Question

Suppose that the economy is summarized by the following: Production- Yt=10Kt^0.3Lt^0.7 Consumption- Ct= 0.8Yt Depreciation rate 10% MPK= 3Kt^-0.7Lt ^0.7 or in capita terms MPK= 3kt ^-.7

1. Find the steady state (long run) equilibrium values of i_t, k_t, y_t, c_t and s_t for the economy.

Answer 1

Yt = 10Kt^0.3Lt^0.7

Yt / Lt = 10 x (Kt / Lt)^0.3

yt = 10 x (kt)^0.3

Consumption rate = 0.8 (from consumption function)

Savings rate (s) = 1 - Consumption rate = 1 - 0.8 = 0.2

Depreciation rate (d) = 10% = 0.1

In steady state,

s / d = kt / yt

0.2 / 0.1 = kt / [10 x (kt)^0.3]

2 = (1/10) x [kt / (kt)^0.3]

20 = (kt)^0.7

kt = (20)^(1/0.7) = 72.21

yt = 10 x (72.21)^0.3 = 10 x 3.611 = 36.11

ct = 0.8 x yt = 0.8 x 36.11 = 28.89

st = yt - ct = 36.11 - 28.89 = 7.22

it = s x yt = 0.2 x 36.11 = 7.22