Chapter 25: Exchange in Insurance Markets


 Polly Long
 1 years ago
 Views:
Transcription
1 Chapter 25: Exchange in Insurance Markets 25.1: Introduction In this chapter we use the techniques that we have been developing in the previous 2 chapters to discuss the trade of risk. Insurance markets exist for that purpose. In particular we look at optimal risksharing between individuals and discuss how the trading of risk can make people better off. We use the techniques of chapters 23 and 24 combined with the analysis of chapter 8 (where we discussed trade in general) to understand how the trading of risk works. We use the framework of chapter 8. We assume a very simple economy consisting of two individuals, A and B, and two possible states of the world, state 1 and state 2. Ex ante, when trading may take place, it is not know which of the two states will occur, though their respective probabilities π 1 and π 2 are known. Ex post, one and only one of the two states will occur. The individuals start with some initial endowments of income/consumption, but they may be able to trade away from this initial point. We work throughout with a specific analysis but the story can obviously be generalised. What is important is that you take away from this chapter an understanding of how insurance markets help to allocate risk efficiently. 25.2: An Edgeworth box We start with individual A. We assume that he or she would have with an income of 75 if state 1 occurs and an income of 50 if state. We assume that the two states of the world are equally likely. As for preferences, we assume that A has Expected Utility preferences and we assume here a constant absolute risk aversion utility function with parameter r = We picture A s preferences and endowment point in figure The straight line is A s certainty line. Now we turn to individual B. We assume exactly the same initial endowment: an income of 75 if state and an income of 50 if state. However we assume that B is more risk averse than A, having a constant absolute risk aversion utility function with parameter r = We portray B s preferences and endowment point the normal way up in figure 22.2 and upside down in figure The straight line in figure 25.3 is B s certainty line.
2 Now we do an Edgeworth. Superimpose B s upside down indifference map on top of A s in such a way that the endowment points coincide. We then get an Edgeworth box of dimension 150 (the total income/consumption if state 1 were to occur) times 100 (the total income/consumption if state 2 were to occur), with the endowment point exactly at the middle as their initial endowments are equal. You might like to think of State 2 as some kind of disaster in which the society as a whole loses 2/3 of its income. Inserted into figure 25.4 are the certainty lines of the individuals: the 45 line starting at the bottom left origin is that for A and the 45 line starting at the top right origin is that for B. Note that the slopes of all the indifference curves for both the individuals along their respective certainty lines is 1 the ratio of the probabilities of the two states. If you study this figure you should be able to see where the contract curve is. In this case, where both individuals have constant absolute risk aversion utility functions, the contract curve is in an interesting position and has an interesting shape: it is a 45 line between the two certainty lines, but nearer to the certainty line of the more risk averse individual (B). This is interesting as it indicates the nature of efficient risk sharing. The contract curve is nearer to the certainty line for the
3 more risk averse individual which means that in any efficient contract B s position is less risky than that of A 1. So A the less riskaverse individual bears more of the risk than the more riskaverse person. (Notice that there is risk to share because the total income is 150 in one state and 100 in the other there is no way to get rid of the risk altogether, though the two individuals can change the way they share it.) Let us look at the competitive equilibrium. It is the point marked C in figure Also drawn in the figure are the two priceoffer curves and the contract curve. Also joined together are the endowment point and the equilibrium point to indicate the equilibrium relative price (the price of state 1 contingent income relative to the price of state 2 contingent income). Let us summarise what happens. Initial allocation Individual A Individual B Society Competitive equilibrium allocation Individual A Individual B Society Note that on a particular individual s certainty line there is no risk for that individual. As we move away say at an angle of 90  the riskiness increases and the further away the more the risk.
