Suppose Peter Brown’s utility for total wealth (A) can be represented by the utility function U(A)=ln(A)....
Suppose Peter Brown’s utility for total wealth (A) can be represented by the utility function U(A)=ln(A). He currently has $1,000 in cash. A business deal of interest to him yields a reward of $100 with probability 0.5 and $0 with probability 0.5.
If he owns this business deal in addition to the $1,000 and considers selling the deal, what is the smallest amount for which he would sell it (i.e., the amount of the deal such that he is indifferent between selling and keeping the deal)? [10 marks]
Suppose he does not own the deal and considers buying this deal, what is the greatest amount he would be willing to pay for it? [8 marks]
Suppose he does not own the deal, and the price of the deal is $45. Will he buy it based on EMV? What if he bases his decision on utility? If buying, what are the certainty equivalent (CE) and his risk premium? [10 marks]
Hint: The following formulas might be used.
where are constants and is the natural logarithm function.
The roots of the quadratic equation (if any) are where are constants.
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Add Answer to:
Suppose Peter Brown’s utility for total wealth (A) can be
represented by the utility function U(A)=ln(A)....
Buying and selling prices for risky investments obviously are related to certainty equiva- lents. This problem,...
Buying and selling prices for risky investments obviously are related to certainty equiva- lents. This problem, however, shows that the prices depend on exactly what is owned in the first place! Suppose that Peter Brown's utility for total wealth (A) can be represented by the utility function U(A) In(A). He currently has $1000 in cash. A business deal of interest to him yields a reward of $100 with probability 0.5 and $0 with probability 0.5. a If he owns this...
2) (15 points) Suppose that Peter is an expected-utility maximizer who derives utility from his disposable...
2) (15 points) Suppose that Peter is an expected-utility maximizer who derives utility from his disposable income according to the function: U(I) = V1001, where I, measured in US dollars, represents his disposable income. Currently, Peter's disposable income is $90,000. There is a 1% chance that his Audi will be stolen. If this happens, his disposable income will be reduced to $10,000, since he will be spending $80,000 getting a new car. a) If Peter does not purchase auto insurance,...
An investor's utility function is ?(?) = ln ?, where w denotes net wealth. He has...
An investor's utility function is ?(?) = ln ?, where w denotes net wealth. He has $100 for investment. There are two assets, a “safe” one and a “risky” one. The safe asset yields 10% return with certainty. The risky asset yields 19% return with probability 0.5, and 2% return with probability 0.5. a.) How much money should the investor invest in each asset? 2. b.) Now suppose instead of 2% it is changed to 1%, while all other information...
Suppose a person has the utility function, U(I)=log(I), where I is income. He has income I2...
Suppose a person has the utility function, U(I)=log(I), where I is income. He has income I2 ($4,000) with the probability of p, but knows that some externally generated risk may reduce his income to I1 ($1,000) with probability of 1-p. Suppose p=0.8. 1) Is this person risk-averse? If so, why? 2) What is the expected income of this person? 3) What is the utility of expected income for this person? 4) What is the expected utility of this person? 5)...
Suppose that a decision maker’s utility as a function of her wealth, x, is given by...
Suppose that a decision maker’s utility as a function of her wealth, x, is given by U(x) = ln (2x) (where ln is the natural logarithm). The decision maker now has $10,000 and two possible decisions. For Alternative 1, she loses $1000 for certain. For Alternative 2, she gains $500 with probability 0.8 and loses $2,000 with probability 0.2. Which alternative should she choose and what is her expected utility (rounded to 2 decimals)? a.She should choose Alternative 1. Her...
ubariho Julius’ utility function is U(W)=ln(W). His current wealth is $5,000. He is now given a...
ubariho Julius’ utility function is U(W)=ln(W). His current wealth is $5,000. He is now given a chance to buy a futures contract on Nickel that gives him 75% chance of winning $5,000, and 25% chance of losing $4,000. What is his, Julius’ certainty equivalent for holding the futures contract?
Suppose the utility function of a decision maker for the amount of money x is given...
Suppose the utility function of a decision maker for the amount of money x is given by U(x) = x2. (a) This decision maker is considering the following two lotteries: A: With probability 1, he gains 3000. B: With probability 0.4, he gains TL 1000, and with probability 0.6, he gains TL 4000. Which of the two lotteries will the decision maker prefer? What is the certainty equivalent (CE) for lottery B? Based on the CE for B, is the...
2. Risk Premium a. Suppose the utility function is given by the equation ?(?) = ln(?...
2. Risk Premium a. Suppose the utility function is given by the equation ?(?) = ln(? + 1). Graph utility at the points $0, $80, $100. b. Suppose there is a lottery where you win $100 with 20% chance, $80 with 30% chance, and $0 with 50% chance. What is the expected winnings (in dollars)? What is the expected utility (in utils)? Add this point to the graph. c. What is the utility at the expected dollar winnings (i.e., what...
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the...
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. $1 invested in the risky asset returns $1.25 when the market state is "good" and returns $0.8 when the market state is "bad". The good state occurs with probability 2/3 and the bad state occurs with probability 1/3. Let x be the amount...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function:...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function: U (X, Y) = X°.270.3 Budget Constraint: I = XP, + YP, a. What is the consumer's marginal utility for X and for Y? b. Suppose the price of X is equal to 4 and the price of Y equal to 6. What is the utility maximizing proportion of X and Y in his consumption? {construct the budget constraint) c. If the total amount...
Buying and selling prices for risky investments obviously are related to certainty equiva- lents. This problem, however, shows that the prices depend on exactly what is owned in the first place! Suppose that Peter Brown's utility for total wealth (A) can be represented by the utility function U(A) In(A). He currently has $1000 in cash. A business deal of interest to him yields a reward of $100 with probability 0.5 and $0 with probability 0.5. a If he owns this...
2) (15 points) Suppose that Peter is an expected-utility maximizer who derives utility from his disposable income according to the function: U(I) = V1001, where I, measured in US dollars, represents his disposable income. Currently, Peter's disposable income is $90,000. There is a 1% chance that his Audi will be stolen. If this happens, his disposable income will be reduced to $10,000, since he will be spending $80,000 getting a new car. a) If Peter does not purchase auto insurance,...
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. $1 invested in the risky asset returns $1.25 when the market state is "good" and returns $0.8 when the market state is "bad". The good state occurs with probability 2/3 and the bad state occurs with probability 1/3. Let x be the amount...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function: U (X, Y) = X°.270.3 Budget Constraint: I = XP, + YP, a. What is the consumer's marginal utility for X and for Y? b. Suppose the price of X is equal to 4 and the price of Y equal to 6. What is the utility maximizing proportion of X and Y in his consumption? {construct the budget constraint) c. If the total amount...
Most questions answered within 3 hours.
-
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 7 minutes ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 2 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 3 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 4 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 5 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 6 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 6 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 6 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 6 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 6 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 6 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 6 hours ago