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Teoria y Politica Monetaria, Spring 2000; Instructor: Marco Del Negro
Problem set 1
1) Let us assume that st-1 and st represent the amount of stocks
held by the household at the end of periods t and t+1 respectively;
dt and qt are the amount of dividends paid by one unit of stocks
in period t and the price of the stock in period t respectively,
and ct is consumption at time t. All variables are expressed in units
of the consumption good. Interpret the intertemporal
budget constraint by explaining the meaning of each of the terms that
appear in it, and why the left hand side has to be less or equal than
the right hand side:
2) The expression:
represents the first order condition of the asset pricing model
seen in class (all variables are defined as in question (1), and u'(ct)
represents the marginal utility of consumption at time t). Interpret
such condition from an economic point of view.
3) In the infinite horizon asset pricing model discussed in class (Class 1) assume that
households are not allowed to hold negative amounts of stocks. In other words, the
problem of the household becomes:
given s0=1, subject to the budget constraint (which holds in each period t):
and subject to the extra constraint
,
all t
a) Write the first order condition (FOC) with respect to st and discuss its
meaning from the economic point of view
b) Show that the pricing formula for the agent is:
and discuss the meaning of the above formula.
c) argue that the equilibrium of this model and of the model studied in class is the same.
(remember that in equilibrium it must be that in each period ct=dt and that st=1)
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Marco Del Negro
2000-01-11