4 Changes between the two allocations Individual A Individual B Society Individual B is easy to understand. He or she starts out with an ex ante risky income (75, 50) by which we mean 75 if state and 50 if state. The expected income is 62.5 and the riskiness is ± 12.5 by which we mean that the two values are 12.5 either side of the mean. After trading to the equilibrium point, B has an ex ante risky income of (67, 55). This has an expected value of 61 which is lower than the expected income before trade but the riskiness is now ± 6. So individual B has reduced the riskiness of his or her ex ante income, at the cost of having to accept a reduction in the expected income. But because he or she is rather riskaverse, he or she is happy to accept this reduction in the expected income in exchange for a reduction in the risk. Note that at C, rather obviously, individual B is on a higher indifference curve than he or she was at E. A, on the other hand, starts out with the same ex ante risky income (75, 50)  which has an expected value of 62.5 and a riskiness of ± After the trade at the competitive equilibrium A has an ex ante risky income of (83, 45). Note that this has an expected income of 64 and a riskiness of ± 19. We see that A has accepted an increase in the riskiness of his or her position but he or she has also benefited with an increase in his or her expected income. Despite the fact that A is moderately riskaverse he or she is prepared to take a little bit of extra risk in return for a little bit of extra expected income. Note that at C, rather obviously, individual A is on a higher indifference curve than he or she was at E. We end up with more efficient risksharing than we had originally: in the original position they were both exposed to the same amount of risk; in the competitive equilibrium A (the relatively less riskaverse) has more of the risk than B (the relatively more riskaverse person) though A is rewarded with a higher expected income, while B has to pay by accepting a lower expected income. [Incidentally this is not a fair insurance market because the relative price is clearly not equal to 1 the ratio of the probabilities. In fact the relative price is less than 1. You might like to ask yourself why.] 25.4: Same Risk Attitudes but Different Endowments Let us explore some other cases. Let us begin with a case in which the individuals have the same risk attitude but different endowments. We take constant absolute risk aversion functions with r = 0.02 for both individuals. You can probably guess where the contract curve is yes half way between the certainty line of A and that of B. We assume different endowments in terms of riskiness but assume the same expected values. Specifically A starts with (100, 25) and B starts with (50, 75). Both have an expected value of 62.5; A s riskiness is ± 37.5 while B s is ± The Edgeworth box is in figure
5 The various allocations are in the table below. Initial allocation Individual A Individual B Society Competitive equilibrium allocation Changes between the two allocations Individual A Individual B Society Individual A Individual B Society The competitive equilibrium is obviously on the contract curve but it is closer to A s origin than to B s. In fact as you will see individual B does rather well out of the deal: starting with a risky income with expected value 62.5 and riskiness ± 12.5, he or she ends up in the competitive equilibrium with (82, 56) which has expected value 69 and riskiness ± 13. He or she accepts a little more riskiness and gets in exchange quite a big increase in the expected value. A, on the other hand, starts out with expected value 62.5 and riskiness ± 37.5 and ends up with (68, 44) which has
6 expected value 56 and riskiness ± 12. He or she accepts a big reduction in the riskiness in exchange for giving up quite a bit of expected value. But then A was initially expose to a lot of risk. 25.5: Similar Endowments but Different Preferences An interesting case is when each individual gets income in just one state of the world: A in state 1 and B in state 2. What do they do? Consider the case when A s ex ante income is 100 in state 1 and 0 in state 2, while B s is 0 in state 1 and 100 in state 2. Between the two of them there is no uncertainty: their joint income is 100 whichever state occurs. So the Edgeworth box is of size 100 by 100 and the endowment point is at the bottom right hand corner. Let us suppose different preferences: A is constant absolute risk averse with parameter r = 0.01 while B is constant absolute risk averse with parameter r = As before the contract curve lies between the two certainty lines but as it happens in this case the certainty lines coincide (with the diagonal from the bottom left to the top right corners), and therefore so does the contract curve. Figure illustrates. The two curves through the endowment point E are the priceoffer curves. They are found in the usual way (see Chapter 8) by finding, for each possible budget line through the initial endowment point, the optimal choice of the individual. They intersect at the point C on the contract curve at the middle of the box. At the competitive equilibrium they are both at the point (50, 50) whichever state of the world happens both have an income 50. This is an interesting case as between the two of them they manage to completely remove the risk that they both had originally. Note also that the slope of the equilibrium budget constraint is 1. Note also that we get this equilibrium, given the endowment, irrespective of the risk aversion of the two individuals. The contract curve is bound to be the main diagonal since this coincides with the certainty line for each of them and so we know that the slopes of both their indifference curves are equal to 1 and hence are equal. Only at point C on the contract curve is the slope of the line joining E and that point on the contract curve also equal to 1. This is quite a reassuring result.
7 25.6: One Risk Neutral Individual When one of the individuals is risk neutral and the other is risk averse, we get a rather nice result. Let A be risk neutral and B risk averse. We get figure In this figure the contract curve coincides with the certainty line of individual B so the competitive equilibrium is on B s certainty line. (It is at the point C given the endowment point E.) So, in fact, wherever is the endowment point, the competitive equilibrium is a position of certainty for individual B moreover, given that the slope of A s priceoffer curve is 1 (equal to the slope of his or her indifference curves) it follows that the expected income of B is the same at the competitive equilibrium as at the endowment point B simply loses the risk. A gets all the risk but he or she does not care as he or she is risk neutral. This example is instructive as it shows that the presence of a riskneutral individual removes the risk from elsewhere. 25.7: Summary We showed that we could use the general exchange apparatus of chapter 8 to examine the exchange of risk between two individuals. We saw that in general some exchange of risk is possible. In some cases we saw the individuals managing to completely eliminate the risk they faced. In others we saw that this was not possible but that some kind of efficient risk sharing was possible usually with the less riskaverse person taking more of the risk. Insurance markets help to achieve an efficient sharing of the risk in society. In general, with an insurance market, the less riskaverse ends up taking more of the risk.
