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’. 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