Start Preparing for the First Midterm 4. Consider the following growth Model (C) N₂c₂ = (1-s)Y, (Y) Y₂ = AK N-8 (K) K+1=(1-8) K +SV (N) N₂+1 = N₂(1 + YN) P₁ (P) Pt+1= 1+YK The new element in this model is that the price of capital falls each period by rate yx. The idea is that each period one unit of output saved can be converted into a greater quantity of physical capital because improvements in the technology for producing machines. For example, in 2010 one unit of output saved could be converted into one machine, but in 2020 that same unit of output saved could be converted into 2 machines. b. a. Take the Aggregate representation above and convert it into its per capita representation. Do we have a Steady State or Balanced growth path for this model? Specifically, solve for the growth rate of per capita output, per capita capital, the price of capital, the wage rate and the rental price of capital along the balanced growth path/steady state.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Start Preparing for the First Midterm
4. Consider the following growth Model
(C) N.c, = (1- s)Y,
(Y) Y, = AK N-
(K) K+1 = (1– 8)K, +*
(N) Ne+1 = N;(1 + YN)
(P) Pe+1 =
1+Yx
The new element in this model is that the price of capital falls each period by rate yk. The idea is
that each period one unit of output saved can be converted into a greater quantity of physical
capital because improvements in the technology for producing machines. For example, in 2010
one unit of output saved could be converted into one machine, but in 2020 that same unit of
output saved could be converted into 2 machines.
a. Take the Aggregate representation above and convert it into its per capita representation.
b. Do we have a Steady State or Balanced growth path for this model? Specifically, solve for
the growth rate of per capita output, per capita capital, the price of capital, the wage rate
and the rental price of capital along the balanced growth path/steady state.
Transcribed Image Text:Start Preparing for the First Midterm 4. Consider the following growth Model (C) N.c, = (1- s)Y, (Y) Y, = AK N- (K) K+1 = (1– 8)K, +* (N) Ne+1 = N;(1 + YN) (P) Pe+1 = 1+Yx The new element in this model is that the price of capital falls each period by rate yk. The idea is that each period one unit of output saved can be converted into a greater quantity of physical capital because improvements in the technology for producing machines. For example, in 2010 one unit of output saved could be converted into one machine, but in 2020 that same unit of output saved could be converted into 2 machines. a. Take the Aggregate representation above and convert it into its per capita representation. b. Do we have a Steady State or Balanced growth path for this model? Specifically, solve for the growth rate of per capita output, per capita capital, the price of capital, the wage rate and the rental price of capital along the balanced growth path/steady state.
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