8 In particular, if one individual is riskneutral and the other riskaverse then the former ends up taking all of the risk. 25.8: What if people are not different? Throughout this book, we have argued that, in general, if people are different, then there will be an opportunity for mutually advantage exchange between them. Indeed, we have shown that if we have a simple society of two individuals, who are different in either their preferences or in their endowments, then mutually advantageous trade is possible as long as their initial position is not on the contract curve. In the examples given in the text, if the preferences are identical then the contract curve is the straight line joining the two origins, which passes through the midpoint of the box. It follows, therefore, that if the endowments are identical, we start at the midpoint of the box on the contract curve  and mutually advantageous trade is not possible. Note, however, that in the examples considered so far, we have assumed convex indifference curves. With such curves the proposition is true: if the individuals are identical in both their preferences and their endowments, then mutually advantageous trade is not possible. But, in the context of risky choice, concave indifference curves are possible they simply mean that the individual likes risk. Clearly there are such people in society: you know someone who plays the National Lottery? Consider now two identical, riskloving, individuals. Possible indifference curves are illustrated in the following figure. The income/consumption of individual A is measured from the bottom lefthand origin his or her indifference curves are those that are concave (with respect to that origin). The income/consumption of individual B is measured from the top righthand origin his or her indifference curves are those that are concave (with respect to that origin), and hence are those convex with respect to the bottom lefthand origin. Note that both goods are still good, so moving upwards and rightwards in the box makes A better off and B worse off.
9 Where is the contract curve? We have to be careful. At first glance it would appear to be the line joining A s origin with B s origin, but a moment s reflection will make you realise that points along this line are not efficient. Indeed we can find a direction to move away from this diagonal and increase the welfare of both A and B. For example, moving from the midpoint to either of the corners C or D makes both individuals better off that is, puts them both on higher indifference curves. In fact it can be shown that in this case, the contract curve is the whole of the perimeter of the box: once we are on it we cannot make one individual better off without making the other worse off; if we are off it, we can always find a direction to move and make both individuals better off. You should be aware that the contract curve is in an odd place in this example precisely because both individuals are risklovers. Around the perimeter they are both exposed to risk which is what they like. Now suppose they start with identical endowments the endowment point is that marked E at the centre of the box. Do they want to trade? Can we find a competitive equilibrium? Can we find the priceoffer curves of the two individuals? These are the points to which they would move at given prices. That for A can be shown to be parts of the perimeter of the box: specifically the part from (100,0) to (100,50) and the part from (0,100) to (50,100). These parts are coloured blue in the above figure. Similarly we can find the price offer curve for B: it can be shown to be parts of the perimeter of the box: specifically the part from (50,0) to (100,0) and the part from (0,50) to (0,100). These parts are coloured red in the above figure. Notice that both individuals would choose to move away from the certainty of the midpoint of the box to a risky point on the perimeter 2. These two priceoffer curves intersect at the points C and D the upper lefthand and the lower righthand corners of the box. Note that C and D are on the contract curve. We therefore have two competitive equilibria, at points C and D, with the same equilibrium budget constraint the line joining C and D. 2 Though not any old point.
10 So we have trade, even though the two individuals have identical preferences and endowments. Note the nature of the trade they start off in a completely safe situation, each getting income 50 in whatever state of the world happens. But they are risklovers, preferring risk to certainty. So they trade to a position in which one gets income 100 in one state of the world and 0 in the other, while it is the other way round for the other individual. It is just as if they agree to a bet: A pays to B 100 if something happens and B pays 100 to A if it does not happen. They are both happier than not having this bet (because points C and D are on higher indifference curves than point E for both of them). They are happier with the bet than without it. Do you not know people like that?
