At date t = 1 the economy will be either in state 1 or in state...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
At date t = 1 the economy will be either in state 1 or in state 2. Two investors A and B only care about one good - wealth at date t = 1. Both investors agree that state 2 is twice as likely as state 1. In state 1 A has 9 units of wealth (his endowment of wealth is 9) and B has 18 units of wealth. In state 2 A has 12 units of wealth but B has 24 units of wealth. There is no wealth at date 0. Both investors can access to the financial markets with the payoff matrix states assets 1 3 34 The prices of the assets are not specified at the moment, but assume that they are such that there is no arbitrage. Investor A is risk-averse, and values wealth y according to vª (y) = √, investor B is risk-neutral and values wealthy according to v³(y) = y+ 1. a. (1 mark) Explain what aggregate risk is. Is there aggregate risk in this econ- omy? b. (2 marks) Suppose investor A's (B's) wealth is w (for sure). Derive the risk tolerances for investors A and B as functions of w. c. (3 marks) Denote with y and y2 the state levels of wealth that investor A can reach at date 1. Given her wealth endowment at t= 0 and the fact she trades at the market as above what combinations of wealth in (y₁, y2) space are feasible for A? Your answer should be an equation that connects y to y or vice versa. Hint: it should involve Arrow security prices (0₁, 02). (1 mark) Derive a similar relationship for the feasible combination of state wealth levels (yi, y2) for investor B? d. (3 marks) State the Mutuality Principle. According to that Principle how should be wealth allocated in this economy accross the investors and accross the states? e. (3 marks) Set a₁ = 1. By Mutuality Principle what price a₂ should will result in equilibrium? Your answer, should, of course, respect the budget constraints and the preferences of the investors. Hint: you should already know the equilibrium allocation of wealth from d. You have to find the price a₂ such that that allocation is the result of the investors' optimization. You can choose which investor to deal with, since they face the same prices (a, a2). f. Derive the equilibrium prices for the original assets (91-92) consistent with your answer in e. At date t = 1 the economy will be either in state 1 or in state 2. Two investors A and B only care about one good - wealth at date t = 1. Both investors agree that state 2 is twice as likely as state 1. In state 1 A has 9 units of wealth (his endowment of wealth is 9) and B has 18 units of wealth. In state 2 A has 12 units of wealth but B has 24 units of wealth. There is no wealth at date 0. Both investors can access to the financial markets with the payoff matrix states assets 1 3 34 The prices of the assets are not specified at the moment, but assume that they are such that there is no arbitrage. Investor A is risk-averse, and values wealth y according to vª (y) = √, investor B is risk-neutral and values wealthy according to v³(y) = y+ 1. a. (1 mark) Explain what aggregate risk is. Is there aggregate risk in this econ- omy? b. (2 marks) Suppose investor A's (B's) wealth is w (for sure). Derive the risk tolerances for investors A and B as functions of w. c. (3 marks) Denote with y and y2 the state levels of wealth that investor A can reach at date 1. Given her wealth endowment at t= 0 and the fact she trades at the market as above what combinations of wealth in (y₁, y2) space are feasible for A? Your answer should be an equation that connects y to y or vice versa. Hint: it should involve Arrow security prices (0₁, 02). (1 mark) Derive a similar relationship for the feasible combination of state wealth levels (yi, y2) for investor B? d. (3 marks) State the Mutuality Principle. According to that Principle how should be wealth allocated in this economy accross the investors and accross the states? e. (3 marks) Set a₁ = 1. By Mutuality Principle what price a₂ should will result in equilibrium? Your answer, should, of course, respect the budget constraints and the preferences of the investors. Hint: you should already know the equilibrium allocation of wealth from d. You have to find the price a₂ such that that allocation is the result of the investors' optimization. You can choose which investor to deal with, since they face the same prices (a, a2). f. Derive the equilibrium prices for the original assets (91-92) consistent with your answer in e.
Expert Answer:
Answer rating: 100% (QA)
a Aggregate risk Aggregate risk is the risk that affects the entire economy rather than individual sectors or firms It is often caused by events such ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these economics questions
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
-
Bird-Bath, Inc., experienced four situations for its supplies. Compute the amounts that have been left blank for each situation. For situations 1 and 2, journalize the needed transaction. Consider...
-
The IRS wants to develop a method for detecting whether or not individuals have overstated their deductions for charitable contributions on their tax returns. To assist in this effort, the IRS...
-
Your neighbors are thinking of selling their two-bedroom home in the suburbs and moving to a two-bedroom condominium. Help them make this decision.
-
Information on four investment proposals is given below: Required: 1. Compute the project profitability index for each investment proposal. 2. Rank the proposals in terms of preference. Investment...
-
Smoky Mountain Corporation makes two types of hiking boots-the Xtreme and the Pathfinder. Data concerning these two product lines appear below: Selling price per unit Direct materials per unit Direct...
-
During 2020, the following transactions were recorded by the Port Hudson Community Hospital, a private sector not-for-profit institution. 1. Gross charges for patient services, all charged to Patient...
-
If log3 32 = a log3 2, then log (a + 3) =? If log3 a = -2 and 2log, 8 = 6, then b a =?
-
Food rots about 30 times more rapidly at 25 C than when it isstored at 4 C. Determine the overall activation energy for theprocesses responsible for its decomposition.
-
What kinds of diversity of peoples and cultures that came together in colonial America and the "hybridities" produced? What are one of the three major colonizing powers used to this fuse of peoples...
-
What Native American Tribes were present in Colonial America (13 original Colonies) during the Colonial America time period? How were they organized? Did they have governments?
-
Find output int[][] array1 = {{1,2,3,4), {5,6,7,8}, {9,10,11,12}, {13,14,15,16}}; for (int i = 0; i
-
At the Gilroy Garlic Festival in California, you can sample avariety of food dishes prepared from fresh garlic, including garlicice cream and garlic cheesecake. The characteristic flavor andaroma of...
-
In this topic, you will have a conversation with someone in your life and discuss the result of your collaboration to explore their thoughts. Have a conversation with someone in your life this week...
-
President Lee Coone has asked you to continue planning for an integrated corporate NDAS network. Ultimately, this network will link all the offices with the Tampa head office and become the...
-
Sally and Charles Heck received the following dividends and interest during 2012: Assuming the Hecks file a joint tax return, complete Schedule B of Form 1040 (on page 2-33) for them for the 2012 tax...
-
Dr. Ivan I. Incisor and his wife Irene are married and file a joint return for 2012. Ivan's Social Security number is 477-34-4321 and he is 48 years old. Irene I. Incisor's Social Security number is...
-
For each of the following situations, indicate whether the taxpayer(s) is (are) required to file a tax return for 2012. Explain your answer. a. Helen is a single taxpayer with interest income in 2012...
-
\((7 \sqrt{33}) \times(8 \sqrt{66})\) Perform the arithmetic operations without a calculator, if possible. If it is not possible, state why.
-
\((4 \sqrt{15}) \times(3 \sqrt{10})\) Perform the arithmetic operations without a calculator, if possible. If it is not possible, state why.
-
\((70 \sqrt{30}) \div(14 \sqrt{6})\) Perform the arithmetic operations without a calculator, if possible. If it is not possible, state why.
Study smarter with the SolutionInn App