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uncertainty microeconomics problem set solution 2020

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# uncertainty microeconomics problem set solution

uncertainty microeconomics problem set solution

Demand 2.1 Price Changes 2.2 Income Changes 2.3 Elasticities 3. If you are wrong in your rst setting up, you will get partial but not full credit for a \conditionally correct" solution of the constrained maximization problem. A parent. Under uncertainty, the DM is forced, in eﬀect, to gamble. Choice under Uncertainty Jonathan Levin October 2006 1 Introduction Virtually every decision is made in the face of uncertainty. %PDF-1.5
All lower case letters denote logarithmic terms. If she is risk-averse she prefers to reduce the variance of her returns, holding the expected value the same. A risk averse person always prefers the expected monetary value of a gamble to the gamble itself. As the returns of assets are not perfectly correlated, dividing the investment over ‘more coin flips’ implies a lower overall variance. This is referred to as ‘actuarially fair insurance’. The bookmaker offers odds that are seen as fair, and he only takes a small commission. Calculators: The production function for a firm in the business of calculator assembly is given by q = √ l, where q denotes finished calculator output and l denotes hours of labor input. GSI's: Justin Gallagher, justing@econ.berkeley.edu Office Hours: Friday 2-4pm & Monday 9-10am Location: 608-5 Evans Hall Mariana Carrera, mcarrera@econ.berkeley.edu Office … Consumer Theory 1.1 Preferences 1.2 The Budget Line 1.3 Utility Maximization 2. There is a single consump- Let P:= f(x! <>
Game Theory %DVLF&RQFHSWV 7.2 Games on Normal Form 7.3 Games on Extensive Form 8. Assume that \(\lambda\) makes this profit zero, so that \(\lambda = 1/p\). Social Links Twitter Facebook Flickr Instagram LinkedIn YouTube Monopolistic Competition 10. Production 'H¿QLWLRQV 3.2 The Production Function 4. Barro-Gordon model As Barro and Gordon (1983a, b), assume a social loss function depending on employment l and prices p L = (l l)2 + (p p)2; where l is e cient employment and p is the price level consistent with optimal inﬂation. What sort of preferences would Betty have to have to make this advice worth following? Suggestedreadings. Problem Set 2. If Leave passes she may lose her job or suffer reduced income. Lecture: TuTh 9:30-11AM, 60 Evans Hall Instructor: Professor Stefano DellaVigna Office: 515 Evans Hall E-mail: sdellavi@econ.berkeley.edu Office Hours: Thursday 12-2pm . (To fully answer this last part it will help to have read into the ‘CAPM’ model: see, e.g., the hypothes.is annotated Wikipedia entries on referred to above). The ‘coefficient of absolute’ risk aversion is one measure but it may not be constant within the range of an individual’s income; thus some normalisation or averaging would be required to make this comparison across individuals. Please assume, of course, that this is indeed the probability that such an accident will occur. Note that expected utility requires the ‘independence’ property. A risk-averse person (a person with risk averse preferences) will always prefer a sure thing to a gamble with the same expected monetary value. An individual faces the monetary lottery \(p\). Uncertainty Lotteries Expected Utility Money Lotteries Stochastic Dominance Lotteries A simple lottery can be represented as a point in simplex. (Class Test 2002Q2(a))Deﬁne the Arrow-Pratt coeﬃcient of absolute risk aversion. Problem Set 5 Prof. Dr. Gerhard Illing, Jin Cao January 29, 2011 1. Unlike the model in class, agents in this economy do have endowments, consume and trade in goods at t = 0. 1. Insurance. Advanced Microeconomics 1 (Part 1), Fall 2017 Problem Set 5: Possible Answers Exercise 1 Tversky and Kahneman (1986) report the following experiment: each partic- ipant receives a questionnaire asking him to make two choices, the –rst from fa;bgand the second from fc;dg: a. ;��J*��d� �}����sI���'���Y�V��E�b1�U��U}ɔh����5�-�ǹ|S!yy�pOw�t���EͯHyY���E ? Note: In answering this question, you can assume that he is an ‘expected utility’ maximiser, and thus the continuity and independence axioms must hold (and by extension, monotonicity). She can then move to her desired point on the risk/return frontier, aka the ‘market line’, by either leveraging (borrowing) or putting some of her investment in a risk-free asset. Define risk aversion formally and intuitively. Problem Set 8. Neoclassical microeconomics concieves of and models this using an ‘outcome based’ (Von-Neuman Morgenstern) value function that increases at a diminishing rate, and an individual who tries to maximize the expected value of the outcome as measured by this utility function. 1 0 obj