11
Chapter 14: Production Possibility Frontiers
Chapter 14: Production Possibility Frontiers 14.1: Introduction In chapter 8 we considered the allocation of a given amount of goods in society. We saw that the final allocation depends upon the initial
More informationChapter 22: Exchange in Capital Markets
Chapter 22: Exchange in Capital Markets 22.1: Introduction We are now in a position to examine trade in capital markets. We know that some people borrow and some people save. After a moment s reflection
More information13 Externalities. Microeconomics I  Lecture #13, May 12, 2009
Microeconomics I  Lecture #13, May 12, 2009 13 Externalities Up until now we have implicitly assumed that each agent could make consumption or production decisions without worrying about what other agents
More informationChapter 27: Taxation. 27.1: Introduction. 27.2: The Two Prices with a Tax. 27.2: The PreTax Position
Chapter 27: Taxation 27.1: Introduction We consider the effect of taxation on some good on the market for that good. We ask the questions: who pays the tax? what effect does it have on the equilibrium
More informationECO 317 Economics of Uncertainty Fall Term 2009 Week 2 Precept September 30 Expected Utility and Risk Aversion Solutions
ECO 37 Economics of Uncertainty Fall Term 2009 Week 2 Precept September 30 Expected Utility and Risk Aversion Solutions First a recap from the question we considered last week (September 23), namely representing
More informationLecture 11 Uncertainty
Lecture 11 Uncertainty 1. Contingent Claims and the StatePreference Model 1) Contingent Commodities and Contingent Claims Using the simple twogood model we have developed throughout this course, think
More informationDecision & Risk Analysis Lecture 6. Risk and Utility
Risk and Utility Risk  Introduction Payoff Game 1 $14.50 0.5 0.5 $30  $1 EMV 30*0.5+(1)*0.5= 14.5 Game 2 Which game will you play? Which game is risky? $50.00 Figure 13.1 0.5 0.5 $2,000  $1,900 EMV
More information1 Uncertainty and Preferences
In this chapter, we present the theory of consumer preferences on risky outcomes. The theory is then applied to study the demand for insurance. Consider the following story. John wants to mail a package
More informationChapter 21: The Discounted Utility Model
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
More informationLecture notes for Choice Under Uncertainty
Lecture notes for Choice Under Uncertainty 1. Introduction In this lecture we examine the theory of decisionmaking under uncertainty and its application to the demand for insurance. The undergraduate
More informationTopic 7 General equilibrium and welfare economics
Topic 7 General equilibrium and welfare economics. The production possibilities frontier is generated using a production Edgeworth box diagram with the input goods on the axes. The following diagram illustrates
More informationRisk and Insurance. Vani Borooah University of Ulster
Risk and Insurance Vani Borooah University of Ulster Gambles An action with more than one possible outcome, such that with each outcome there is an associated probability of that outcome occurring. If
More informationChapter 29: Natural Monopoly and Discrimination
Chapter 29: Natural Monopoly and Discrimination 29.1: Introduction This chapter discusses two things, both related to the fact that, in the presence of a monopoly, there is less surplus generated in the
More informationEconomics 100A Prof. McFadden Fall 2001 Due the week of 11/26/01. Answer Key to Problem Set #11
Economics 100 Prof. McFadden Fall 01 Due the week of 11/26/01 nswer Key to Problem Set #11 1. Currently, there is an incumbent monopoly in the market. Next year, a potential entrant may. The incumbent
More informationPART IV INFORMATION, MARKET FAILURE, AND THE ROLE OF GOVERNMENT CHAPTER 16 GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY
PART IV INFORMATION, MARKET FAILURE, AND THE ROLE OF GOVERNMENT CHAPTER 6 GENERAL EQUILIBRIUM AND ECONOMIC EFFICIENCY QUESTIONS FOR REVIEW. Why can feedback effects make a general equilibrium analysis
More informationProblem Set 2  Answers. Gains from Trade and the Ricardian Model
Page 1 of 11 Gains from Trade and the Ricardian Model 1. Use community indifference curves as your indicator of national welfare in order to evaluate the following claim: An improvement in the terms of
More informationChoice Under Uncertainty Insurance Diversification & Risk Sharing AIG. Uncertainty
Uncertainty Table of Contents 1 Choice Under Uncertainty Budget Constraint Preferences 2 Insurance Choice Framework Expected Utility Theory 3 Diversification & Risk Sharing 4 AIG States of Nature and Contingent
More informationChoice under Uncertainty
Choice under Uncertainty Theoretical Concepts/Techniques Expected Utility Theory Representing choice under uncertainty in statecontingent space Utility Functions and Attitudes towards Risk Risk Neutrality
More informationChapter 6  Practice Questions
Chapter 6  Practice Questions 1. If a Tbill pays 5 percent, which of the following investments would not be chosen by a riskaverse investor? A) An asset that pays 10 percent with a probability of 0.60
More informationChoice under Uncertainty
Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory
More informationGeneral Equilibrium. The Producers
General Equilibrium In this section we will combine production possibilities frontiers and community indifference curves in order to create a model of the economy as a whole. This brings together producers,
More information2. Efficiency and Perfect Competition
General Equilibrium Theory 1 Overview 1. General Equilibrium Analysis I Partial Equilibrium Bias 2. Efficiency and Perfect Competition 3. General Equilibrium Analysis II The Efficiency if Competition The
More informationWhen the price of a good rises (falls) and all other variables affecting the
ONLINE APPENDIX 1 Substitution and Income Effects of a Price Change When the price of a good rises (falls) and all other variables affecting the consumer remain the same, the law of demand tells us that
More informationSELECTION IN INSURANCE MARKETS by Steven E. Landsburg University of Rochester
SELECTION IN INSURANCE MARKETS by Steven E. Landsburg University of Rochester Consider an insurance market say, for insurance against accidental injuries. Agents face different levels of accident risk,
More informationSome Notes on Taylor Polynomials and Taylor Series
Some Notes on Taylor Polynomials and Taylor Series Mark MacLean October 3, 27 UBC s courses MATH /8 and MATH introduce students to the ideas of Taylor polynomials and Taylor series in a fairly limited
More informationEconomics of Insurance
Economics of Insurance In this last lecture, we cover most topics of Economics of Information within a single application. Through this, you will see how the differential informational assumptions allow
More informationLecture 13: Risk Aversion and Expected Utility
Lecture 13: Risk Aversion and Expected Utility Uncertainty over monetary outcomes Let x denote a monetary outcome. C is a subset of the real line, i.e. [a, b]. A lottery L is a cumulative distribution
More informationGeneral Equilibrium Analysis and Economic Efficiency
CHAPTER 19 General Equilibrium Analysis and Economic Efficiency How is equilibrium determined in all markets simultaneously and to what extent do markets promote the wellbeing of the members of a society
More informationProblem Set #5Key. Economics 305Intermediate Microeconomic Theory
Problem Set #5Key Sonoma State University Economics 305Intermediate Microeconomic Theory Dr Cuellar (1) Suppose that you are paying your for your own education and that your college tuition is $200 per
More informationThe Graphical Method: An Example
The Graphical Method: An Example Consider the following linear program: Maximize 4x 1 +3x 2 Subject to: 2x 1 +3x 2 6 (1) 3x 1 +2x 2 3 (2) 2x 2 5 (3) 2x 1 +x 2 4 (4) x 1, x 2 0, where, for ease of reference,
More informationChapter 5 Uncertainty and Consumer Behavior
Chapter 5 Uncertainty and Consumer Behavior Questions for Review 1. What does it mean to say that a person is risk averse? Why are some people likely to be risk averse while others are risk lovers? A riskaverse
More informationProblem Set 6  Answers
Page 1 of 15 Problem Set 6 Tariffs  Answers 1. The graph below shows domestic supply and demand for a good in a small country. Suppose that it faces a world price of the good of $4 per pound. Show the
More informationNoBetting Pareto Dominance
NoBetting Pareto Dominance Itzhak Gilboa, Larry Samuelson and David Schmeidler HEC Paris/Tel Aviv Yale Interdisciplinary Center Herzlyia/Tel Aviv/Ohio State May, 2014 I. Introduction I.1 Trade Suppose
More informationindustry depends on both the relative productivities of the industries and the relative wages across industries.
1. a. The production possibility curve is a straight line that intercepts the apple axis at 400 (1200/3) and the banana axis at 600 (1200/2). b. The opportunity cost of apples in terms of bananas is 3/2.
More informationChapter 16 General Equilibrium and Economic Efficiency
Chapter 16 General Equilibrium and Economic Efficiency Questions for Review 1. Why can feedback effects make a general equilibrium analysis substantially different from a partial equilibrium analysis?
More informationThe fundamental question in economics is 2. Consumer Preferences
A Theory of Consumer Behavior Preliminaries 1. Introduction The fundamental question in economics is 2. Consumer Preferences Given limited resources, how are goods and service allocated? 1 3. Indifference
More informationSUPPLEMENT TO CHAPTER
SUPPLEMENT TO CHAPTER 6 Linear Programming SUPPLEMENT OUTLINE Introduction and Linear Programming Model, 2 Graphical Solution Method, 5 Computer Solutions, 14 Sensitivity Analysis, 17 Key Terms, 22 Solved
More informationTaylor Polynomials and Taylor Series Math 126
Taylor Polynomials and Taylor Series Math 26 In many problems in science and engineering we have a function f(x) which is too complicated to answer the questions we d like to ask. In this chapter, we will
More informationCompetitive Market Equilibrium
Chapter 14 Competitive Market Equilibrium We have spent the bulk of our time up to now developing relationships between economic variables and the behavior of agents such as consumers, workers and producers.
More informationc 2008 Je rey A. Miron We have described the constraints that a consumer faces, i.e., discussed the budget constraint.
