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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 TASSO
 Economics, Macroeconomics, Inflation, Utility, Quantity Theory of Money

Click to edit the document details