Hint what does a stable growth rate imply about

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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 steady-state output for the Solow model with the given parameters. In steady-state, 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.

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