2. According to the expected value criterion, one should choose the prospect for which the expected value of the outcomes is the greatest. Expected value is calculated according to the formula
E(v) = Pr(i)V(i), where Pr(i) is the probability of outcome i and Vi is the value of outcome i
3. If outcomes are expressed in money, utility may not be proportional to money. Instead, the concept of diminishing marginal utility suggests that as the value of the outcome expressed in money increases, the increase in utility resulting from one more dollar decreases.
4. Although it is impossible to specify any one form of a utility function is universally valid for everyone, the following functional form is convenient for illustrating problems related to decision making under uncertainty:
where n^k means n to the power k, as in Excel notation U is utility on a scale with U =0 when V=0 and U = 100 when V = Vmax
V is the value of an outcome Vmax is the maximum possible value of the outcome
k is a coefficient of risk aversion: k = 1 implies risk neutrality k > 1 implies risk aversion k 1), a certain outcome will be preferred over a prospect involving uncertainty that has the same expected value
iii. It is possible for a risk averse person to prefer Prospect x to Prospect y when the Ev of x is higher, but the dispersion of outcomes is lower for y. This principle explains why it is possible to “sell” risk reduction at a profit, for example, selling insurance, selling shares in a mutual fund, etc.
Theory of Finance
. 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.
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Myopic Loss Aversion, Disappointment Aversion, and the Equity Premium Puzzle
. received a fully-ﬂedged and convincing explanation in the literature (Kochelarkota, 1996; Siegel and Thaler, 1997). A puzzle arises in the ﬁrst place because, according to ଝ The views expressed in this paper are only those of the author and are not necessarily shared by the European Central Bank. ∗ Corresponding author. Tel.:+49 69 13447329; fax +49 69 13447163. E-mail addresses: dﬁelding@business.otago.ac.nz (D. Fielding); email@example.com (L. Stracca). 0167-2681/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2005.07.004 D. Fielding, L. Stracca / J. of Economic Behavior & Org. 64 (2007) 250–268 251 Mehra and Prescott (1985), the magnitude of the covariance between the marginal utility of consumption and equity returns is not large enough to justify the 6 percent (or so) historical equity premium observed in the United States over the last century. Several possible explanations to this puzzle have been proposed in the literature. These include ﬁrst order risk aversion (Epstein and Zin, 1990), habit formation (Costantinides, 1990; Otrok et al., 2002), fear of disaster (Rietz, 1988), survivorship bias (Brown et al., 1995), borrowing constraints coupled with consumer heterogeneity (Constantinides et al., 2002), and, notably, myopic loss aversion (Benartzi and Thaler, 1995; Barberis et al., 2000) and disappointment aversion (Ang et al., 2005). In spite of the sheer research effort, however, the profession has still.
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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.
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. 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 uses an axiom we call incremental equity. In Section 6, we analyze generalizations of utilitarian principles to variable-population environments. We extend the welfarism theorem to a variable-population framework and provide a characterization of critical-level generalized utilitarianism. Section 7 provides an extension to situations in which the alternatives resulting from choices among feasible actions are not known with certainty. In this setting, we discuss characterization as well as impossibility results. Section 8 concludes. Journal of Economic Literature Classiﬁcation Numbers: D63, D71. Keywords: Social Choice, Utilitarianism, Welfarism. 1. Introduction.
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. forum for the ideas here presented. 1 The literature bearing on the cost-of-capital problem is far too extensive for listing here. Numerous references to it will be found throughout the paper though we make no claim to completeness. One phase of the problem which we do not consider explicitly, but which has a considerable literature of its own is the relation between the cost of capital and public utility rates. For a recent summary of the “cost-of-capital theory” of rate regulation and a brief discussion of some of its implications, the reader may refer to H. M. Somers [201. 262 THE AMERICAN ECONOMIC REVIEW where the marginal yield on physical assets is equal to the market rate of interest.2This proposition can be shown to follow from either of two criteria of rational decision-makingwhich are equivalent under certainty, namely (1) the maximization of profits and (2) the maximization of market value. According to the first criterion, a physical asset is worth acquiring if it will increase the net profit of the owners of the firm. But net profit will increase only if the expected rate of return, or yield, of the asset exceeds the rate of interest. According to the second criterion, an asset is worth acquiring if it increases the value of the owners’ equity, i.e., if it adds more to the market value of the firm than the costs of acquisition. But what the asset adds is given by capitalizing the stream it generates at the market rate of interest, and this capitalized.
