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Unformatted text preview: nd the Solow model? (Hint: What does a
stable growth rate imply about whether the economy is on a transition path or in
steady state?)
If each state had a relatively stable growth rate, it implies that each state was in
“steady state”. Thus, we need to solve for the steadystate output for the Solow
model with the given parameters. In steadystate, we have two equations and two
unknowns, so we can solve analytically. The two equations correspond to the
production function and to capital accumulation (with the resource allocation
equation substituted in to express capital accumulation in terms of output instead of
investment): 1 Production function: Yt = K t1/2
Capital Accumulation: !K t+1 " K t+1 # K t = I t # 0.1K t = 0.2Yt # 0.1K t
Note that in steady state, values at time t equal values at time t+1. Or put another
way, we can remove the timing subscripts and put asterisks to denote steady state
values:
S.S. Production function: Y ! = ( K ! )1/2
K ! " K ! = 0.2Y ! " 0.1K !
S.S. Capital Accumulation:
# 0.2Y ! = 0.1K !
To solve the two equations with two unknowns, substitute the first equation into the
second one:
0.2( K ! )1/2 = 0.1K ! S.S. equilibrium: " ( K ! )1/2 = 2
" K! = 4
"Y! = 2 Therefore, we would predict output to be equal to 2 in each state prior to the floods.
(d) Now suppose that the floods lower the Queensland capital stock by 75%. Plot the
Solow diagram for Queensland. (Hint: it should look like Figure 5.2, but with
actual numbers of the y and x axes.)
K*=4, Y*=2 K0=1, Y0=1 2 (e) Solve for the level of output in Queensland in each of the first ten years following
the flood. (Hint: make a table somewhat like Table 5.1 and plot the level of output
over time, much like Figure 5.12.) What are the implied growth rates for output in
each of the first ten years? How do these compare to the implied growth rates for
the other states, which are assumed to be in steady state? Should Treasury worry
about lower growth in Queensland? What is the economic intuition for why
growth rates are predicted to be diff...
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This document was uploaded on 03/15/2014.
 Spring '11
 Macroeconomics

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