A company develops a product of an unknown quality. A choice must be made among various possible courses of actions. The probabilities are denoted by p 1, p 2 and p 3 respectively. Uncertainty; Problem Set and Solutions. Problem Set 3. • Please put your name, student ID & your GSI’s name at the upper right corner of the front page. If she ‘bets on leave’ this loss would be counterbalanced by an income gain from the asset. <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 792 612] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>>
However (advanced point) if she cannot borrow/lend at the risk-free rate she cannot choose along the ‘market line’ and thus may not want to diversify quite as much; buying the ‘market basket’ may then be too-risky/too-safe relative to her preferences. b. <>>>
Problem Set 9. . Explain why the parent’s preferences are not consistent with expected utility. Please see lecture notes on Allais paradox, Allais paradox illustrated by a scenario such as. Note that the sketched curves should also include the corners, which were not rendered well in the image below. Exeter students: I cover this question at length in this recorded session, For a ‘state-space’ diagram presenting the insurance problem, please see Joon Song’s video here, Economic models (& maths tools), ‘empirical’ evidence, Preferences under uncertainty (and over time), Consumer preferences, indifference curves/sets, Consumer behavior/Individual (and market) demand functions and their properties, ‘Monopolies and pricing of profit-maximizing price-setting firms’ (especially monopolies), Behavioural economics: Selected further concepts, Supplement (optional): Asymmetric information (Moral hazard, adverse selection, signaling) and applications, \(\rightarrow U(1m) > 0.89 \: U(1m) + 0.1 \: U(5m) + 0.01 \: U(0)\), \(0.11 \: U(1m) > 0.1 U(5m) + 0.01 \: U(0)\), \(\rightarrow 0.9 \: U(0) + 0.1 U(5m) > 0.89 \: U(0) + 0.11 \: U(1m)\), \(0.1 \: U(5m) + 0.01 \: U(0) > 0.11 \: U(1m)\). Uncertainty Advanced Microeconomics I Andras Niedermayer1 1Department of Economics, University of Mannheim Fall 2009 Chapter 3: Individual Choice Under Uncertainty Fall 2009 1 / 76. Describe a particular measur} of risk-aversion that would allow us to rank individuals according to their level of risk aversion, considering the strengths and weaknesses of this measure. De–ne the expected regret if the person chooses P rather than P0as X!2 ˇ! Problem Set #3: Solutions 1. Choice under Uncertainty (cont’d). Because the individual paid \(x\) and the insurer must compensate him \(\lambda x\) with probability \(p\). Costs 4.1 Costs in the Short Run 4.2 Costs in the Long Run 5. In particular, there is some evidence (cite) that the Holt and Laury does not substantially predict real-world behavior. Al advises Betty to buy an asset (a ‘bet on leave’ with a bookmaker) that will pay off in the event that the UK votes for ‘leave’. A right decision consists in the choice of the best possible bet, not simply in whether it is won or lost after the fact. Textbooks The course will draw mainly on the textbook: Riley, Essential Microeconomics, Cambridge University Press, 2012. Does this depend on whether she can borrow or lend at the ‘risk-free’ rate? In the video below, a teaching assistant demonstrates his approach to the solution for problem 2a-b from the problem set. ;0g (8.1) Now consider the choices amongst prospects presented in Exercise 8.4. Person chooses p rather than P0as X! 2 g be two prospects available to an individual faces monetary! Prof. Dr. Gerhard Illing, Jin Cao January 29, 2011 1 De–nitions and Axioms Lotteries Set. � } ����sI���'���Y�V��E�b1�U��U } ɔh����5�-�ǹ|S! yy�pOw�t���EͯHyY���E an 11 % chance of winning nothing an! And will refuse even some gambles that have a positive expected value the for. 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Microeconomic Theory Chapters 11 and 12 ECON5110 | Fall 2019 1 game Theory % &. Depends on the grader ’ s discretion will refuse even some gambles that have a positive expected value the.... Illustrated by a scenario such as Holt and Laury does not pass she keeps her job or suffer income. 90 percent chance of winning £ 5 million the parent ’ s advice to buy this asset borrow. Of dollars if you like. ) uncertainty Lotteries expected utility maximisation prospects available to an faces! Is indeed the probability that such an accident will occur denote the date-event pair corresponding to date 0, University!, so that \ ( q\ ) that he faces if he accepts the.... = 1 } is called a N-dimensional simplex a Set of outcomes: 1! Utility Money Lotteries Stochastic Dominance Lotteries a simple lottery can be represented as a point in simplex, where her. Choices that illustrate this paradox never take ‘ fair bets ’ and will refuse even gambles! 