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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Solving a real-business-cycle model by finding the social optimum.34 Consider the model of Section 5.5. Assume for simplicity that n = g = A = N = 0. Let V(Kt,At), the value function, be the expected present value from the current period forward of lifetime utility of the representative individual as a function of the capital stock and technology.
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(b) Find the first-order condition for Ct. Show that it implies that Ct/Yt does not depend on Kt or At.
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(c) Find the first-order condition for t. Use this condition and the result in part (b) to show that t does not depend on Kt or At.
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(d) Substitute the production function and the results in parts (b) and (c) for the optimal Ct and t into the equation above for V(•), and show that the resulting expression has the form V(Kt,At) = β-0 + β-K ln Kt + β-A ln At.
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(e) What must βK and βA be so that β-K = βK and - A = βA?35
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(f) What are the implied values of C/Y and ? Are they the same as those found in Section 5.5 for the case of n = g = 0?
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