Problem 1 Derive individual demand for the risky asset at t=0,, by writing out the first order condition (for an interior solution to) the maximization problem. Does the solution depend on the initial level of wealth? Why?
Problem 1 Derive individual demand for the risky asset at t=0,, by writing out the first order condition (for an interior solution to) the maximization problem. Does the solution depend on the initial level of wealth? Why?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:The CARA (Constant Absolute Risk Aversion)
utility function generates easy to use linear
demands for normally distributed assets. For
agent i, the function quantifies an individual's
utility for a given level of wealth,, and risk
tolerance, (risk aversion coefficient is a reciprocal
of risk tolerance,):
Consider a one-period economy with a single
risk asset and a risk-free rate equal to zero. The
risky asset, present in positive fixed supply Q
(with Q>0), is a claim on a single cash flow, Z,
that is realized at the end of the period (t=1). Z is
normally distributed with variance equal to 1.
The risky asset is traded at price Pat the
beginning of the period (t=0).
Agent i (who takes price P) as given) solves the
problem of maximizing her expected utility at
t=0,
whereis agent is initial level of wealth.
Problem 1
Derive individual demand for the risky asset at
t=0, by writing out the first order condition (for
an interior solution to) the maximization
problem. Does the solution depend on the initial
level of wealth? Why?
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