Question

Again consider the Solow model economic production function,

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

Assume the following initial conditions:

A = 1.7

a = 0.48

K = 12

L = 112

Additionally, you know that depreciation rate is 23 % and the savings rate is 23 %.

What will be the total capital (K) at the end of the first period (beginning of second period)?

Answer #1

Production function is given by

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

in beginning period two we assume K to be K2

so K2= (1-d)K1+I ......eq 1

where d is the depreciation of capital and I is the investment

also we know that I=S =sY

so finding Y by putting the values available we have

Y = 1.7(12)^{0.48}112^{0.52} =1.7*3.29* 11.62=
65.04

so sY = 0.23*65.04 = 14.95

which is lso the investment

putting the values in equation 1

K2= (1-0.23)12+14.95

= 24.19

so K in the next year is 24.19

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