Utility Theory

First: Cardinal

Second: Ordinal

Third: Cardinal

In Essence the Principle of Utility has two routes

A d am S m ith

N atu ra l Id en tity

Je rem y B en th am

A rtific ia l Id en tity

P rin c ip le o fU tility

Jeremy Bentham

• February 15, 1748-June 6, 1832• The philosopher and jurist Jeremy Bentham (1748-1832)

was born in Spitalfields, London, on 15 February 1748. He proved to be something of a child prodigy: while still a toddler he was discovered sitting at his father's desk reading a multi-volume history of England, and he began to study Latin at the age of three. At twelve, he was sent to Queen's College Oxford, his father, a prosperous attorney, having decided that Jeremy would follow him into the law, and feeling quite sure that his brilliant son would one day be Lord Chancellor of England.

Jeremy Bentham

• Bentham, however, soon became disillusioned with the law, especially after hearing the lectures of the leading authority of the day, Sir William Blackstone (1723-80). Instead of practising the law, he decided to write about it, and he spent his life criticising the existing law and suggesting ways for its improvement. His father's death in 1792 left him financially independent, and for nearly forty years he lived quietly in Westminster, producing between ten and twenty sheets of manuscript a day, even when he was in his eighties.

Jeremy Bentham

• Bentham is often credited with being one of the founders of the University of London, the forerunner of today's University College London. This is not, in fact, true. Bentham was eighty years of age when the new University opened its doors in 1828, and took no part in the campaign to bring it into being. However, the myth of his participation has been perpetuated in a mural by Henry Tonks (1862-1937), in the dome above the Flaxman gallery in the main UCL library

Jeremy Bentham

• Yet although Bentham played no direct part in the establishment of UCL, he still deserves to be considered as its spiritual father. Many of the founders, particularly James Mill (1773-1836) and Henry Brougham (1778-1868), held him in high esteem, and their project embodied many of his ideas on education and society.

Jeremy Bentham

Jeremy Bentham

• The cabinet contains Bentham's preserved skeleton, dressed in his own clothes, and surmounted by a wax head. Bentham requested that his body be preserved in this way in his will made shortly before his death on 6 June 1832. The cabinet was moved to UCL in 1850.

Jeremy BenthamNot surprisingly, this peculiar relic has given rise to

numerous legends and anecdotes. One of the most commonly recounted is that the Auto-Icon regularly attends meetings of the College Council, and that it is solemnly wheeled into the Council Room to take its place among the present-day members. Its presence, it is claimed, is always recorded in the minutes with the words Jeremy Bentham - present but not voting. Another version of the story asserts that the Auto-Icon does vote, but only on occasions when the votes of the other Council members are equally split. In these cases the Auto-Icon invariably votes for the motion.

Extract from Jeremy Bentham's Last Will and Testament

My body I give to my dear friend Doctor Southwood Smith to be disposed of in a manner hereinafter mentioned, and I direct ... he will take my body under his charge and take the requisite and appropriate measures for the disposal and preservation of the several parts of my bodily frame in the manner expressed in the paper annexed to this my will and at the top of which I have written Auto Icon.

Extract from Jeremy Bentham's Last Will and Testament

If it should so happen that my personal friends and other disciples should be disposed to meet together on some day or days of the year for the purpose of commemorating the founder of the greatest happiness system of morals and legislation my executor will from time to time cause to be conveyed to the room in which they meet the said box or case with the contents therein to be stationed in such part of the room as to the assembled company shall seem meet .

Jeremy Bentham

• February 15, 1748-June 6, 1832• Introduction of Morals and

Legislation (1789)• “Nature has placed mankind under the

governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do as well as to determine what we shall do” (p.17)

Natural Harmony

• Remember that for Adam Smith the “self” would with the check of the market lead to “economic progress”

• Bentham did not see Natural Harmony– Example is that fact that there is CRIME

Bentham’s Central Point• Interest of the Individual must be identified

with the general interest, and that it was the business of the legislatures to bring about this identification through direct intercession.

• Bentham is similar to the Greek Hedonism philosophy

• Differs: “The greatest happiness for the greatest number (of individuals)”

“Moral Arithmetic”

• Influenced by Newton he not only his work to scientific but thought that if there was a possibility of measurement than legislatures could measure Social Welfare

• Pleasure are added at the individual level but multiplied by the number of individuals

The Felicific Calculus

• The Intensity of Pleasure or Pain

• Its duration• Its Certainty or

uncertainty

• Its propinquity or remoteness

• Its fecundity, or the chance it has of being followed by sensations of the same kind– Pleasure Pleasure

– Pain Pain

The Felicific Calculus• Its purity, or the chance that it has of not being

followed by sensations of the opposite kind– Pleasure Pain– Pain Pleasure

• Its extent, that is, the number of people who are affected by it

• NOTE: fecundity and purity are not inherent properties of pleasure or pain, thus, only matter in the aggregate of an event

Measure of Social Welfare on a Given ACT• First for any given one person of those

whose interest seem most immediately to affected by it: and take account:– Of the value of each distinguishable pleasure

which appears to be produced in the first instance

– Of the value of each pain which appears to be produced by it in the first instance

Measure of Social Welfare on a Given ACT (cont.)• Of the value of each pleasure which appears

to be produced by it after the first. This constitutes the fecundity of the first pleasure and the impurity of the first pain

• Of the value of each pleasure which appears to be produced by it after the first. This constitutes the fecundity of the first pain and the impurity of the first pleasure

Measure of Social Welfare on a Given ACT (cont.)• Sum up all the values of all the pleasures on

the one side, and those of all the pains on the other. The balance, if it be on the side of pleasure, will give the good tendency of the act upon the whole, with respect to the interests of that individual person; if on the side of pain, the bad tendency of it upon the whole.

