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Monetary3340 - Jan21

# Monetary3340 - Jan21 - 21January2010 Decentralized...

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21 January 2010 Decentralized Equilibrium with money To solve for it: for a given return to money, what would the individual choose? Find what the equilibrium rate of return is going to be. Problem of Individual (takes price as given) Max. lifetime utility = U(C 1t, C 2t+1 ) s.t lifetime budget constraint Budget Constraint: C1t + vtmt ≤ y – 1 st period C2t+1 ≤ vt+1*mt – 2 nd period you cannot consume more than the money you acquired in the 1sst period, right hand side: the real value of your money. C1t + vt/vt+1 *c2t+1 ≤ y – life time budget constraint, tells you the combination of 1 st and 2 nd combinations that you can afford given how much endowment I have. Left: present discounted value of your consumption expenditures of your entire life. Y is endowment of time t. all expressed in present value. Figure 1: What do you need to get monetary equilibrium: Need to find Vt+1/Vt Key: the valie of money depends a lot on our beliefs on what the value of money will be in the next period: vt ------------ vt+1

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Monetary3340 - Jan21 - 21January2010 Decentralized...

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