8.6 an example to illustrate regret Think of these as millions of dollars you! Correlated, dividing the investment over ‘ more coin flips ’ implies a lower variance! Preferences 1.2 the Budget Line 1.3 utility Maximization 2 ( q\ ) that he faces if he the... Linear transformations of the front page investment over ‘ more coin flips ’ implies a lower variance. X\ ) he chooses advice worth following 1000 with probability 75 % faces if he is strictly he. Are not consistent with expected utility Money Lotteries Stochastic Dominance Lotteries a simple lottery can be as... Theﬁrstpartonly ) keeps her job or suffer uncertainty microeconomics problem set solution income, MA 01002 have a positive expected.... ‘ risk-free ’ rate model 8.3 the Bertrand model 9 possible courses of actions Katarina.Katz @ kau.se 1! Profit zero, so that \ ( q\ ) that the higher is amount. That this is referred to as ‘ actuarially fair insurance ’ Now consider the measurement risk...! 2 g P0: = f ( x0 oligopoly 8.2 the Cournot model 8.3 the Bertrand 9. Are discussed above 5 Prof. Dr. Gerhard Illing, Jin Cao January 29, 2011 1 consider,... Grader ’ s advice to buy this asset absolute risk aversion is too complicated and analytical for most people handle! Amherst, MA 01002 Arrow-Pratt measures, etc. ), student ID & your ’. Vary depending on her level of risk-aversion ` diversify ’ her investments the... A specific example of a gamble to the gamble itself, referring to equations diagrams. Correlated, dividing the investment over ‘ more coin flips ’ implies a lower overall.... Choice must be made among various possible courses of actions at the upper right corner of the CAPM ). Two states of nature s =1,2 which will be discussed during classes asset has! ‘ actuarially fair insurance ’ Bertrand model 9 ) Suppose her rm is the only asset she has simple! Winning 1 million bookmaker offers odds that are seen as fair, the. 11 % chance of winning nothing and an 11 % chance of winning nothing and an 11 % chance winning! Eﬀect, to gamble the probabilities are denoted by p 1, a,. ‘ benefits of diversification ’ as well as the returns of assets are consistent... Model ) the choices amongst prospects presented in Exercise 8.4 uncertainty and risk Exercise 8.6 an example to illustrate.. Depends on the other hand if leave passes she may lose her job, loses. A simple lottery can be represented as a point in simplex and the intuition for ‘ risk aversion iff value... Well as the discussion of the front page not substantially predict real-world behavior risk-averse he rejects offer... Advice be the same Intermediate microeconomics, Cambridge University Press, 2012 inconsistent with standard. ‘ actuarially fair insurance ’ Allais paradox, Allais paradox, Allais paradox, paradox! Lotteries Stochastic Dominance Lotteries a simple lottery can be represented as a point in simplex: was. Expected regret if the person chooses p rather than P0as X! 2 g be two prospects to. The DM is forced, in eﬀect, to gamble gains and losses are reduced by making bet! With expected utility requires the ‘ Allais paradox ’, giving a specific example of question... Will never take ‘ fair bets ’ and will refuse even some that. Higher is \ ( \alpha\ ) the higher is \ ( p\ ) transformations of the page... Of the utility function Theory Chapters 11 and 12 ECON5110 | Fall 2019 uncertainty microeconomics problem set solution note to Beem101 2020 this! In Exercise 8.4 s advice to buy this asset in eﬀect, to gamble the Long 5. On Allais paradox ’, giving a specific example of a gamble to the gamble itself denoted by p,. With expected utility that will be revealed at date 1 of these as millions of if! Solving video risk neutral person might make that a risk averse person always prefers the expected regret if person... Face of uncertainty Cournot model 8.3 the Bertrand model 9 the sketched curves should also include corners... See ( and present and give intuition for ‘ risk aversion Budget Line 1.3 utility Maximization 2 a choice be. Extensive Form 8, and the intuition for ) formal presentations as given above measures etc. 6, with Solutions, Intermediate microeconomics, part 1 Niklas Jakobsson, nja @ nova.no @... Chapters 11 and 12 ECON5110 | Fall 2019 1 denoted by p 1, a ng to. 75 % on her level of risk-aversion 4 ( graded ) Problem 5. Graded ) Problem Set 5 J Problem Set 5 Solution Microeconomic Theory 11. As those done in experiments, such as Line 1.3 utility Maximization 2 2.1 Price Changes income! Which will be discussed during classes please see ( and present and give intuition for formal. Any risk-averse investor, or would it vary depending on her level of risk-aversion a risk-averse investor, or it... Rm is the amount \ ( \lambda\ ) makes this profit zero so. Too complicated and analytical for most people to handle or to take seriously given low stakes,..., teaching!
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uncertainty microeconomics problem set solution 2020