Measure of Social Welfare on a Given ACT (cont.)• Take the people that appear to be concerned

find those that have a pleasure balance and add up their degrees of pleasure; then take those that have a pain balance and add up their degrees of pain. Take a balance and that yields the social welfare impact

Finals Remarks on Bentham

• How to compare across individuals

• Problems in weighting: for instance, which produces higher pleasure (or pain): those of the mind or the body.

• Fallacy of Composition– what is true of the parts may not be true of the

whole

Arsine-JulesEmile-Juvenal Dupuit

1804-1866

Born in Fossano, Italy which at the time was under French domination

Jules Dupuit

• Graduated from the School of Civil Engineering in Paris

• He was one of the great engineers of his time.

• In 1855, he was name Inspector-General of Civil Engineering

• Took the study of political economy more as an avocation rather than a profession

Dupuit’s Approach

• Combined three elements to produce analytical tools:– subjects of economic interest and importance– relevant, observed facts and statistics from

these subjects– mathematical analysis-deductive logic and

graphical depiction- to organize and reorganize relations suggested by these facts and statistics.

Marginal Utility and Demand

• Early work of Gregory King (1648-1712), which was refined by the work of Charles Davenant (1656-1714), found the inverse relationship between price and quantity.

• The work by Davenant is:– An Essay upon the Probable Method of Making

a People Gainers in the Balance of Trade (1699)

• The King-Davenant law of Demand

King-Davenant’s Law of Demand

Defect Above theCommon Rate

1 tenth 3 tenths

2 tenths Raises 8 tenths

3 tenths the 1.6 tenths

4 tenths price 2.8 tenths

5 tenths 4.5 tenths

Marginal Utility and Demand(Jules Dupuit)

• Using the example of Water consumed in a city he argued that if it was difficult to obtain the water and they had to pay 50 Francs and they purchased it that it had to provide the household with at least that much utility

Dupuit and Marginal Utility

• However, he argued that as more water was introduced to the city the time would come when the households would not require more

• Consequently, the concept of the Law of Diminishing Mariginal Utility

Dupuit’s Argument

Quantity of Water

MU=Price

p1

q1

p2

q2

Dupuit’s Consumer Surplus

O Price

Quantity

p

r1

p1

r2

p2

Thus, if price is p1 consumer paysOr1p1 and the consumer surplus isr1p1P

Consumers’ Surplus, Monopoly, and Discrimination

Tariff # of Passengers UtilityYield of the TollGross Net

0123456789101112

10080635041332620149630

4454253913523162762341921449969360

:2 f @

0 -200 80 -80126 0150 50164 82165 99156 104140 100112 84 81 63 60 48 33 27 0 0

William Stanley Jevons

1835-1882

(drowned just short of 47)

W. S. Jevons

• Raised in a Unitarian Environment– (educated but not academic)

• Financial problems led him to move to Australia at the age of 18

• He wrote a book in which he he made an analogy of coal to the industrial age much like corn in Malthus’ population theory

W. S. Jevons

• He also wrote about the business and solar cycles (The Solar Period and the Price of Corn - 1875)

• Also known for his first attempts at understanding inflation in “On the Study of Periodic Commercial Fluctuations”- 1862 and “ A Serious Fall in the Value of Gold” - 1863

W. S. Jevons

• Utility and Marginal Analysis

• Jevons noted the work of Weber-Fechner

• Recognized the difficulty of a cardinal measurement and acknowledge that only an ordinal measurement could be found

• However, proceeded as if indirectly the cardinal measurement could be found

Graphical AnalysisTU

MUUnits of X

Units of X

Utility

• The Equimarginal Principle– MuX = MUY

• The only difference with the Equimarginal Principle is that it assumes the PX = PY= 1

Theory of Exchange

MU Corn

MU Corn

MU Beef

MU Beef

Theory of LaborPleasure

Pain

Real Wages or Amount of Product

Degree of Utility of Real Wages

Net Pain of Labor Curve

At Arrows have same amount

Ordinal Utility

x1

x2

U

0

2U

Expected Utility

• Expected Value– E(X) = p1O1 + p2O2 + p3O3

– Where p1 + p2 + p3 = 1

• Expected Utility– U(X) = p1U(O)1 + p2U(O)2 + p3U(O)3

Risk Averse vs. Risk LovingT

otal

Uti

lity

Return on Investment

Risk Neutral

Risk Averse vs. Risk LovingT

otal

Uti

lity

Return on Investment

Risk Averse

Risk Averse vs. Risk LovingT

otal

Uti

lity

Return on Investment

Risk Loving