steady state level of real output/income? d) Calculate the steady state level of investment? e) Calculate the steady state level of consumption? f) What effect does a higher...
Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...
Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...
Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α <...
Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α < 1, satisfies all assumptions made in lecture 5. Assumptions: 1) Output increases when either the capital stock or the number of workers increase 2) Both the marginal product of capital and the marginal product of labor are decreasing 3) The marginal product of labor increases when capital increases, and the marginal product of capital increases when labor increases 4) For any constant x >...
The Cobb-Douglas production function is a classic model from economics used to model output as a...
The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form: f(L,C) = c0Lc1Cc2 where c0, c1, and c2 are constants. The variable L represents the units of input of labor, and the variable C represents the units of input of capital. In this example, assume c0 = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs $20 and each unit...
Consider an economy with the following Cobb-Douglas production function:
Chapter 7, Labor Market Regulation (3 points):• Consider an economy with the following Cobb-Douglas production function:Y =k^1/3L^2/3The economy has 1,000 units of capital and a labor force of 1,000 workers.(a) Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock (Hint: Review Chapter 3.)(b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and...
The total production of a particular commodity is given by the Cobb-Douglas function: f(x,y)=bx^α*y^(1−α), b is...
The total production of a particular commodity is given by the Cobb-Douglas function: f(x,y)=bx^α*y^(1−α), b is a given positive constant and 0<α<1 . Assume that we want to maximize production with a given cost constraint mx+ny−p=0 where m and n are the cost of a unit of labour and a unit of capital, respectively, and p the total cost. Show that each term will always be negative guaranteeing a maximum (in the sufficiency H test) using the values obtained of...
Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time,...
Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time, derive the conditional input demands ? ∗ (?, ?, ?) and ? ∗ (?, ?, ?) and the associated long-run cost function ?(?, ?, ?) under the assumption that ? + ? = 1. b) Describe the average cost and marginal cost functions. How do they depend on output q and factor prices w and r? Explain. c) Continuing to assume ? + ?...
An economy has a Cobb-Douglas production function: Y=K^α(LE)^1-α The economy has a capital share of 1/3,...
An economy has a Cobb-Douglas production function: Y=K^α(LE)^1-α The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in steady state. A. At what rates do total output, output per worker, and output per effective worker grow? B. Solve for capital per effective worker, output per effective worker, and the...
Consider the standard Solow model with saving rate is 30%, and depreciation rate is 5%, Cobb-douglas...
Consider the standard Solow model with saving rate is 30%, and depreciation rate is 5%, Cobb-douglas production function with A = 1, α = 0.3. Suppose initially the economy is at the steady state. If we increase the saving rate from 30% to 50% once for all. Plot the first 20 periods of the following after the change: • capital sequence • output sequence • consumption sequence
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT