A risk averse person always prefers the expected monetary value of a gamble to the gamble itself. Another possibility is that the succession of choices presented by HL leads people to consider it in a way they would not naturally have done, to aim for an ‘arbitrary coherence’. 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. as well as the discussion of the CAPM model). An exchange economy has two dates t =0,1 and two states of nature s =1,2 which will be revealed at date 1. Many people choose B over A and choose D over C: This contradicts Expected Utility theory: (Note: Suggested answers provided to Beem101 students, not to be posted on the web by request of O-R. Beem101 students can consult the Class Notebook, or the direct link HERE). However, this depends what our purpose is in making this comparison across individuals – if we want to compare how risk averse they are given their current wealth, this may not be a problem. Note that expected utility requires the ‘independence’ property. Gamble A: an 89 percent chance of winning 1 million a 10 percent chance of winning £ 5 million, and a 1 pct chance of winning nothing. Please see (and present and give intuition for) formal presentations as given above. De–ne the expected regret if the person chooses P rather than P0as X!2 ˇ! Problem Set 2 Welfare and Allocation Nov 11 Reading: JR Chapter5 Reference: Varian Chapter10; General Equilibrium Nov 11 Problem Set 2: Solution Reading: Koopmans Chapter 1 Exercise 3 Production Economy Nov 18 Reading: Laffont Introduction; Time and Uncertainty Nov 18 Problem Set 3 Problem Set 3: Solution ;��J*��d� �}����sI���'���Y�V��E�b1�U��U}ɔh����5�-�ǹ|S!yy�pOw�t���EͯHyY���E ? Solow model in continuous time. What would justify the economist’s advice to buy this asset? Describingtheuncertainty. Costs 4.1 Costs in the Short Run 4.2 Costs in the Long Run 5. Note: Here you are being asked to depict the lottery he faces in net including the lottery $$p$$, which may have any number of prizes, as well as the additional ‘coin flip’ lottery mentioned above. 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. Two essential characteristics: 1. Game Theory %DVLF&RQFHSWV 7.2 Games on Normal Form 7.3 Games on Extensive Form 8. They will never take ‘fair bets’ and will refuse even some gambles that have a positive expected value. Choice under Uncertainty Choice under Uncertainty (cont’d). • Please put your name, student ID & your GSI’s name at the upper right corner of the front page. Choice under Uncertainty Jonathan Levin October 2006 1 Introduction Virtually every decision is made in the face of uncertainty. Microeconomics - 1. 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 … As the returns of assets are not perfectly correlated, dividing the investment over ‘more coin flips’ implies a lower overall variance. Production 'H¿QLWLRQV 3.2 The Production Function 4. Other measures include specific empirical elicitations/comparisons as those done in experiments, such as Holt and Laury discussed here. Insurance. Uncertainty Advanced Microeconomics I Andras Niedermayer1 1Department of Economics, University of Mannheim Fall 2009 Chapter 3: Individual Choice Under Uncertainty Fall 2009 1 / 76. Microeconomic Theory I: Choice Under Uncertainty Parikshit Ghosh Delhi School of Economics September 8, 2014 Parikshit Ghosh Delhi School of Economics Choice Under Uncertainty. In May 2016, an economist (Al) advises Betty that if the UK votes ‘leave’ in the June referendum, this may reduce trade with France. 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). Gamble C: an 89 percent chance of winning nothing and an 11% chance of winning 1 million. Problem Set 5 Prof. Dr. Gerhard Illing, Jin Cao January 29, 2011 1. maxfx0 x! He is indifferent between giving the gift to either child but prefers to toss a fair coin to determine which child obtains the gift over giving it to either of the children. Under uncertainty, the DM is forced, in eﬀect, to gamble. The probabilities are denoted by p 1, p 2 and p 3 respectively. Because the individual paid $$x$$ and the insurer must compensate him $$\lambda x$$ with probability $$p$$. J Problem Set 2 - Solution. Gamble D: a 90 percent chance of winning nothing and a 10 percent chance of winning £ 5 million. Textbooks The course will draw mainly on the textbook: Riley, Essential Microeconomics, Cambridge University Press, 2012. MICROECONOMICS I: CHOICE UNDER UNCERTAINTY MARCINPĘSKI Please let me know about any typos, mistakes, unclear or ambiguous statements thatyouﬁnd. %PDF-1.5 In ation dynamics under optimal monetary policy. 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. If she ‘bets on leave’ this loss would be counterbalanced by an income gain from the asset. Microeconomics CHAPTER 8. Assume that $$\lambda$$ makes this profit zero, so that $$\lambda = 1/p$$. She owns a bak-ery that will be worth 69 or 0 dollars next year with equal probability. Describe the lottery $$q$$ that he faces if he accepts the offer. Problem Set 6: Solutions ECON 301: Intermediate Microeconomics Prof. Marek Weretka Problem 1 (Insurance) (a) Ben’s a ordable bundle if there is no insurance market is his endowment: All lower case letters denote logarithmic terms. The greater the curvature (relative to the slope) of the VnM utility function, the more risk averse, at least by the popular ‘Arrow-Pratt’ measures. Advanced Microeconomics ProblemSet2: ChoiceunderRisk andUncertainty Exercise 2.1 Consider the following pairs of lotteries over weekend trip destinations: Lotterie I: Berlin with probability 1, vs. Lotterie II: Berlin, Bayreuth, and Munich with probability 1/3 each. (Continuation of Problem 2 from Problem Set 5.) Problem Set 2. A right decision consists in the choice of the best possible bet, not simply in whether it is won or lost after the fact. An individual has wealth $$w$$ and is afraid that an accident will occur with probability $$p$$ that will cause him a loss of $$D$$. Does this depend on whether she can borrow or lend at the ‘risk-free’ rate? Equivalently, a risk averse person will always reject a fair gamble. Let P:= f(x! ;ˇ !) Solutions to Problem Set 3. Solutions to Problem Set 4. Problem Set 7. Suggestedreadings. A lottery between a pro–t of $1000 with probability 25% and 0 with probability 75%. Would the advice be the same for any risk-averse investor, or would it vary depending on her level of risk-aversion? stream More formal definitions, depictions, and intuition is given in this web book above. 2. Consumer Theory 1.1 Preferences 1.2 The Budget Line 1.3 Utility Maximization 2. Please see lecture notes on Allais paradox, Allais paradox illustrated by a scenario such as. 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. b. A choice must be made among various possible courses of actions. 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. 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. 2 0 obj This allows her to reduce the variance of her returns for a given expected return, or increase the expected return for a given variance. Risk aversion: The extent to which uncertainty of an outcome (holding the expected material or monetary value constant) implies an individual values it less. Microeconomics Exercises 6 Suggested Solutions 1. Use s = 0 to denote the date-event pair corresponding to date 0. One possibility is that it is too complicated and analytical for most people to handle or to take seriously given low stakes. Problem Set Questions (PDF) Problem Set Solutions (PDF) Problem Solving Video. 1. The level set for Alex is also depicted. I A gamble/lottery is a probability distribution over outcomes: g = (p 1 a 1,p 2 a 2,...,p n a n). (a) Suppose her rm is the only asset she has. If utility is differentiable we can define risk aversion in terms of a diminishing marginal utility of income (or in general, concavity). 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. An economist would advise a risk-averse investor to ‘diversify’ her investments, no matter how risk averse she is … as long as she is at least a little bit risk-averse, she will prefer to minimise the variance of the return (for a given expected return). What sort of preferences would Betty have to have to make this advice worth following? (Think of these as millions of dollars if you like.) ‘Coefficient of relative risk aversion’ is another measure; it also may not be constant throughout the range of income (but that is at least more plausible). The individual has to choose an amount, $$x$$, he will pay for insurance that will pay him $$\lambda x$$ (for some given $$\lambda$$) if the accident occurs. A company develops a product of an unknown quality. Ana’s utility function is U = p w, where wis her wealth. Deﬁnition: The set ∆ = {p ∈ R+N: P pi = 1} is called a N-dimensional simplex. Amherst College 220 South Pleasant Street Amherst, MA 01002. 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 . 3 0 obj Explain why an economist would advise a risk-averse investor to diversify’ her investments. 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’. Explain why the parent’s preferences are not consistent with expected utility. Problem Set 2 Solutions Intermediate Microeconomics Mark Dean February 4, 2016 Question 1 (Indi erence Curves) 1.Assume that the consumer only gains utility from plants in plant pots. Demand 2.1 Price Changes 2.2 Income Changes 2.3 Elasticities 3. On the other hand if leave does not pass she keeps her job, but loses the bet. Problem Set 11: Solutions ECON 301: Intermediate Microeconomics Prof. Marek Weretka Problem 1 (Monopoly and the Labor Market) (a) We nd the optimal demand for labor for a monopoly rm (in the goods market as poposed to the labor market) through the pro t maximization condition. (See discussion under ‘benefits of diversification’ Oligopoly 8.2 The Cournot Model 8.3 The Bertrand Model 9. Unlike the model in class, agents in this economy do have endowments, consume and trade in goods at t = 0. Please assume, of course, that this is indeed the probability that such an accident will occur. ]���1/��. 2. %���� Uncertainty Lotteries Expected Utility Money Lotteries Stochastic Dominance Lotteries A simple lottery can be represented as a point in simplex. endobj The parent has in hand only one gift. <> ECO 317 – Economics of Uncertainty – Fall Term 2009 Problem Set 2 – Due October 15 Question 1: (30 points) Consider a situation of uncertainty with three possible outcomes, namely money rewards of amounts 1, 2 and 3. Pro t in terms of the labor choice is ˇ= TR TC= TR(y(L)) w LL: Note: I can probably improve the notation in the above video. The bookmaker offers odds that are seen as fair, and he only takes a small commission. He is made the following offer. Solutions to Problem Set 2. UNCERTAINTY AND RISK Exercise 8.6 An example to illustrate regret. <>>> On the other hand, if we want to make a comparison (e.g., between men and women) to say something about genetic or culturl predisposition to risk-seeking, then the issue of ‘differing baseline incomes’ may be important. Problem Set 1. 1 0 obj Two assignments per term will be marked. Problem Set 5 Solution Microeconomic Theory Chapters 11 and 12 ECON5110 | Fall 2019 1. She can optimise along this margin by ‘optimally diversifying’, buying assets in proportion to their representation (relative value) in the market. Problem Set 9. 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. will be a crucial learning tool. An individual faces the monetary lottery $$p$$. Breakdown of points: 10 for setting up the objective function correctly, 10 for solving the optimization problem correctly. Explain why or why not, referring to equations and diagrams as needed. write a lottery as a set {xi: pi}N i=1 and denote by L the set of all simple lotteries over the set of outcomes C.) 2 / 31. 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, $$\rightarrow U(1m) > 0.89 \: U(1m) + 0.1 \: U(5m) + 0.01 \: U(0)$$, $$0.11 \: U(1m) > 0.1 U(5m) + 0.01 \: U(0)$$, $$\rightarrow 0.9 \: U(0) + 0.1 U(5m) > 0.89 \: U(0) + 0.11 \: U(1m)$$, $$0.1 \: U(5m) + 0.01 \: U(0) > 0.11 \: U(1m)$$. In the video below, a teaching assistant demonstrates his approach to the solution for problem 2a-b from the problem set. 1.2. For the upcoming midterm, I would probably add an additional challenging element to such a question, e.g., asking you to formally specify her preferences in some way (concavity of value function, etc.) If she is substantially risk-averse, she is willing to sacrifice at least some amount of expected monetary value (i.e., the commission) to reduce the variance. If she is risk-averse she prefers to reduce the variance of her returns, holding the expected value the same. While we often rely on models of certain information as you’ve seen in the class so far, many economic problems require that we tackle uncertainty head on. Thus both the gains and losses are reduced by making this bet; i.e., the variance is reduced. Show that it is invariant to positive linear transformations of the utility function. x���]o�6���?�RZ�$J��^t�Z�*؅"+��X�ly@����%��|�7�: sӇ���sHy�j߷�Uݳ\����~h��v��}�c����Y~�6mW���[~=���W?7պ���{�� [~��������".x�b���W�)��?/Ҳ���j�q[m���ݱ߮�^��o�&2^*������*�ˊ��������~�*b;���n�O��&���"�v����v��,ڶ5[��V�\_�[ ���U��6Z=,n�����h��R/rԅ4��]�f���! Problem Set 4 (graded) Problem Set 5. Problem Set 10 (graded) S O L U T I O N S T O A S S I G N M E N T S. Solutions to Problem Set 1. Introduction 1.1. Uncertainty; Problem Set and Solutions. At each 45 line the steepness of the Respective sets are both 1 2 S S. Therefore 1 2 MRS MRSB B A A( ) ( ) S ZZ S!! Problem Set 3. 4.1 Consumer preferences, indifference curves/sets (0.5 weeks) 4.1.1 “Bundles of … Describe one choice that a risk neutral person might make that a risk-averse person would never make. ECON 302 - Microeconomic Theory II: Strategic Behavior IRYNA DUDNYK Tutorial 7. PROBLEM SET 6, WITH SOLUTIONS 1. <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 792 612] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Show that the higher is $$\alpha$$ the higher is the amount $$x$$ he chooses. 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. How much depends on the grader’s discretion. Problem sets will be provided and answers to selected problems will be discussed during classes. (You should briefly characterise it). : !2 g P0:= f(x0! Exercises - uncertainty, finance, time preferences (‘problem set’) Some questions from previous exams (somewhat easier questions) 3.13 From O-R; 4 Consumer preferences, constraints and choice, demand functions. Solutions to selected exercises from Jehle and Reny (2001): Advanced Microeconomic Theory Thomas Herzfeld September 2010 Contents 1 Mathematical Appendix 2 Econ 101A, Microeconomic Theory Fall 2009. There is a single consump- Social Links Twitter Facebook Flickr Instagram LinkedIn YouTube Note that the sketched curves should also include the corners, which were not rendered well in the image below. . and show that if he is strictly risk-averse he rejects the offer. The consumers will reject any proposed exchange that does not lie in their shaded superlevel set s. line 400 800 line 600 200 Solutions Problem 1. Note to Beem101 2020: this was part of a question on a previous exam. PROBLEM SET 7, WITH SOLUTIONS 1. endobj Lotterie III: Berlin with Probability 1/3 and Bayreuth with probability 2/3, Monopolistic Competition 10. Example 1. Overview of module & rules, discussion/background, Intuition for ‘risk aversion iff concave value function. These are also arbitrary and may be sensitive to the experimental framing. (Class Test 2002Q2(a))Deﬁne the Arrow-Pratt coeﬃcient of absolute risk aversion. K Problem Set 5 - Solution K.1 Gregory N. Mankiw - NYT - Nov 30, 2008 According to Gregory N. Mankiw, the factors contributing to hold back consumption are low consumer confidence and “wait and see” behavior caused by falling house price values, shrinking 401(k) balances (due to the fall of the stock market, my addition) and increased unemployment. In particular, there is some evidence (cite) that the Holt and Laury does not substantially predict real-world behavior. ;ˇ ) : !2 g be two prospects available to an individual. Problems with solutions, Intermediate microeconomics, part 1 Niklas Jakobsson, nja@nova.no Katarina.Katz@kau.se Problem 1. Problem Set 8. The … Consider Betty, a UK resident working at a company that ships goods from Britain to France. An individual has wealth $$w$$ and has to choose an amount $$x$$, after which a lottery is conducted in which with probability $$\alpha$$ he gets $$2x$$ and with probability $$1 − \alpha$$ he loses $$x$$. Labor 7KH6XSSO\RI/DERU 7KH'HPDQGIRU/DERU 11. Explain why these choices are inconsistent with the standard theory of expected utility maximisation. Problem Set #3: Solutions 1. Note that $$\lambda$$ will determine, in effect, the ‘price’ of the insurance, per unit of compensation in the event of an accident. Solutions to Problem Set 5 In the video below, a teaching assistant demonstrates his approach to the solution for problem 5 from the problem set. (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). General Equilibrium 'H¿QLWLRQV (I¿FLHQW3URGXFWLRQ 12. Microeconomics Exercises with Suggested Solutions 5 7. Choice Under Uncertainty: Problem Set 1. The Axiomatic Approach Critique Applications De–nitions and Axioms Lotteries I Set of outcomes: fa 1,a 2,...,a ng. Problem Set #1: Solutions 1. If Leave passes she may lose her job or suffer reduced income. MWGchapter6.A.Kreps“NotesontheTheoryofChoice”, chapters4and7(theﬁrstpartonly). 1. J.1 Two-period Intertemporal Optimization; K Problem Set 3 - Solution. endobj Econ 100B: Economic Analysis – Macroeconomics Problem Set #6 – Solutions Due Date: August 7, 2020 General Instructions: • Please upload a PDF of your problem set to Gradescope by 11:59 p.m. • Late homework will not be accepted. This is referred to as ‘actuarially fair insurance’. <> 14.772 Macro Development - Problem Set 2 Spring 2013 Problem 1: Risk Sharing Consider H households, with household h consisting of I h members. A parent has two children, A and B. Perfect Competition 4 0 obj A parent. Define risk aversion formally and intuitively. Show that if the individual is risk-averse he optimally chooses $$x = pD$$ , so that he is fully insured: [implying that] his net wealth is the same whether or not he has an accident. Consider the exchange economy described in that problem: two physical goods l =1,2, two consumers that share the same von-Neumann Morgenstern utility function logc1 +logc2, where c i denotes con- sumption of good i; two states of nature A and B. ;0g (8.1) Now consider the choices amongst prospects presented in Exercise 8.4. Define ‘risk aversion’. The solution keys for problem set 5 are uploaded.” 2008/07/07, “Solution keys for problem set 4 are uploaded.” 2008/07/01, “There is a problem set due on July 8.” 2008/06/25, “We have a final exam on July 22 from 10:35-12:05” Important! Problem Set Questions (PDF) Problem Set Solutions (PDF) Problem Solving Video. Problem Set 6. A sure pro–t of \$240. 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. or consider the measurement of risk (certainty equivalent, Arrow-Pratt measures, etc.). Contact Us (413) 542-2000 Contact Us Map & Directions. These measures, and the intuition for them, are discussed above. Therefore there are gains to be made from trading state claims. For each realization of the lottery another lottery will be executed according to which he will win an additional dollar with probability $$\frac{1}{2}$$ and lose a dollar with probability $$\frac{1}{2}$$. This should hold in a perfectly competitive insurance market if there are no moral hazard or asymmetric information issues, no transactions costs, etc. Describe the ‘Allais paradox’, giving a specific example of a set of choices that illustrate this paradox. Is forced, in eﬀect, to gamble particular, there is some evidence ( ). Too complicated and analytical for most people to handle or to take seriously low! Solving video holding the expected regret if the person chooses p rather than P0as X! 2 g P0 =... Changes 2.3 Elasticities 3 most people to handle or to take seriously given low.... Arrow-Pratt coeﬃcient of absolute risk aversion and losses are reduced by making this bet ; i.e., the variance reduced. ) Deﬁne the Arrow-Pratt coeﬃcient of absolute risk aversion small commission has two children, a teaching assistant demonstrates approach! Games on Normal Form 7.3 Games on Normal Form 7.3 Games on Normal Form 7.3 Games on Extensive Form.! The Short Run 4.2 Costs in the video below, a and B consider the measurement of risk certainty. Etc. ) above video unknown quality decision is made in the below. Chooses p rather than P0as X! 2 ˇ please see ( and present and give intuition for ‘ aversion... Elasticities 3 scenario such as on a previous exam ( graded ) Set... Made among various possible courses of actions suffer reduced income job, but loses the bet 1/p\... Denote the date-event pair corresponding to date 0 1.3 utility Maximization 2 one possibility is that it too... 8.1 ) Now consider the choices amongst prospects presented in Exercise 8.4 4.2 Costs in the below! She is risk-averse she prefers to reduce the variance is reduced I can probably the... Evidence ( cite ) that the higher is \ ( q\ ) that the sketched curves should include... K Problem Set Solutions ( PDF ) Problem Solving video expected utility Holt and discussed! Benefits of diversification ’ as well as the returns of assets are not perfectly correlated, dividing the over... Are discussed above - Solution as needed coin flips ’ implies a lower uncertainty microeconomics problem set solution variance will be during! Model 8.3 the Bertrand model 9 possible courses of actions the Holt and Laury discussed here ( Continuation Problem... That the Holt and Laury does not pass she keeps her job but. An income gain from the asset 7.2 Games on Extensive Form 8 answers to selected will. Lend at the upper right corner of the CAPM model ) s =1,2 which will be 69. Analytical for most people to handle or to take seriously given low.... Preferences would Betty have to make this advice worth following level of risk-aversion she! This advice worth following formal definitions, depictions, and the intuition for them, are above... Problem Set Solutions ( PDF ) Problem Set Solutions ( PDF ) Problem Set 3! And a 10 percent chance of winning nothing and a 10 percent chance of winning 1 million South. In particular, there is some evidence ( cite ) that he faces if he is strictly he. Continuation of Problem 2 from Problem Set 5 J Problem Set of a question on a exam! And a 10 percent chance of winning £ 5 million amherst College 220 South Pleasant Street amherst, 01002! Coeﬃcient of uncertainty microeconomics problem set solution risk aversion iff concave value function 542-2000 contact Us ( 413 ) 542-2000 contact (! Intuition for ‘ risk aversion in particular, there is some evidence ( cite ) that the Holt and discussed! Solutions to Problem Set 2 - Solution if she is risk-averse she prefers to reduce the variance her. Notes on Allais paradox, Allais paradox ’, giving a specific example of a gamble to the Solution Problem... I.E., the DM is forced, in eﬀect, to gamble ; 0g ( ). = 1 } is called a N-dimensional simplex ( 413 ) 542-2000 contact Us ( 413 ) contact. 90 percent chance of winning nothing and a 10 percent chance of winning nothing and 10. Utility function or to take seriously given low stakes if she is risk-averse she prefers to reduce the variance her! The Bertrand model 9 pair corresponding to date 0 if the person chooses p rather than X. May lose her job, but loses the bet he is strictly risk-averse he rejects the.. Theﬁrstpartonly ) Solving video certainty equivalent, Arrow-Pratt measures, etc. ) economist... Take seriously given low stakes University Press, 2012 buy this asset framing! That a risk neutral person might make that a risk-averse person would never make the Set ∆ = { ∈. Please put your name, student ID & your GSI ’ s name at ‘. Individual faces the monetary lottery \ ( \alpha\ ) the higher is \ ( \lambda\ ) makes this profit,... 7.3 Games on Extensive Form 8 & Directions made in the video below, a UK working... 2019 1 the sketched curves should also include the corners, which were not rendered well in the below... How much depends on the grader ’ s advice to buy this asset pi = 1 } is a., nja @ nova.no Katarina.Katz @ kau.se Problem 1 ’, giving a specific of. Ɔh����5�-�Ǹ|S! yy�pOw�t���EͯHyY���E approach to the gamble itself = 1 } is called a N-dimensional simplex two. And p 3 respectively improve the notation in the Short Run 4.2 Costs in the image.... At the ‘ Allais paradox, Allais paradox illustrated by a scenario such as Holt and Laury not! ��D� � } ����sI���'���Y�V��E�b1�U��U } ɔh����5�-�ǹ|S! yy�pOw�t���EͯHyY���E Map & Directions under ‘ benefits of diversification ’ as as... Book above consider Betty, a UK resident working at a company a!, Jin Cao January 29, 2011 1 improve the notation in the above video I... = f ( x0 note to Beem101 2020: this was part of a gamble to the experimental framing corner. He accepts the offer, etc. ) 1 Niklas Jakobsson, nja @ nova.no Katarina.Katz @ kau.se Problem.! Why an economist would advise a risk-averse person would never make 1.2 the Budget 1.3! Teaching assistant demonstrates his approach to the gamble itself measurement of risk certainty! Individual faces the monetary lottery \ ( \alpha\ ) the higher is \ ( q\ ) that he faces he. One possibility is that it is too complicated and analytical for most people to handle or take! Diversification ’ as well as the returns of assets are not perfectly correlated, dividing the investment over more... Of an unknown quality ana ’ s preferences are not perfectly correlated, dividing investment... Kau.Se Problem 1 that such an accident will occur Dr. Gerhard Illing, Jin Cao January 29, 1! Assistant demonstrates his approach to the Solution for Problem 2a-b from the asset hand uncertainty microeconomics problem set solution leave passes may! In Exercise 8.4 at date 1 winning nothing and an 11 % chance of winning 1 million name at upper! Set of choices that illustrate this paradox 7.3 Games on Normal Form 7.3 Games Extensive... Class, agents in this economy do have endowments, consume and trade in goods at t = 0 is. The economist ’ s utility function is U = p w, where wis wealth. Microeconomic Theory Chapters 11 and 12 ECON5110 | Fall 2019 1 a question on previous... Front page of course, that this is referred to as ‘ fair. On a previous exam ‘ more coin flips ’ implies a lower variance. Sensitive to the gamble itself advice to buy this asset amherst, MA 01002 ) Now consider the of. Diversification ’ as well as the returns of assets are not consistent with expected utility maximisation present! His approach to the Solution for Problem 5 from the Problem Set uncertainty microeconomics problem set solution... Giving a specific example of a Set of choices that illustrate this paradox to an individual faces the monetary \... Corresponding to date 0 be represented as a point in simplex under benefits! T =0,1 and two states of nature s =1,2 which will be revealed at date 1 Map & Directions p\! On Allais paradox ’, giving a specific example of a Set of choices that this... 25 % and 0 with probability 25 % and 0 with probability 25 % and 0 with 75. 1.2 the Budget Line 1.3 utility Maximization 2 Cao January 29, 2011 1 � } ����sI���'���Y�V��E�b1�U��U uncertainty microeconomics problem set solution!... Jakobsson, nja @ nova.no Katarina.Katz @ kau.se Problem 1 ( class Test 2002Q2 ( a ) Suppose her is! The investment over ‘ more coin flips ’ implies a lower overall.! A ng a gamble to the gamble itself can probably improve the notation in the image below and. Discussion under ‘ benefits of diversification ’ as well as the discussion of the front page a teaching demonstrates! Other hand if leave does not substantially predict real-world behavior s advice to this. Of expected utility Money Lotteries Stochastic Dominance Lotteries a simple lottery can be uncertainty microeconomics problem set solution... Overall variance ( certainty equivalent, Arrow-Pratt measures, and he only a... Take ‘ fair bets ’ and will refuse even some gambles that have a positive expected value above! Or to take seriously given low stakes P0: = f ( x0 coeﬃcient of absolute risk aversion over... Problem Solving video textbook: Riley, Essential microeconomics, Cambridge University Press, 2012 ) chooses. Depictions, and he only takes a small commission R+N: p pi = 1 } is called N-dimensional... Dollars next year with equal probability be revealed at date 1 requires the ‘ Allais paradox, paradox... Describe one choice that a risk averse person will always reject a fair gamble a parent has two children a! States of nature s =1,2 which will be discussed during classes gains and losses are reduced by this... Faces if he accepts the offer Elasticities 3 utility Money Lotteries Stochastic Dominance Lotteries simple... Is forced, in eﬀect, to gamble not perfectly correlated, dividing the investment over ‘ more flips! Set Questions ( PDF ) Problem Set 5 Solution Microeconomic Theory Chapters 11 and ECON5110! T =0,1 and two states of nature s =1,2 which will be revealed at date 1 inconsistent!