...2012 Due in Class, April 11, 2012 Problem 1 Certainty Equivalence If you are exposed to a 50/50 probability of gaining or losing USD 1000 and an insurance that removes the risk costs USD 500, at what level of wealth will you be indifferent between taking the gamble or paying the insurance? That is, what is your certainty equivalent wealth for this gamble? Assume that your utility function is U (Y ) = −1/Y . What would the solution be if the utility function were logarithmic? ......... Problem 2 Insurance An agent with a logarithmic utility function of wealth tries to maximize his expected utility. He faces a situation in which he will incur a loss of L with probability p. He has the possibility to insure against this loss. The insurance premium depends on the extent of the coverage. The amount covered is denoted by h and the price of the insurance per unit of coverage is p (hence the amount he has to spend on the insurance will be hp). 1. Calculate the amount of coverage h demanded by agent as a function of his wealth level Y , the loss L, the probability π and the price of the insurance p. 2. What is the expected gain of an insurance company offering such a contract ? 3. If there is perfect competition in the insurance market ( zero profit), what price p will the insurance company set? 4. What amount of insurance will the agent buy at the price calculated under c. What is the influence of the form of the utility function ? ......... Problem 3 Stochastic Dominance ...
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...Tradeoff Weights Tradeoff weights refer weights of various trade attributes that are developed by using different methods or techniques such as direct method, swing weight method, equivalence lottery method, and hierarchical weight method. Advantages and Disadvantages of Methods There are various advantages and disadvantages of using various methods like indifference trade-off method, swing weight method, direct weight method etc. for developing or calculating tradeoff weights. In the context of benefits, swing weight method is quick and easy to operate that can help the decision maker to make appropriate decision by developing effective tradeoff weights (Bekiaris & Nakanishi, 2004). In addition, all these methods are useful in a project for a decision maker in spatial decision problems. The main advantage of tradeoff analysis methods is the ability to provide different relative weights to each of the alternative or attributes. By using these methods, it is possible to derive weights from a ranking of limited alternatives and easy to achieve an agreement between decision makers. On the other hand, historical weights are still valid in decision and risk analysis that can be helpful to effectively develop tradeoff weights (Guinto, 2008). At the same time, there are some disadvantages of using these methods for developing tradeoff weights. Some of them are as follow: There is no assurance that swing weight method provides accurate eliciting weights. Some of these...
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...Journal of Economic Behavior & Organization Vol. 64 (2007) 250–268 Myopic loss aversion, disappointment aversion, and the equity premium puzzleଝ David Fielding a , Livio Stracca b,∗ b a Department of Economics, University of Otago, Dunedin, New Zealand European Central Bank (ECB), Kaiserstrasse 29, 60311 Frankfurt am Main, Germany Received 7 March 2003; accepted 5 July 2005 Available online 24 May 2006 Abstract This paper takes a close look at the “behavioural finance” explanations of the equity premium puzzle, namely myopic loss aversion [Benartzi, S., Thaler, R.H.,1995. Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics 110, 73–92] and disappointment aversion [Ang, A., Bekaert, G., Liu, J., 2005. Why stocks may disappoint. Journal of Financial Economics 76, 471–508]. The paper proposes a simple specification of loss and disappointment aversion and brings these theories to the data. The main conclusion is that a highly short-sighted investment horizon is required for the historical equity premium to be explained by loss aversion, while reasonable values for disappointment aversion are found also for long investment horizons; stocks may not only lose in the short term, but also disappoint in the long term. © 2006 Elsevier B.V. All rights reserved. JEL classification: G11; G12 Keywords: Myopic loss aversion; Disappointment aversion; Equity premium puzzle; Investment horizon; Reference dependence 1. Introduction The...
