Question
In: Economics
CHOICE UNDER UNCERTAINTY III. Consider an individual with an initial wealth of $50,000. They have the...
CHOICE UNDER UNCERTAINTY
III. Consider an individual with an initial wealth of $50,000. They have the opportunity to
invest in a project where they may win $40,000 with a probability of 0.8 and may lose
$40,000 with a probability of 0.2. There are no out-of-pocket costs for investing in the
project but if they lose then that will be deducted from their initial wealth.
1. What would be the individual’s expected wealth if they participate in the investment
project?
2. If the individual’s preference towards risk are defined by the function: ? = √?, would
they invest in the project? (Hint: Calculate the expected utility of wealth if the individual
participates in the investment and compare it with the utility of their current wealth)
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
Uncertainty and initial wealth: a. Explain why it may be important to consider an individual’s initial...
Uncertainty and initial wealth: a. Explain why it may be
important to consider an individual’s initial wealth when analyzing
how that person will react to uncertainty (Hint: think about
expected utility). b. Under what circumstances will initial wealth
be irrelevant to a person’s choice when faced with uncertainty?
Consider a risk averse individual who faces uncertainty with two outcomes: good, bad. The individual has...
Consider a risk averse individual who faces uncertainty with two
outcomes: good, bad. The individual has income $360 under good and
$90 under bad outcome. The probability of good outcome is 5/9 (so
the probability of bad outcome is 1 − 5/9 = 4/9). The individual
can buy any non-negative x units of insurance. Every unit of
insurance has price $p and it pays $1 in the event of bad
outcome.
(a) Suppose the unit price of insurance is p...
Consider a risk averse individual who faces uncertainty with two outcomes: good, bad. The individual has...
Consider a risk averse individual who faces uncertainty with two
outcomes: good, bad. The individual has income $360 under good and
$90 under bad outcome. The probability of good outcome is 5/9 (so
the probability of bad outcome is 1 − 5/9 = 4/9). The individual
can buy any non-negative x units of insurance. Every unit
of insurance has price $p and it pays $1 in the event of
bad outcome.
(a) Suppose the unit price of insurance is p...
You have a choice between a Lexus ($50,000) and a Toyota ($25,000). How much will that...
You have a choice between a Lexus ($50,000) and a Toyota
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How much will that Lexus cost you in retirement funds over the
Toyota, if you retire in 40 years earning 8%?
A consumer with a utility function U = W 1 / 2 (square root of W , wealth) has an initial wealth of $50,000, the cost of illness is $25,000, with the probability of illness p = 0.25
A consumer with a utility function U = W 1 / 2 (square root of W
, wealth) has an initial wealth of $50,000, the cost of illness is
$25,000, with the probability of illness p = 0.25. a. Calculate an
actuarially fair health insurance premium for this consumer. b.
Illustrate the consumer's utility and expected utility on a graph.
Indicate pure premium, different wealth amounts, etc. c. Can you
tell how much extra this consumer will be willing to pay for health...
Consider an investor with expected utility function who invests her initial wealth between a risky asset...
Consider an investor with expected utility function who invests
her initial wealth between a risky asset with state-dependent rate
of return r and a risk-free asset with rate of return r0. The
investor is strictly risk averse. Suppose that E(r) < r0, that
is, negative risk premium. Show - using either a diagram or
calculus - that the optimal investment in the risky asset is to
short sell the asset, that is, hold a portfolio with negative
fraction of wealth...
Consider an investor with expected utility function who invests her initial wealth between a risky asset...
Consider an investor with expected utility function who invests
her initial wealth between a risky asset with state-dependent rate
of return r and a risk-free asset with rate of return r0. The
investor is strictly risk averse. Suppose that E(r) < r0, that
is, negative risk premium. Show - using either a diagram or
calculus - that the optimal investment in the risky asset is to
short sell the asset, that is, hold a portfolio with negative
fraction of wealth...
An individual who wishes to participate in crowdfunding a company must Multiple Choice have at least...
An individual who wishes to participate in crowdfunding a
company must
Multiple Choice
have at least 10 years of investment experience and a net worth
of $500,000 or more.
have a net worth of at least $1 million and net income of
$200,000 or more in 2 of the last 3 years.
be an SEC registered investor and have annual income of $250,000
or more.
have a net worth of at least $500,000, annual net income of
$200,000 or more...
You have a choice between taking two jobs. The first job pays $50,000 annually. The second...
You have a choice between taking two jobs. The first job
pays $50,000 annually. The second job has a base pay of $40,000
with a $30% chance that you will receive an annual bonus of
$25,000. You decide to take the $40,000 job. On the bases of this
decision, can we tell if you are risk averse or risk taker. Explain
your response.
Consider an individual making choices over two goods, x and y with initial prices px= 2...
Consider an individual making choices over two goods, x and y
with initial prices px= 2 and py= 1, with income I= 100: (a) If an
individual has the utility function u(x;y) = 3x+y. what would the
total, income and substitution effects of a price of x increase to
5? Show your work (b) If an individual has the utility function
u(x;y) =x^2+y^2; what would the total, income and substitution
effects of a price of x decrease to 0:50? Show...
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