Question

Again consider the Solow model economic production function,

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

Assume the following initial conditions:

A = 1.5

a = 0.31

K = 11

L = 86

Additionally, you know that depreciation rate is 15 % and the savings rate is 20 %. Assuming no changes in any of the parameters, besides the change in K over time, what is the long-run equilibrium level of capital?

Answer 1

Consider the given problem here the production function is given by, “Y=A*K^a*L^1-a. Now, here “L” is fixed, => we don’t have to take “L” into consideration.

So, the change in the “K” is given by the difference between “s*Y” and the “d*K”.

=> Change in K = s*Y – d*K . Now, in the LR equilibrium the “change in K” must be zero.

=> change in K = 0, => s*Y = d*K, => (s/d)* A*K^a*L^1-a = K.

=> (0.2/0.15)* 1.5*K^a*(86^1-0.31) = K, => 1.3333* 1.5*21.6174 = K^1-a.

=> K^1-0.31 = 43.2337, => K^0.69 = 43.2337, => K = (43.2337)^(1/0.69) = 234.83, => K=234.83.

So, the LR equilibrium “K” is given by, “K = 234.83.