Question

suppose that the growth rate of output per worker is 2% and that the growth rate of capital per worker is 1% calculate the growth rate of total factor productivity assuming a production function of Y

4. (20 points) Suppose that the growth rate of output per worker is 2% and that the growth rate of capital per worker is 1%. Calculate the growth rate of total factor productivity assuming a production tu of Y = AK -9, with a = 1/3. Briefly explain the intuition behind the Solow Residual.

Answer 1

Solution:

Given the production function as: Y = A*K^1/3*L^2/3

Then, in terms of per worker, we can write this (by dividing whole by L) as:

Y/L = A*K^1/3*L^2/3/L

y = A*k^1/3 ; where y and k are per worker levels of output and capital, respectively.

So, in growth terms, this is

%y = %A + (1/3)*%k

%A = %y - (1/3)*%k

Substituting for values of %y = 2% and %k = 1%:

%A = 2 - (1/3)*1 = (5/3)% or 1.667%

So, growth rate of total factor productivity is 1.667%.