Numerical Assignment Assignment | Numerical Assignment

Except question a,f,g,j can be write in word form, ithers have to make in the spreadsheet.

Suppose that you have a standard Solow model with a Cobb-Douglas production function, f(kt)=Aktα. The central equation of the model can be written as Δkt+1=sf(kt)−dkt.

(a) Derive the closed-form solution for steady-state capital stock, k⋅, by hand.  (5 points points)

(b) Suppose that A = 1, s = 0.2, d=0.1, and α= 1/3. Create a new spreadsheet. In the top-left cell, using your answer from (a), numerically solve for k⋅(you should get a number). (5 points)

(c) Create a column in your spreadsheet corresponding to periods. Let these periods run from period 0 to period 100. Create additional columns for capital stock, output, consumption, investment, depreciation, and change in capital stock (see video  #4 for a walk-through). (2 points)

(d) Suppose that in period 0, the capital stock per worker equals its steady-state, computed in (b).  Compute and fill in for output, consumption, investment, depreciation, and change in capital stock in period 0. (3 points)

(e) Using the central equation of the Solow model, compute capital stock per worker in period 1. Then repeat the process and fill in for output, consumption, investment, depreciation, and change in capital stock in period 1. (2 points)

(f) Iterate this process until you have filled all of the columns up to period 9. What is true about the capital stock in periods 0 through 9 when the capital stock starts in the steady-state in period 0? (3 points)

(g) Suppose that in period 10, the saving rate increases to 0.25 and is expected to forever remain there. What will happen to the capital stock in period 10? (2 points)

(h) Compute the capital stock in period 11, given the capital stock in period 10 and the new, higher saving rate.  Compute and fill in for output, consumption, investment, depreciation, and change in capital stock in period 11. (1 point)

(i) Iterate and fill in all of the columns all the way to period 100. (2 points)

(j) Approximately how many periods does it take the capital stock to get halfway to its new, higher steady-state value when s increases from 0.2 to 0.25? (5 points)