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...Humanities Research Council of Canada is gratefully acknowledged. August 20, 2001 Abstract This chapter provides a survey of utilitarian theories of justice. We review and discuss axiomatizations of utilitarian and generalized-utilitarian social-evaluation functionals in a welfarist framework. Section 2 introduces, along with some basic definitions, socialevaluation functionals. Furthermore, we discuss several information-invariance assumptions. In Section 3, the welfarism axioms unrestricted domain, binary independence of irrelevant alternatives and Pareto indifference are introduced and used characterize welfarist social evaluation. These axioms imply that there exists a single ordering of utility vectors that can be used to rank all alternatives for any profile of individual utility functions. We call such an ordering a social-evaluation ordering, and we introduce several examples of classes of such orderings. In addition, we formulate some further basic axioms. Section 4 provides characterizations of generalized-utilitarian social-evaluation orderings, both in a static and in an intertemporal framework. Section 5 deals with the special case of utilitarianism. We review some known axiomatizations and, in addition, prove a new characterization result that...
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...The American economic JUNE 1958 Revlew NUMBER THREE VOLUME XLVIII THE COST OF CAPITAL, CORPORATION FINANCE AND THE THEORY OF INVESTMIENT By FRANCO MODIGLIAN1 AND MERTON H. MILLER* What is the "cost of capital" to a firm in a world in which funds are used to acquire assets whose yields are uncertain; and in which capital can be obtained by many different media, ranging from pure debt instruments, representing money-fixed claims, to pure equity issues, giving holders only the right to a pro-rata share in the uncertain venture.? This question has vexed at least three classes of economists: (1) the corporation finance specialist concerned with the techniques of financing firms so as to ensure their survival and growth; (2) the managerial economist concerned with capital budgeting; and (3) the economic theorist concerned with explaining investment behavior at both the micro and macro levels.' In much of his formal analysis, the economic theorist at least has tended to side-step the essence of this cost-of-capital problem by proceeding as though physical assets-like bonds-could be regarded as yielding known, sure streams. Given this assumption, the theorist has concluded that the cost of capital to the owners of a firm is simply the rate of interest on bonds; and has derived the familiar proposition that the firm, acting rationally, will tend to push investmnent to the point * The authors are, respectively, professor and associate professor of economics in...
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...American Economic Association The Cost of Capital, Corporation Finance and the Theory of Investment Author(s): Franco Modigliani and Merton H. Miller Source: The American Economic Review, Vol. 48, No. 3 (Jun., 1958), pp. 261-297 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1809766 Accessed: 10/09/2009 09:51 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. ...
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...American Economic Association The Cost of Capital, Corporation Finance and the Theory of Investment Author(s): Franco Modigliani and Merton H. Miller Source: The American Economic Review, Vol. 48, No. 3 (Jun., 1958), pp. 261-297 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1809766 Accessed: 03-09-2015 15:21 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org This content downloaded from 145.90.63.121 on Thu, 03 Sep 2015 15:21:00 UTC All use subject to JSTOR Terms and Conditions The American VOLUME XLVIII Revlew economic JUNE 1958 NUMBER THREE THE COST OF CAPITAL, CORPORATION FINANCE AND THE THEORY OF INVESTMIENT By FRANCO MODIGLIAN1 AND MERTON H. MILLER* What is the "cost of capital" to a firm in a world in which funds are used to acquire assets whose yields are uncertain; and in...
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...Utility means satisfaction which consumers derive from commodities and services by purchasing different units of money.From Wikipedia, the free encyclopedia “Ineconomics, utility is a measure of satisfaction;it refers to the total satisfaction received by a consumer from consuming a good or service. “Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility. Utility is often affected by consumption of various goods and services, possession of wealth and spending of leisure time. According to Utilitarian’s, such as Jeremy Bentham (1748–1832) and John Stuart Mill (1806–1873), theory “Society should aim to maximize the total utility of individuals, aiming for "the greatest happiness for the greatest number of people". Another theory forwarded by John Rawls (1921–2002) would have society maximize the utility of those with the lowest utility, raising them up to create a more equitable distribution across society. Utility is usually applied by economists in such constructs as the indifference curve, which plot the combination of commodities that an individual or a society would accept to maintain at given level of satisfaction. Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively. When coupled with production or commodity constraints, under some assumptions, these functions can be used to analyze...