Lecture 2b: Utility c 2008 Je rey A. Miron Outline: 1. Introduction 2. Utility: A De nition 3. Monotonic Transformations 4. Cardinal Utility 5. Constructing a Utility Function 6. Examples of Utility Functions
More informationChulalongkorn University: BBA International Program, Faculty of Commerce and Accountancy. Solution to Selected Questions: CHAPTER 3 CONSUMER BEHAVIOR
Chulalongkorn University: BBA International Program, Faculty of Commerce and Accountancy 2900111 (Section 1) Chairat Aemkulwat Economics I: Microeconomics Spring 2015 Solution to Selected Questions: CHAPTER
More informationEconomics 1011a: Intermediate Microeconomics
Lecture 12: More Uncertainty Economics 1011a: Intermediate Microeconomics Lecture 12: More on Uncertainty Thursday, October 23, 2008 Last class we introduced choice under uncertainty. Today we will explore
More informationARE211, Fall2012. Contents. 2. Linear Algebra Preliminary: Level Sets, upper and lower contour sets and Gradient vectors 1
ARE11, Fall1 LINALGEBRA1: THU, SEP 13, 1 PRINTED: SEPTEMBER 19, 1 (LEC# 7) Contents. Linear Algebra 1.1. Preliminary: Level Sets, upper and lower contour sets and Gradient vectors 1.. Vectors as arrows.
More informationTastes and Indifference Curves
C H A P T E R 4 Tastes and Indifference Curves This chapter begins a 2chapter treatment of tastes or what we also call preferences. In the first of these chapters, we simply investigate the basic logic
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
More informationInsurance. Michael Peters. December 27, 2013
Insurance Michael Peters December 27, 2013 1 Introduction In this chapter, we study a very simple model of insurance using the ideas and concepts developed in the chapter on risk aversion. You may recall
More informationManagerial Economics
Managerial Economics Unit 9: Risk Analysis Rudolf WinterEbmer Johannes Kepler University Linz Winter Term 2012 Managerial Economics: Unit 9  Risk Analysis 1 / 1 Objectives Explain how managers should
More informationThe Theory and Practice of Using a Sine Bar, version 2
The Theory and Practice of Using a Sine Bar, version 2 By R. G. Sparber Copyleft protects this document. 1 The Quick Answer If you just want to set an angle with a sine bar and stack of blocks, then take
More informationCHAPTER 3 CONSUMER BEHAVIOR
CHAPTER 3 CONSUMER BEHAVIOR EXERCISES 2. Draw the indifference curves for the following individuals preferences for two goods: hamburgers and beer. a. Al likes beer but hates hamburgers. He always prefers
More informationLecture 10  Risk and Insurance
Lecture 10  Risk and Insurance 14.03 Spring 2003 1 Risk Aversion and Insurance: Introduction To have a passably usable model of choice, we need to be able to say something about how risk affects choice
More informationFundamentals of Operations Research Prof.G. Srinivasan Department of Management Studies Lecture No. # 03 Indian Institute of Technology, Madras
Fundamentals of Operations Research Prof.G. Srinivasan Department of Management Studies Lecture No. # 03 Indian Institute of Technology, Madras Linear Programming solutions  Graphical and Algebraic Methods
More informationProspect Theory Ayelet Gneezy & Nicholas Epley
Prospect Theory Ayelet Gneezy & Nicholas Epley Word Count: 2,486 Definition Prospect Theory is a psychological account that describes how people make decisions under conditions of uncertainty. These may
More informationClarkeGroves mechanisms for optimal provision of public goods
ClarkeGroves mechanisms for optimal provision of public goods Yossi Spiegel Consider an economy with one public good G, and one private good y. If the preferences of all agents in the economy are common
More informationQuiz Sensitivity Analysis
1 Quiz Sensitivity Analysis 1. The difference between the righthand side (RHS) values of the constraints and the final (optimal) value assumed by the lefthand side (LHS) formula for each constraint is
More informationMidterm Exam:Answer Sheet
Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a riskfree and risky asset, with returns given by r f and E(r p ), respectively. Let y be the
More informationBasic Utility Theory for Portfolio Selection
Basic Utility Theory for Portfolio Selection In economics and finance, the most popular approach to the problem of choice under uncertainty is the expected utility (EU) hypothesis. The reason for this
More informationKnots as mathematical objects
Knots as mathematical objects Ulrich Krähmer = Uli U Glasgow Ulrich Krähmer = Uli (U Glasgow) Knots as mathematical objects 1 / 26 Why I decided to speak about knots They are a good example to show that
More informationDecision Tree Analysis for the Risk Averse Organization
Go to the website ~ www.projectrisk.com Introduction Decision Tree Analysis for the Risk Averse Organization By David T. Hulett, Ph.D. The decision tree analysis technique for making decisions in the presence
More informationEconomics of incomplete information
Economics of incomplete information Traditional microeconomic analysis deals with economic agents making decisions under complete information. Examples of such assumptions: Consumers know the utility they
