Suppose we have an economy described by the Solow growth model, with a Cobb-Douglas production function (Y=F(K,AL) = K^α(AL)^-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?© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/economics/microeconomics/cobb-douglas-1h4
...-α)] = [0.225/(0.045+0.01+0)]^[0.5/(1-0.5)] = 4.09
K/Y = (K/AL)/(Y/AL) = k* / y* = 16.74 / 4.09 = 4.09
Since AL = (e^x) L, L = AL / (e^x) = AL / (e^0) = AL
Then Y/L = ...