Cobb-Douglas

Suppose we have an economy described by the Solow growth model, with a Cobb-Douglas production function (Y=F(K,AL) = K^α(AL)^1-α ),  a capital share of 0.5; with population, labor-augmenting productivity growth, and depreciation rates given by
n =0.01 per year, x = 0.02 per year, and depreciation = 0.045 per year; and with a savings rate s = 0.225 of output Y per year.


Suppose that x suddenly and permanently falls from 2% per year to 0% per year.

i) Calculate the paths over time after the slowdown of k, the ratio of capital to effective labor, of y, the ratio of output to effective labor, of K/Y, the capital-output ratio, and of Y/L, output per worker.

ii) How do these paths compare to the paths had the slowdown in productivity growth not occurred?