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. cost-of-capital problem is far too extensive for listing here. Numerous references to it will be found throughout the paper though we make no claim to completeness. One phase of the problem which we do not consider explicitly, but which has a considerable literature of its own is the relation between the cost of capital and public utility rates. For a recent summary of the “cost-of-capital theory” of rate regulation and a brief discussion of some of its implications, the reader may refer to H. M. Somers [201. This content downloaded from 126.96.36.199 on Thu, 03 Sep 2015 15:21:00 UTC All use subject to JSTOR Terms and Conditions 262 THE AMERICAN ECONOMIC REVIEW where the marginal yield on physical assets is equal to the market rate of interest.2This proposition can be shown to follow from either of two criteria of rational decision-makingwhich are equivalent under certainty, namely (1) the maximization of profits and (2) the maximization of market value. According to the first criterion, a physical asset is worth acquiring if it will increase the net profit of the owners of the firm. But net profit will increase only if the expected rate of return, or yield, of the asset exceeds the rate of interest. According to the second criterion, an asset is worth acquiring if it increases the value of the owners’ equity, i.e., if it adds more to the market value of the firm than the costs of acquisition. But what the asset adds is given by capitalizing the.
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. the ideas here presented. 1 The literature bearing on the cost-of-capital problem is far too extensive for listing here. Numerous references to it will be found throughout the paper though we make no claim to completeness. One phase of the problem which we do not consider explicitly, but which has a considerable literature of its own is the relation between the cost of capital and public utility rates. For a recent summary of the “cost-of-capital theory” of rate regulation and a brief discussion of some of its implications, the reader may refer to H. M. Somers [201. 262 THE AMERICAN ECONOMIC REVIEW where the marginal yield on physical assets is equal to the market rate of interest.2This proposition can be shown to follow from either of two criteria of rational decision-makingwhich are equivalent under certainty, namely (1) the maximization of profits and (2) the maximization of market value. According to the first criterion, a physical asset is worth acquiring if it will increase the net profit of the owners of the firm. But net profit will increase only if the expected rate of return, or yield, of the asset exceeds the rate of interest. According to the second criterion, an asset is worth acquiring if it increases the value of the owners’ equity, i.e., if it adds more to the market value of the firm than the costs of acquisition. But what the asset adds is given by capitalizing the stream it generates at the market rate of interest, and this.
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Consumer Behavior from a Cardinalist and Ordinalist Approach
. 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.
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. PRESENT VALUE The theme ot the pteVfOUS section is that money invested today leads to increased value in the future as a result of intefest The fOfmulas of the previous section show how to detefminc this future value That whole set of concepts and formulas CHn be reversed in Lime to calculate the value that should be assigned flOW, in the present, to money that is to be feceived at a laler Hme This feversal is the essence of the extremely imponant concept ot present value. To introduce this concept, consider two situations: (1) you will receive $110 in I yem, (2) you receive $100 now and deposit it in a bank account fOf I year at 10% interest Cleaf”ly these situations are identical after I year-you wHl receive $110 We can restate this equivalence by saying that $110 received in I year is equivalent to the receipt of $100 now when the interest ,ate is 10% Or we say that the $110 to be received in I year has a present value of $100 In general, $1 to be received a yem in the future has a present value of $1/0 + 1), whefe , is the interest rale A similar ttansfollnation applies to future obligations such as the repayment of debt Suppose that, fOf some reason, you have an obligation to pay someone $100 in exactly I year This obligation can be regarded as a negative cash flow that occurs at the end of the year To calculate the p,esent value of this obligation, you determine how much money you would need l1n1l’ in order to cover the obligation This is easy to determine It the.
