2 The CARA (Constant Absolute Risk Aversion)utility function generates easy to use lineardemands for normally distributed assets. Foragent i, the function quantifies an individual'sutility for a given level of wealth,, and risktolerance, (risk aversion coefficient is a reciprocalof risk tolerance,):Consider a one-period economy with a singlerisk asset and a risk-free rate equal to zero. Therisky 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 isnormally distributed with variance equal to 1.The risky asset is traded at price Pat thebeginning of the period (t=0).Agent i (who takes price P) as given) solves theproblem of maximizing her expected utility att=0,whereis agent is initial level of wealth.Problem 1Derive individual demand for the risky asset att=0, by writing out the first order condition (foran interior solution to) the maximizationproblem. Does the solution depend on the initiallevel of wealth? Why?

The first order condition for the maximization problem. The first order condition is:where: is the…

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?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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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