Question

Consider the Solow model economic production function,

Y = A * K^a * L^(1-a)

Assume the following initial conditions:

A = 1.8

a = 0.4

K = 11

L = 109

Additionally, you know that depreciation rate is 6 % and the savings rate is 13 %. What will be the total capital (K) at the end of the first period (beginning of second period)?

Answer 1

Consider the given problem here the production function is given by, “Y=A*K^a*L^1-a.

So, the change in the capital stock per worker is given below.

=> change in k = s*y – d*k, s=13%=0.13 and d=6%=0.06. So, initially “K=11”, “L=109”, => k=K/L = 0.1009.

Now, Y=A*K^a*L^1-a, => y = Y/L = A*(K/L)^a = A*k^a, => y = A*k^a = 1.8*(0.1009)^0.4 = 0.7192, => y = 0.7192, here “y” is the output per worker.

So, the change in “k” is given by, “s*y – d*k”, => “0.13*0.7192 – 0.06*0.1009 = 0.0874 > 0”.

Now, the “k” at the end of the 1^st period and beginning of the 2^nd period is given by.

=> k2 = k1 + 0.0874 = 0.1009 + 0.0874 = 0.1883, => k2 = K2/L, => K2 = k2*L = 0.1883*109 = 20.53. So, the level of “K” at the end of the 1^st period and beginning of 2^nd period is “K2=20.53”.