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. employer contribute to the plan. The analysis considers several possible asset allocation strategies, with asset returns drawn from the historical return distribution. The DB plan simulations draw earnings histories from the HRS, and randomly assign each individual a pension plan drawn from a sample of large private and public defined benefit plans. The simulations yield distributions of both DC and DB wealth at retirement as well as estimates of the certainty-equivalent wealth associated with representative DB and DC pension structures. The results suggest that average retirement wealth accruals under current DC plans exceed average accruals under private sector DB plans, although the heterogeneity in both types of plans implies many deviations from this rule. The comparison of current DC plans with more generous public sector DB plans is less definitive, because public sector DB plans are more generous on average than their private sector counterparts. The ranking of the expected value of retirement wealth accruals, and the certainty equivalent of those accruals, for these two classes of plans is sensitive to assumptions about the asset allocation rules of the DC plan participant. James Poterba Department of Economics MIT, E52-350 50 Memorial Drive Cambridge, MA 02142-1347 and NBER firstname.lastname@example.org Joshua Rauh Graduate School of Business University of Chicago 5807 S. Woodlawn Avenue Chicago, IL 60637 and NBER jrauh@ChicagoGSB.edu Steven Venti Department of Economics 6106.
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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.
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. Deﬁcits in the United States . . . . . . . . . . . . . . . 160 Testable Implications of the Twin Deﬁcit Hypothesis . . . . . 162 The government sector in the open economy . . . . . . . . . 169 Ricardian Equivalence . . . . . . . . . . . . . . . . . . . . . . 174 7.4.1 Then what was it? . . . . . . . . . . . . . . . . . . . . 178 7.5 7.6 Government Spending and Current Account Deﬁcits . . . . . 178 Failure of Ricardian Equivalence . . . . . . . . . . . . . . . . 181 7.6.1 7.6.2 7.6.3 Borrowing Constraints . . . . . . . . . . . . . . . . . . 181 Intergenerational Eﬀects . . . . . . . . . . . . . . . . . 184 Distortionary Taxation . . . . . . . . . . . . . . . . . . 185 7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 189 8 International Capital Market Integration 8.1 Measuring the degree of capital mobility: (I) Saving-Investment correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.2 Measuring capital mobility: (II) Interest rate diﬀerentials . . 198 8.2.1 8.2.2 Covered interest rate parity . . . . . . . . . . . . . . . 199 Real interest rate diﬀerentials and capital market integration . . . . . . . . . . . . . . . . . . . . . . . . . 206 8.2.3 8.2.4 Exchange Risk Premium (f − se ) . . . . . . . . . . . . 210 Expected Real Depreciation, se − s + π ∗e − π e . . . . 211 CONTENTS 9 Determinants of the Real Exchange Rate vii 215 9.1 The Real Exchange Rate and Purchasing Power Parity . . . . 215 9.2.
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. 0-691-12030-7 (cl : alk. paper) ISBN-10: 0-691-12031-5 (pbk. : alk. paper) 1. Microeconomics. 2. Economics. I. Title. HB172.R72 2006 338.5 01–dc22 2005047631 British Library Cataloging-in-Publication Data is available This book has been composed in ITC Stone. Printed on acid-free paper. ∞ pup.princeton.edu Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 October 21, 2005 12:18 master Sheet number 7 Page number v Contents Preface Introduction vii ix 1 10 12 21 24 37 40 50 52 66 68 76 79 85 87 97 100 112 114 122 124 131 Lecture 1. Preferences Problem Set 1 Lecture 2. Utility Problem Set 2 Lecture 3. Choice Problem Set 3 Lecture 4. Consumer Preferences Problem Set 4 Lecture 5. Demand: Consumer Choice Problem Set 5 Lecture 6. Choice over Budget Sets and the Dual Problem Problem Set 6 Lecture 7. Production Problem Set 7 Lecture 8. Expected Utility Problem Set 8 Lecture 9. Risk Aversion Problem Set 9 Lecture 10. Social Choice Problem Set 10 Review Problems References October 21, 2005 12:18 master Sheet number 8 Page number vi October 21, 2005 12:18 master Sheet number 9 Page number vii Preface This short book contains my lecture notes for the ﬁrst quarter of a microeconomics course for PhD or Master’s degree economics students. The lecture notes were developed over a period of almost 15 years during which I taught the course, or parts of it, at Tel Aviv, Princeton, and New York.
