Question

Economics

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).

Suppose that in period 11 the savings rate increases to 0.2 and stays there permanently. Use Excel to compute the dynamic adjustment in the capital stock per worker as a result of the change in the savings rate for periods t = 11, 12, …. , 150).

Plot adjustment in the capital stock per worker for periods 1 through 150. What is the new steady-state level of k, which the capital stock approaches asymptotically? How many periods will it take for capital stock per worker to reach its new steady state level?​

Answer 1

Explanation:

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).

Suppose that in period 11 the savings rate increases to 0.2 and stays there permanently. Use Excel to compute the dynamic adjustment in the capital stock per worker as a result of the change in the savings rate for periods t = 11, 12, …. , 150).

Plot adjustment in the capital stock per worker for periods 1 through 150. What is the new steady-state level of k, which the capital stock approaches asymptotically? How many periods will it take for capital stock per worker to reach its new steady state level.