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 15 scale to 0100 scores When you look at your report, you will notice that the scores are reported on a 0100 scale, even though respondents
More informationAn Introduction to Utility Theory
An Introduction to Utility Theory John Norstad jnorstad@northwestern.edu http://www.norstad.org March 29, 1999 Updated: November 3, 2011 Abstract A gentle but reasonably rigorous introduction to utility
More informationAnswer Key to Problem Set #2: Expected Value and Insurance
Answer Key to Problem Set #2: Expected Value and Insurance 1. (a) We have u (w) = 1 2 w 1 2, so u (w) = 1 4 w 3 2. As we will see below, u (w) < 0 indicates that the individual is riskaverse. (b) The
More informationDemand for Health Insurance
Demand for Health Insurance Demand for Health Insurance is principally derived from the uncertainty or randomness with which illnesses befall individuals. Consequently, the derived demand for health insurance
More informationTrade and Technology: The Ricardian Model. Professor Ralph Ossa International Commercial Policy
Trade and Technology: The Ricardian Model Professor Ralph Ossa 33501 Introduction Countries trade either because they are different from one another or because of increasing returns to scale. Countries
More informationWeek 1 Efficiency in Production and in Consumption and the Fundamental Theorems of Welfare Economics
1. Introduction Week 1 Efficiency in Production and in Consumption and the Fundamental Theorems of Welfare Economics Much of economic theory of the textbook variety is a celebration of the free market
More informationOn the optimality of optimal income taxation
Preprints of the Max Planck Institute for Research on Collective Goods Bonn 2010/14 On the optimality of optimal income taxation Felix Bierbrauer M A X P L A N C K S O C I E T Y Preprints of the Max Planck
More informationChapter 12: Cost Curves
Chapter 12: Cost Curves 12.1: Introduction In chapter 11 we found how to minimise the cost of producing any given level of output. This enables us to find the cheapest cost of producing any given level
More informationRisk and Uncertainty. Vani K Borooah University of Ulster
Risk and Uncertainty Vani K Borooah University of Ulster Basic Concepts Gamble: An action with more than one possible outcome, such that with each outcome there is an associated probability of that outcome
More informationReview of Utility Theory, Expected Utility
Review of Utility Theory, Expected Utility Utility theory is the foundation of neoclassical economic demand theory. According to this theory, consumption of goods and services provides satisfaction, or
More informationDecentralization and Private Information with Mutual Organizations
Decentralization and Private Information with Mutual Organizations Edward C. Prescott and Adam Blandin Arizona State University 09 April 2014 1 Motivation Invisible hand works in standard environments
More information1. Briefly explain what an indifference curve is and how it can be graphically derived.
Chapter 2: Consumer Choice Short Answer Questions 1. Briefly explain what an indifference curve is and how it can be graphically derived. Answer: An indifference curve shows the set of consumption bundles
More informationTOPIC 4: DERIVATIVES
TOPIC 4: DERIVATIVES 1. The derivative of a function. Differentiation rules 1.1. The slope of a curve. The slope of a curve at a point P is a measure of the steepness of the curve. If Q is a point on the
More informationUNIVERSITY OF VIENNA
WORKING PAPERS Egbert Dierker Hildegard Dierker Birgit Grodal Nonexistence of Constrained Efficient Equilibria when Markets are Incomplete August 2001 Working Paper No: 0111 DEPARTMENT OF ECONOMICS UNIVERSITY
More informationAn example of externalities  the multiplicative case
An example of externalities  the multiplicative case Yossi Spiegel Consider an exchange economy with two agents, A and B, who consume two goods, x and y. This economy however, differs from the usual exchange
More informationLecture Notes 5: General Equilibrium. mrkts
Lecture Notes 5: General Equilibrium We are now ready to analyze the equilibrium in all markets, that is why this type of analysis is called general equilibrium analysis. Recall our graphical overview
More informationDecision Analysis. Here is the statement of the problem:
Decision Analysis Formal decision analysis is often used when a decision must be made under conditions of significant uncertainty. SmartDrill can assist management with any of a variety of decision analysis
More informationECON 301: General Equilibrium I (Exchange) 1. Intermediate Microeconomics II, ECON 301. General Equilibrium I: Exchange
ECON 301: General Equilibrium I (Exchange) 1 Intermediate Microeconomics II, ECON 301 General Equilibrium I: Exchange The equilibrium concepts you have used till now in your Introduction to Economics,
More informationLecture 3 The Standard Trade Model
Lecture 3 he Standard rade Model he previous model assumed a fixed coefficient technology: α and β of capital and labour were required to produce one computer and α and β of capital and labour were needed
More informationNotes  Gruber, Public Finance Section 12.1 Social Insurance What is insurance? Individuals pay money to an insurer (private firm or gov).
