The Fabric Of Felicity

The Fabric of Felicity Presented by: Rajan Thakur Fin700

Introduction Which risk should we take?  Which risk should we hedge?  What information is relevant?  How confident do we hold our beliefs about the future?  And ultimately, how do we introduce management into dealing with risk? 

What is essential to decisionmaking? From preference to utility In the market, people respond to new information on the basis of a clearly defined preferences.  Preference means liking one thing better than another.  How to measuring our preferences? With the concept of Utility. 

The concept of Utility Daniel Bernoulli  Jeremy Bentham  William Stanley Jevons 

Daniel Bernoulli (29 January 1700 – Basel, 27 July 1782)

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Born in Groningen, Netherlands. Dutch-Swiss mathematician. He spent most of his career in University of Basel. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.

Bernoulli’s concept of Utility 

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Daniel Bernoulli first introduced the utility as the unit for measuring preferences—for calculating how much we like one thing more than another. The amount that people are willing to pay for desirable things differs from one person to another. The more we have of something, the less we are willing to pay to get more.

Comment of Bernoulli’s work 

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Bernoulli’s Utility concept provide definition, quantification, and guides to rational decisions in risk evaluation. Most later development of utility theory were new discoveries rather than extensions of Bernoulli’s original formulations. An impressive innovation, but with some limitation due to its one-dimensional.

Jeremy Bentham (15 February 1748–6 June 1832)

Born in Spitalfields, London.  English jurist, philosopher, and legal and social reformer.  He was a political radical, and a leading theorist in Anglo-American philosophy of law.  He is best known for his advocacy of utilitarianism, for the concept of animal rights, and his opposition to the idea of natural rights. 

Bentham’s concept of utility  

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Major work: “The Principles of Morals and Legislation. ” Published in 1789. The property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness…when the tendency it has to augment the happiness of the community is greater than any it has to diminish it. Focus on whether one opportunity was superior to another.

Comment on Bentham’s work  

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Actually, Bentham’s concept of utility was only a talking about life in general. But it was attracted most of economists in nineteenth century to use utility as a tool to discover how prices result from interactive decision by buyer and seller. His detour directly led to the law of supply and demand. The possibility of loss was still not a consideration in Bentham’s work.

William Stanley Jevons (September 1, 1835 - August 13, 1882)

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Born in Liverpool, England. English economist and logician. Earned his B.A. and M.A. degrees at University of London. Spent most of his life time as professor is Owens College and University College, London. On the 13 August 1882 he was drowned whilst bathing near Hastings. Only 45.

Jevons’ improvement on Utility Theory Masterwork: The Theory of Political Economy. 1871. Main argument:  Value depends entirely upon utility.  Utility varies with the quantity of a commodity already in one’s possession.  The degree of utility of a commodity is some continuous mathematical function of the quantity of the commodity available 

Comment of Jevons’ work Made big efforts to introduce mathematics into economics.  Attract the attention of an indifferent public to the field of economy.  Did not explicitly distinguish between the concepts of ordinal and cardinal utility. 

About economy fluctuation Jevons found that economy do fluctuate over time.  Jevons came up with a theory based on the influence of sunspots on weather, of weather on harvests, and of harvests on prices, wages, and the level of employment. 

Modern version Of Utility Theory

Definition 

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In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. Given the measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility. For illustrative purposes, changes in utility are sometimes expressed in units called utils.

Cardinal and Ordinal Utility 

Cardinal utility The utility (roughly, satisfaction) gained from a particular good or service can be measured and that the magnitude of the measurement is meaningful.

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Ordinal utility The utility of a particular good and service cannot be measured using an objective scale, a consumer is capable of ranking different alternatives available. Goods are often considered in ‘bundles’ or ‘baskets’.

Utility functions 

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While preferences are the conventional foundation of microeconomics, it is often convenient to represent preferences with a utility function and reason indirectly about preferences with utility functions. Let X be the consumption set, the set of all mutuallyexclusive packages the consumer could conceivably consume. The consumer's utility function ranks each package in the consumption set. If u(x) ≥ u(y), then the consumer strictly prefers x to y or is indifferent between them.

Example of utility function 

Suppose a consumer's consumption: set is X = {nothing, 1 apple, 1 orange, 1 apple and 1 orange, 2 apples, 2 oranges}

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Utility function u(nothing) = 0 u (1 orange)= 2 u (2 oranges) = 3

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u (1 apple) = 1 u (2 apples) = 2 u (1 apple and 1 orange) = 4

Conclusion:This consumer prefers 1 orange to 1 apple, but prefers one of each to 2 oranges.

Some assumptions of utility functions In order to simplify calculations, various assumptions have been made of utility functions.  CES (constant elasticity of substitution, or isoelastic) utility  Exponential utility  Quasilinear utility  Homothetic utility

Expected utility 

Definition: The "betting preferences" of people with regard to uncertain outcomes can be described by a mathematical relation which takes into account the size of a payout , the probability of occurrence, risk aversion, and the different utility of the same payout to people with different assets or personal preferences.

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The expected utility theory deals with the analysis of choices among risky projects with (possibly multidimensional) outcomes.

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The expected utility model was first proposed by Nicholas Bernoulli in 1713 and solved by Daniel Bernoulli in 1738 as the St. Petersburg paradox.

Inadequacy of expected value 

A very simple economic theory is that outcomes with a higher expected value are always preferred.

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For example, the expected value of getting a $100 payment with a 1 in 80 chance is $1.25. Given the choice between this gamble and a guaranteed payment of $1, by this simple theory, people should choose the $100 gamble.

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A key insight is that people do not consider real assets and "expected" assets to be equivalent. In the example, no one will ever end up with a payment of $1.25; real payments are made only in the amounts of $0, $1, and $100.

Conclusion 

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Theory of how people make decisions and choices had been detached in our everyday life, especially in the investment market. With the concept of utility, we can precisely determine different people’s risk preference. Once risk preference is determined, expected return can be calculated and investment can be finally made.

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