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...I NVESTMENT SCI ENCE I NVESTMENT SCI ENCE DA YID G. LUENBERGER STANFORD UNIVERSITY New York Oxford OXFORD UNIVERSITY PRESS 1998 OXFORD UNIVERSITY PRESS Oxford New York Auckland Bangkok Bogota Bombay Buenos Aires Cnlcutta Cape Town Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Athens Kuala Lumpur Mexico City Madras Nairobi Mndrid Paris Melbourne Singapore Taipei Tokyo Toronto F \--1& ljS1S,'L (Jml aHociated compallies ill Berlin Jbndon ' LE 4 /3 en where that last expression is valid in the limit as In goes to infinity, cOllesponding to continuous compounding Hence continuous compounding leads to the familiar expo~ nential growth CUlve Such a curve is shown in FigUle 2 2 for a 10% nominal interest late Debt We have examined how a single investment (say a bank deposit) glows over time due to intelest compounding It should be clem that exactly the same thing happens 10 debt It I bonoll' money from the biwk at an intelest rate 1 and make no payments to the bank, then my debt increases accOJding to the same formulas Specifically, if my debt is compounded monthly, then after k months my debt will have grown by a factor of [I + (I /12) l' 21 14 12 10 PRINCIPAL AND INTEREST 17 FIGURE 2.2 Expollential growth curve; cOllfinuous compoUlld growth, Under conl;nuotls compounding at 1D'X" the value of $1 doubles in abotll 7 yems In 20 yems it grows by a factor of ilbotll B !5 ~ 4 0...
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...NBER WORKING PAPER SERIES DEFINED CONTRIBUTION PLANS, DEFINED BENEFIT PLANS, AND THE ACCUMULATION OF RETIREMENT WEALTH James Poterba Joshua Rauh Steven Venti David Wise Working Paper 12597 http://www.nber.org/papers/w12597 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 October 2006 We are extremely grateful to Tonja Bowen for extraordinary and tireless research assistance, to Gary Engelhardt and Anil Kumar for graciously providing us with tabulations from their HRS Defined Contribution Plan imputation algorithm, to Paul Bingley, Peter Diamond, Gary Engelhardt, Jon Gruber, Helena Stolyarova, and many seminar participants for helpful comments, and to the National Institute of Aging for research support under grant number P01 AG005842. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research. © 2006 by James Poterba, Joshua Rauh, Steven Venti, and David Wise. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Defined Contribution Plans, Defined Benefit Plans, and the Accumulation of Retirement Wealth James Poterba, Joshua Rauh, Steven Venti, and David Wise NBER Working Paper No. 12597 October 2006 JEL No. J14,J26,J32 ABSTRACT The private pension structure in the United States, once dominated by defined benefit (DB) plans...
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...International Macroeconomics1 Stephanie Schmitt-Groh´2 e April 26, 2013 Mart´ Uribe3 ın 1 The seeds for this manuscript were lecture notes taken by Alberto Ramos in a course on International Finance that Mike Woodford taught at the University of Chicago in the Winter of 1994. 2 Columbia University. E-mail: stephanie.schmittgrohe@columbia.edu. 3 Columbia University. E-mail: martin.uribe@columbia.edu. ii Contents 1 Global Imbalances 1.1 Balance-of-Payments Accounting . . . . . . . . . . . . . . . . 1.2 The Current Account . . . . . . . . . . . . . . . . . . . . . . 1 1 5 1.3 The Current Account and the Net International Investment Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Valuation Changes and the Net International Investment Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 The Negative-NIIP-Positive-NII Paradox: Dark Matter? 1.5.1 1.5.2 . . 20 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . 22 Return Differentials . . . . . . . . . . . . . . . . . . . 23 1.6 Who Lends and Who Borrows Around the World? . . . . . . 26 1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 35 2 Current Account Sustainability 2.1 Can a Country Run a Perpetual Trade Balance Deficit? . . . 35 2.2 Can a Country Run a Perpetual Current Account Deficit? . 39 2.3 Savings, Investment, and the Current Account . . . . . . . . 41 iii iv 2.3.1 CONTENTS Current Account Deficits...