Notes  Gruber, Public Finance Section 12.1 Social Insurance What is insurance? Individuals pay money to an insurer (private firm or gov). These payments are called premiums. Insurer promises to make a
More informationChapter 6. Noncompetitive Markets 6.1 SIMPLE MONOPOLY IN THE COMMODITY MARKET
Chapter 6 We recall that perfect competition was theorised as a market structure where both consumers and firms were price takers. The behaviour of the firm in such circumstances was described in the Chapter
More informationQuestion 1: (35 points)
The grade distribution was as follows: General comments: EO 352 Spring 10 International Trade Problem Set 2 Answer Key Score/range 100 9099 8089 7079 6069 5059 Number of students 14 6 2 3 5 5 1. Overall
More information(Refer Slide Time: 00:00:56 min)
Numerical Methods and Computation Prof. S.R.K. Iyengar Department of Mathematics Indian Institute of Technology, Delhi Lecture No # 3 Solution of Nonlinear Algebraic Equations (Continued) (Refer Slide
More informationUnraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets
Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that
More informationAdvanced Electric Drives Prof. S.P. Das Department of Electrical Engineering Indian Institute of Technology, Kanpur. Lecture 30
Advanced Electric Drives Prof. S.P. Das Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture 30 Hello and welcome to this lecture on advanced electric drives. In the last
More informationThe Theory of Consumer Equilibrium
The Theory of Consumer Equilibrium The consumer problem is defined thus: assuming a given income (M) Assuming the consumer has full knowledge of all available goods and services, and their prices Assuming
More informationFall 2007 PHY126 Experiment 8 LENS OPTICS. 1 s + 1 s' = 1 f
Fall 2007 PHY126 Experiment 8 LENS OPTICS In this experiment we will investigate the imageforming properties of lenses, using the thinlens equation: 1 s + 1 s' = 1 f where s and s are the object and
More informationDemand and supply of health insurance. Folland et al Chapter 8
Demand and supply of health Folland et al Chapter 8 Chris Auld Economics 317 February 9, 2011 What is insurance? From an individual s perspective, insurance transfers wealth from good states of the world
More informationMaths Vocabulary Support Booklet
Maths Vocabulary Support Booklet The aim of this booklet is to help parents to understand and use the technical maths vocabulary accurately and confidently so you can help your children to do the same.
More informationChapter 3 Consumer Behavior
Chapter 3 Consumer Behavior Read Pindyck and Rubinfeld (2013), Chapter 3 Microeconomics, 8 h Edition by R.S. Pindyck and D.L. Rubinfeld Adapted by Chairat Aemkulwat for Econ I: 2900111 1/29/2015 CHAPTER
More informationWhat Is Risk and How Can We Manage It? By William C. Wood
What Is Risk and How Can We Manage It? By William C. Wood Risk is defined as the possibility that an injury or loss will occur, and there is risk in everything. To see this, consider whether there is any
More information2. Information Economics
2. Information Economics In General Equilibrium Theory all agents had full information regarding any variable of interest (prices, commodities, state of nature, cost function, preferences, etc.) In many
More informationMoral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania
Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 PrincipalAgent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically
More informationMATH MODULE 11. Maximizing Total Net Benefit. 1. Discussion M111
MATH MODULE 11 Maximizing Total Net Benefit 1. Discussion In one sense, this Module is the culminating module of this Basic Mathematics Review. In another sense, it is the starting point for all of the
More informationSimultaneous linear equations
Simultaneous linear equations The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding
More informationCOLLABORATIVE PROJECTS IN CALCULUS I. John D. Baildon Penn State Worthington Scranton Dunmore PA 18512
COLLABORATIVE PROJECTS IN CALCULUS I John D. Baildon (JDB8@PSU.EDU) Penn State Worthington Scranton Dunmore PA 18512 ABSTRACT: Students often benefit from testing their understanding of calculus concepts
More informationCHAPTER 4 INDIVIDUAL AND MARKET DEMAND
CHAPTER 4 INDIVIDUAL AND MARKET DEMAND EXERCISES 1. The ACME corporation determines that at current prices the demand for its computer chips has a price elasticity of 2 in the short run, while the price
More informationThe Fisher Model. and the. Foundations of the Net Present Value Rule
The Fisher Model and the Foundations of the Net Present Value Rule Dr. Richard MacMinn mailto:macminn@mail.utexas.edu Finance 374c Introduction Financial markets perform of role of allowing individuals
More informationIncreasing Returns to Scale
Increasing Returns to Scale 1 New Trade Theory According to traditional trade theories (Ricardian, speci c factors and HOS models), trade occurs due to existing comparative advantage between countries
More informationUsing 3 D SketchUp Design Software. Building Blocks Tools
Using 3 D SketchUp Design Software Building Blocks Tools Introduction Google s SketchUp is an easy to use drawing program capable of building 3 dimensional (or 3 D) objects (SketchUp also does 2 D easily).
More information(Refer Slide Time: 1:21)
Introduction to Computer Graphics Dr. Prem Kalra Department of Computer Science and Engineering Indian Institute of Technology, Delhi Lecture  5 Polygon Clipping and Polygon Scan Conversion We have been
More information