Question

Assume that the per-worker production function is y_t = 10∙k_t^1/2. 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*.

Answer 1

Given, y_t = 10∙k_t^1/2

  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 S_t = I_t

_{This means that s* = i* = 10}