Consider an economy in which there are two dates, t = 0 and t = 1,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider an economy in which there are two dates, t = 0 and t = 1, and two possible states i = 1 and i = 2, at t = 1, which occur with equal probability,so that 1 = 2 = 1/2. Suppose, as well, that there are two types of investors, j = 1 and j = 2, both of whom have logarithmic Bernoulli utility functions, so that in particular the representative investor of type j has expected utility In c + BE[In č;], (1) where the discount factor = 0.9, c denotes this investors consumption at t = 0, and c, is the investor's consumption at t = 1. In state i = 1, c, = c) and in state i = 2, č, = c². Suppose that the aggregate endowment is wo = 30 at t = 0, w₁ i = 1 at t = 1, and w₂= 60 in state i = 2 at t = 1. = 30 in state A social planner in the economy maximizes a weighted sum of investors' ex- pected utility: (In c + BE[In či]) + (1 - 0) (In c₂ + BE[In č₂]). (2) (a) Write down the Lagrangian for the social planners problem: choose c and c to maximize the weighted sum of utilities subject to the resource constraints. (b) Write down the first-order conditions for the optimal choices of c and c (c) Suppose that the social planner attaches a weight of = 2/3 to the type j = 1 investors expected utility that is twice as large as the weight 1-0 = 1/3 given to the type j = 2 investors expected utility. Under this assumption, what are the numerical values of the optimal choices of cand c. Consider an economy in which there are two dates, t = 0 and t = 1, and two possible states i = 1 and i = 2, at t = 1, which occur with equal probability,so that 1 = 2 = 1/2. Suppose, as well, that there are two types of investors, j = 1 and j = 2, both of whom have logarithmic Bernoulli utility functions, so that in particular the representative investor of type j has expected utility In c + BE[In č;], (1) where the discount factor = 0.9, c denotes this investors consumption at t = 0, and c, is the investor's consumption at t = 1. In state i = 1, c, = c) and in state i = 2, č, = c². Suppose that the aggregate endowment is wo = 30 at t = 0, w₁ i = 1 at t = 1, and w₂= 60 in state i = 2 at t = 1. = 30 in state A social planner in the economy maximizes a weighted sum of investors' ex- pected utility: (In c + BE[In či]) + (1 - 0) (In c₂ + BE[In č₂]). (2) (a) Write down the Lagrangian for the social planners problem: choose c and c to maximize the weighted sum of utilities subject to the resource constraints. (b) Write down the first-order conditions for the optimal choices of c and c (c) Suppose that the social planner attaches a weight of = 2/3 to the type j = 1 investors expected utility that is twice as large as the weight 1-0 = 1/3 given to the type j = 2 investors expected utility. Under this assumption, what are the numerical values of the optimal choices of cand c.
Expert Answer:
Answer rating: 100% (QA)
Solution In a gap option there are 21strike prices X and x x in the strike Price a... View the full answer
Related Book For
Intermediate Accounting
ISBN: 978-1118742976
16th edition
Authors: Donald E. Kieso, Jerry J. Weygandt, Terry D. Warfield
Posted Date:
Students also viewed these finance questions
-
On July 1, 2018, Tony and Suzie organize their new company as a corporation, Great Adventures Inc. The following transactions occur from August 1 through December 31. Also, the balances are provided...
-
On the 1st of April, your company has sold some product to a customer on terms 3/10 net 30, Dec 10. This means that the customer will get 3 percent discount for paying within 10th of December,...
-
Tran Company issued $900,000, 10-year, 6 percent bonds on July 1, 2017. Interest is payable semiannually on June 30 and December 31. Determine the issuance price of the bonds assuming a market yield...
-
Determine the number of valence electrons for each of thefollowing four elements. Part A Ga _______ Express your answer as an integer. Part B Pb ________ Express your answer as an integer. Part C Cl...
-
The average grass maintenance engineer mows 1.4 acres of grass per day in Barron, Montana. Because labor costs are increasing, the city decides to try a new brand of mower. Ten randomly selected...
-
(a) Could 25 g of argon gas in a vessel of volume 1.5 dm3 exert a pressure of 2.0 bar at 30C if it behaved as a perfect gas? If not, what pressure would it exert? (b) What pressure would it exert if...
-
Explain Maslow's hierarchy of needs. Why is it important?
-
Green Tee produces 100 percent cotton t-shirts, with the following standard direct material and labor quantities and costs: Direct material ......... 2.0 yards à $3.00 Direct labor ............
-
What does it mean about Treasury stock at cost and noncontrolling interest in the statement of balance sheet? Will Treasury stock and non controlling interest be included in the calculation of ROE?...
-
Refer to Figure 11.45. A square footing, 2 x 2 m in size, supports a column load of 300 kN. The soil characteristics are given in the figure. Field monitoring indicated that the foundation settlement...
-
The peak value of an alternating voltage is 100 V. What is the average of the voltage measured over one complete cycle when the frequency of the source is 50 Hz?
-
The Power of Vision: Dreaming of Peace View Pray the Devil Back to Hell (Information about documentary available at http://www.praythedevilbacktohell.com/). This is the story of how Liberian women...
-
Table 9.7 illustrates the hypothetical demand and supply schedules of labor in the United States. Assume that labor and capital are the only two factors of production. On graph paper, plot these...
-
The Beauty of Data Visualization18:17 minutes https://www.bing.com/videos/search? q=the+beauty+of+data+visualization&docid=608019685193287796&mid=FA748A7...
-
Would the Lorenz curve for the world be more or less bowed out compared to the Lorenz curve for the United States?
-
Should poverty be defined absolutely or relatively? Why?
-
2 Testing Okun's Law Okun's law is a statement in macroeconomics about how changes in the unemployment rate can predict changes in the GDP growth rate of a country. Broadly speaking, it states that a...
-
Global.asax is used for: a. declare application variables O b. all other answers are wrong O c. declare global variables O d. handle application events
-
As a certified public accountant, you have been contacted by Joe Davison, CEO of Sports-Pro Athletics, Inc., a manufacturer of a variety of athletic equipment. He has asked you how to account for the...
-
Angelou Corporation was organized in 2016 and began operations at the beginning of 2017. The company is involved in interior design consulting services. The following costs were incurred prior to the...
-
When does a company satisfy a performance obligation? Identify the indicators of satisfaction of a performance obligation.
-
Discuss the approach you would take to building a system for playing Scrabble or another word game of the sort. What limitations does your system have? How likely do you think it is that your system...
-
Discuss the current state of the art of game-playing computer systems in relation to the following games: chess, checkers, Go, bridge, Othello, tic-tac-toe. What advances are likely in the near...
-
What problems did the developers of Chinook face? What new techniques did they add to simple Minimax with alpha-beta pruning? Would these techniques extend well to other games?
Study smarter with the SolutionInn App