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...COPYRIGHT NOTICE: Ariel Rubinstein: Lecture Notes in Microeconomic Theory is published by Princeton University Press and copyrighted, c 2006, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. Follow links for Class Use and other Permissions. For more information send email to: permissions@pupress.princeton.edu Lecture Notes in Microeconomic Theory Ariel Rubinstein Updates to the Printed Version The file you are viewing contains the printed version of the book. In relevant places throughout the text you will find small icons indicating the existence of updates to the text: A red icon indicates there is a correction for a mistake on this line. A green icon indicates an addition to the text at this point. The corrected and added text can be obtained from the author's homepage at http://arielrubinstein.tau.ac.il/ . October 21, 2005 12:18 master Sheet number 1 Page number 1 October 21, 2005 12:18 master Sheet number 2 Page number 2 October 21, 2005 12:18 master Sheet number 3 Page number i Lecture Notes in Microeconomic Theory October 21, 2005 12:18 master Sheet number 4 Page number ii October 21...
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...C H A P T E R 5 Uncertainty and Consumer Behavior CHAPTER OUTLINE 5.1 Describing Risk S o far, we have assumed that prices, incomes, and other variables are known with certainty. However, many of the choices that people make involve considerable uncertainty. Most people, for example, borrow to finance large purchases, such as a house or a college education, and plan to pay for them out of future income. But for most of us, future incomes are uncertain. Our earnings can go up or down; we can be promoted or demoted, or even lose our jobs. And if we delay buying a house or investing in a college education, we risk price increases that could make such purchases less affordable. How should we take these uncertainties into account when making major consumption or investment decisions? Sometimes we must choose how much risk to bear. What, for example, should you do with your savings? Should you invest your money in something safe, such as a savings account, or something riskier but potentially more lucrative, such as the stock market? Another example is the choice of a job or career. Is it better to work for a large, stable company with job security but slim chance for advancement, or is it better to join (or form) a new venture that offers less job security but more opportunity for advancement? To answer such questions, we must examine the ways that people can compare and choose among risky alternatives. We will do this by taking the following steps: 1. In order to compare the riskiness...
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...BACHELOR OF COMMERCE (B.COM.,) PAPER – 2.1 MANAGERIAL ECONOMICS UNIT – I CHAPTER - I SECTION - I Definition of Managerial Economics Managerial economics refers to those aspects of economics and its tools of analysis most relevant to the firm’s decision-making process. According to MeNair and Meriam, managerial economies consists of the use of economic models of thought to analyze business situations. Some writers consider managerial economics as the integration of economic theory with business practice for the purpose of facilitating decision-making and forward planning by management. The underlying idea of all these definitions is that managerial economics means economics applied in decision-making. So we may consider managerial economics as a special branch of economics bridging the gap between abstract theory and managerial practice. It may be pointed out here that effective decision-making at the firms’ level calls for a careful analysis of a choice between alternative courses of action. Economic theory offers a variety of concepts and analytical tools which can be of considerable assistance to the manager in his decision-making process. In fact actual problem-solving may require many skills and tools which are not available in the traditional economist’s. For example, knowledge of accounting and of statistical concepts and methods, which are not taught in economics, can help the analyses to apply more effectively the economic...
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...clarity required making the symbolic representation more precise (e.g., by being more specific as to the time dimension of an interest rate). Roman Alphabet a Amount invested in the risky asset; in Chapter 14, fraction of wealth invested in the risky asset or portfolio AT Transpose of the matrix (or vector)A c Consumption; in Chapter 14 only, consumption is represented by C, while c represents ln C ck Consumption of agent k in state of nature θ θ CE Certainty equivalent CA Price of an American call option CE Price of a European call option d Dividend rate or amount ∆ Number of shares in the replicating portfolio (Chapter xx E The expectations operator ek Endowment of agent k in state of nature θ θ f Futures position (Chapter 16); pf Price of a futures contract (Chapter 16) F, G Cumulative distribution functions associated with densities: f, g Probability density functions K The strike or exercise price of an option K(˜) Kurtosis of the random variable x x ˜ L A lottery L Lagrangian m Pricing kernel M The market portfolio k M Uθ Marginal utility of agent k in state θ p Price of an arbitrary asset P Measure of Absolute Prudence q Arrow-Debreu price qb Price of risk-free discount bond, occasionally denoted prf e q Price of equity rf Rate of return on a risk-free asset Rf Gross rate of return on a risk-free asset r ˜ Rate of return on a risky asset ˜ R Gross...
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