In: Economics
Assume that the per-worker production function is yt = 10∙kt1/2. Further, assume that the saving rate, s = 0.2, the depreciation rate, ?=0.4, and the population growth rate, n= 0. Calculate the following:
The steady-state values of the capital-labor ratio, k* , output per worker, y*, investment and saving per worker, i* and s*, and , and consumption, c*.
Given, yt = 10∙kt1/2
s = 0.2
?=0.4
n= 0
At steady state, Δk = 0, i.e sf(k)-(n+?)k = 0
sf(k) = (n+?)k
k* = [10 x s/ (n+?)]2 = 25
Thus, y* = 10 x (25)0.5 = 50
c* = (1 − s)y* = (1 - 0.2) 50 = 40
i* = s.y* = 0.2 x 50 = 10
Also, since goods market equilibrium requires St = It
This means that s* = i* = 10