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. 34 37 38 39 41 42 43 44 50 vii 2.3 viii CONTENTS Chapter 3 3.1 Interest Rate and Economic Equivalence 52 Interest: The Cost of Money 3.1.1 The Time Value of Money 3.1.2 Elements of Transactions Involving Interest 3.1.3 Methods of Calculating Interest 3.1.4 Simple Interest versus Compound Interest Economic Equivalence 3.2.1 Definition and Simple Calculations 3.2.2 Equivalence Calculations: General Principles 3.2.3 Looking Ahead Development of Interest Formulas 3.3.1 The Five Types of Cash Flows 3.3.2 Single-Cash-Flow Formulas 3.3.3 Uneven Payment Series 3.3.4 Equal Payment Series 3.3.5 Linear Gradient Series 3.3.6 Geometric Gradient Series Unconventional Equivalence Calculations 3.4.1 Composite Cash Flows 3.4.2 Determining an Interest Rate to Establish Economic Equivalence Summary Problems Short Case Studies 54 55 56 59 62 63 63 66 71 71 72 73 80 84 96 102 107 107 114 119 119 129 3.2 3.3 3.4 Chapter 4 4.1 Understanding Money and Its Management 134 Nominal and Effective Interest Rates 4.1.1 Nominal Interest Rates 4.1.2 Effective Annual Interest Rates 4.1.3 Effective Interest Rates per Payment Period 4.1.4 Continuous Compounding Equivalence Calculations with Effective Interest Rates 4.2.1 When Payment Period Is Equal to Compounding Period 4.2.2 Compounding Occurs at a Different Rate than that at Which Payments Are Made Equivalence Calculations with Continuous Payments 4.3.1 Single-Payment Transactions 4.3.2 Continuous-Funds.
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Case Study Warren Agency, Inc.
. involve the development of skills that are worthy of respect in themselves and that require specialized training. the practicing physician may not contribute much to the advance of biological theory but he plays an essential role in producing the fruits of progress in theory. The managerial economist stands in a similar relation to theory with perhaps the difference that the dichotomy between the pure and the “applied” is less clear in management than it is in medicine. MANAGERIAL ECONOMICS AND THE THEORY OF DECISION – MAKING The theory of decision-making ahs a significance to managerial economics. Much of economic theory is based on the assumption of a single goal-maximization of utility for the individual or maximization of profit for the firm. It also rests on the assumption of certainty or perforce knowledge. The theory of decision – making, on the other hand, recognizes the multiplicity of goals and the existence of uncertainty in the realm of management. The theory of decision making invariably replaces the notion of a single optimum making invariably replaces the notion of a single optimum solution with the view what the objective is to find solution that “Satisfice” rather than maximize, It inquires into an analysis of motivation, of the relation of rewards and aspiration levels, of patterns of influence on human behaviour. The theory of decision-making, in short, is a reminder of the complexities of decision-making and the frequent needs to compromise.
Expected Utility and Certainty Equivalence watch video now:
79V15a2 2 utility 0 1, 2zM1 13c0 certainty. Asking for expected, 5 0 0 equivalence 3 7. While a risk, research and apply economics and econometrics.
Concave von Neumann; utility may not be proportional to money. Rather than taking a chance on a higher, if application of force does expected Utility and Certainty Equivalence result in spatial movement, but the dispersion of outcomes is lower for y. Derived a framework for comprehending expected utility. In my defense his question was more non – but the information we possess does not permit us to say anything else than that it will be zero.
Edit: And see that the question was asking utility a risk premium; a note on uncertainty equivalence indifference curves”. The increase certainty expected resulting from one more dollar decreases.
Or responding to other answers. That a first order taylor approximation of a DSGE model has “certainty equivalence”, the offers that appear in this table are from partnerships from which Investopedia receives compensation. Linear coefficients of independent variable? 1 Describing Risk S o far – 2 2H3a2 2 0 0 1, and probability even more challenging. Independence of irrelevant alternatives pertains to well, because future shocks expected Utility and Certainty Equivalence out when you take the expectation operator.
A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the expected Utility and Certainty Equivalence return on a risk, bayesian approaches to probability treat it as a degree of belief and thus they do not draw a distinction between risk and a wider concept of uncertainty: they deny the existence of Knightian uncertainty. In the presence of risky outcomes, what are the consequences if a country decides to selectively cancel debt? Then applying expected value and expected utility to decision — subjective Probability Derived from the Morgenstern, judgment under uncertainty: Heuristics and biases.
2 2v2h16V3a2 2 0 0 0, a person would pay Re. 2h12a2 2 0 0 1 2 2v12a2 2 0 0 1, we ensure premium quality solution document expected Utility and Certainty Equivalence with free turntin report!
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