Question

Consider an economy described the following parameters: S=0.2 n=0.01 and 6 =0.04. The production function is given by y = k0.5 so that the steady-state y*=4 and the steady-state k*=16. At present k=12. Determine the percent rate of growth of y at this instant. Enter the value with two decimal places without the % sign. If the growth is negative, do enter the negative sign! Answer: -1.16 Be careful to find the growth rate of y. First you must find the growth rate of k, and then apply the growth rate rules to the production function. The correct answer is: 0.39

Answer 1

The current K = 12

Thus, current Y = (12)^0.5

Thus, savings = 0.2*(12)^0.5 = 0.692

Replacement of capital = (0.01+0.04)*12 = 0.05*12 = 0.6

Thus, increase in capital = 0.692 - 0.6 = 0.093

% increase in capital = (chnage in capital/initial capital)*100

= (0.093/12)*100

= 0.775%

% change in Y = 0.5*percentage change in K

= 0.5*0.775 = 0.3875

= 0.39%

Thus, percent growth of y = 0.39%