Question

With a per-worker production function y = k1/2, the steady-state capital stock per worker (k*) as a function of the saving rate (s) is given by:

A) k* = (s/ $\delta$ )2.

B) k* = ($\delta$/s)2.

C) k* = s/$\delta$.

D) k* = $\delta$ /s.

Answer is A, I need to understand the process. Thanks

Answer 1

Answer

The correct answer is (A) k* = (s/ $\delta$ )²

Steady state occurs when change in capital per worker(k) = 0 i.e. $\Delta k = 0$

Change in k($\Delta k = 0$) = Investment per worker - depreciation per worker.

At equilibrium C + I = C + S where C = consumption per worker, I = investment per worker and S = saving per worker

At equilibrium C + I = C + S => I = S.

S = saving per worker = sy where s = saving rate and y = output per worker

Hence I = S = sy and as y = k^1/2 => I = S = sk^1/2

depreciation per worker.= depreciation rate* Initial capital stock = $\delta k$

Hence Steady state occurs when $\Delta k = 0$

As discussed above, $\Delta k = 0$ => Investment per worker - depreciation per worker = 0

=> sk^1/2 - $\delta k$ = 0

=> k^1/2 = (s/$\delta$)²

Thus, Steady state level of capital per worker (k*) = (s/$\delta$)²

Hence, the correct answer is (A) k* = (s/ $\delta$ )²