3 Homework 3 - Homepage Usask

From the Mankiw-Romer-Weil (1992) model, we have the production function:
Divide both sides by AL to get
Y = K α H β (AL) 1−α−β .
y
A =
α β k h
.
A A
Using the (˜) to denote the ratio of a variable to A, this equation can be rewritten as
˜y = ˜ k α˜ h β .
Now turn to the capital accumulation equation:
˙K = sKY − dK.
As usual, this equation can be written to describe the evolution of ˜ k as
˙˜k = sK ˜y − (n + g + d) ˜ k.
Similarly, we can obtain an equation describing the evolution of ˜ h as
and
˙˜h = sH ˜y − (n + g + d) ˜ h.
In steady state, ˙˜ k = 0 and ˙˜ h = 0. Therefore,
˜k =
˜h =
sK
n + g + d ˜y,
sH
n + g + d ˜y.
Substituting this relationship back into the production function,
˜y = ˜ k α˜
β sK
h =
n + g + d ˜y
α
sH
n + g + d ˜y
Solving this equation for ˜y yields the steady-state level
˜y ∗ α
sK
sH
=
n + g + d n + g + d
β
.
β 1
1−α−β
.
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