4. A decision-maker faces a lottery that gives her a final wealth of 1 dollar with probability 1/4, 3 dollars with probability 1/2, and 8 dollars with probability 1/4. (a) Suppose this decision-maker is an expected utility maximizer with von Neumann-Morgenstern utility u₁(x) = √2+1, where z is her final wealth. Find the risk premium associated with this lottery. Solution: The expected value of the lottery is 1/4+3/2+8/4 = 15/4. The certainty equivalent, CE, solves √CE+1= √²+V+V_7+√² Hence CE = (35+14√/2)/16 and the risk premium is (25-14√2)/16. (b) Now suppose that a second decision-maker who maximizes expected utility with von Neumann-Morgenstern utility u₂(x)=√ faces the same lottery. Without calculating this decision-maker's risk premium, determine whether it is higher than, lower than, or the same as that for the decision-maker in part (a). Solution: The first decision-maker has Arrow-Pratt measure 7₁(z) = and the second has Arrow-Pratt measure r₂(x) = (2) 1 u₁(x) 2(x+1) 22 (3 Since r₂(x) > r₁(x) for every x > 0, the second decision-maker is more risk averse than

4. A decision-maker faces a lottery that gives her a final wealth of 1 dollar with probability 1/4, 3 dollars with probability 1/2, and 8 dollars with probability 1/4. (a) Suppose this decision-maker is an expected utility maximizer with von Neumann-Morgenstern utility u₁(x) = √2+1, where z is her final wealth. Find the risk premium associated with this lottery. Solution: The expected value of the lottery is 1/4+3/2+8/4 = 15/4. The certainty equivalent, CE, solves √CE+1= √²+V+V_7+√² Hence CE = (35+14√/2)/16 and the risk premium is (25-14√2)/16. (b) Now suppose that a second decision-maker who maximizes expected utility with von Neumann-Morgenstern utility u₂(x)=√ faces the same lottery. Without calculating this decision-maker's risk premium, determine whether it is higher than, lower than, or the same as that for the decision-maker in part (a). Solution: The first decision-maker has Arrow-Pratt measure 7₁(z) = and the second has Arrow-Pratt measure r₂(x) = (2) 1 u₁(x) 2(x+1) 22 (3 Since r₂(x) > r₁(x) for every x > 0, the second decision-maker is more risk averse than

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

In your own words, explain what is meant by the "invisible hand" in economics. Use a specific example where this concept can be seen in the real world
There are three thing that economist study about, what are they? Explain!
6. Write four differences between Microeconomics and Macroeconomics?
please answer asap
1. What is the need for studying econometrics? What procedures onefollows in econometrics?
. Write the definition of Macroeconomics with example?
Please do not give solution in image formate thanku One of these countries or geographic regions are the most likely to sacrifice economi output for the sake of a cleaner environment. Which one?
Economics is the science that studies human behavior as a relationship between ends and scarce means which have alternative uses. How do you apply this statement in actual economic situations in our economy?
-1h-future-act-1 - Word Hernandez, Joshua Layout References Mailings Review View Help O Tell me what you want to do -A A Aa - E-E-E, EE A T AaBbCcD. AaBbCJ AaBbC 1. AaBbC AaBbCcD AABI AaBbC x A A = 三 , 田。 Body Text1 Bullet poi. Checkboxes Numbere. Student A. Heading 1 Heading 2 Paragraph Styles Review Jason's assets and debts. Then answer the questions. JASON'S ASSETS AND DEBTS Assets Debts House: $150,000 Mortgage: $110,000 Car: $10,000 Car loan: $6,000 Checking and savings accounts: $5,000 Stocks and bonds: $3,000 Student loans: $12,000 Credit card debt: $5,000 Possessions: $4,000 3. What is Jason's net worth? 4. What would Jason's net worth be if he received a bonus at work and used all of it to completely pay off his credit card debt? 5. What can happen if you pay your mortgage, car loan, student loan, or credit card bill late? 6. Describe a situation in which it would be wise to use a credit card to pay for something. Home D00 F11 F12 F9 F10
Explain what is meant by opportunity cost of choice
How the time affects supply, perishable Goods and how it affects the reproducible goods?