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Utility Theory

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Utility Theory First: Cardinal Second: Ordinal Third: Cardinal In Essence the Principle of Utility has two routes Jeremy Bentham February 15, 1748-June 6, 1832 The ... – PowerPoint PPT presentation

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Title: Utility Theory


1
Utility Theory
  • First Cardinal
  • Second Ordinal
  • Third Cardinal

2
In Essence the Principle of Utility has two routes
3
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.

4
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.

5
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

6
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.

7
Jeremy Bentham
8
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.

9
Jeremy Bentham
  • Not 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.

10
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.

11
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 .

12
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)

13
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

14
Benthams 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)

15
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

16
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 Þ Pleasure
  • Pain Þ Pain

17
The Felicific Calculus
  • Its purity, or the chance that it has of not
    being followed by sensations of the opposite kind
  • Pleasure Þ Pain
  • Pain Þ 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

18
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

19
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

20
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.

21
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

22
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

23
Arsine-JulesEmile-Juvenal Dupuit
  • 1804-1866
  • Born in Fossano, Italy which at the time was
    under French domination

24
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

25
Dupuits 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.

26
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

27
King-Davenants Law of Demand
28
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

29
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

30
Dupuits Argument
MU Price
p1
p2
q1
q2
Quantity of Water
31
Dupuits Consumer Surplus
Quantity
Thus, if price is p1 consumer pays Or1p1 and the
consumer surplus is r1p1P
r1
r2
p
p1
p2
O
Price
32
Consumers Surplus, Monopoly, and Discrimination
Yield of the Toll
Tariff
of Passengers
Utility
Gross
Net
2 f _at_
100
445 425 391 352 316 276 234 192 144 99 69 36 0
0 -200
0 1 2 3 4 5 6 7 8 9 10 11 12
80 63 50 41 33 26 20 14 9 6 3 0
80 -80
126 0 150 50 164
82 165 99 156 104 140
100 112 84 81
63 60 48 33 27 0
0
33
William Stanley Jevons
  • 1835-1882
  • (drowned just short of 47)

34
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

35
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

36
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

37
Graphical Analysis
TU
Units of X
MU
Units of X
38
Utility
  • The Equimarginal Principle
  • MuX MUY
  • The only difference with the Equimarginal
    Principle is that it assumes the PX PY 1

39
Theory of Exchange
MU Beef
MU Corn
MU Beef
MU Corn
40
Theory of Labor
Pleasure
Degree of Utility of Real Wages
Real Wages or Amount of Product
Net Pain of Labor Curve
At Arrows have same amount
Pain
41
Ordinal Utility
U
2
U
x1
0
x2
42
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

43
Risk Averse vs. Risk Loving
Total Utility
Risk Neutral
Return on Investment
44
Risk Averse vs. Risk Loving
Total Utility
Risk Averse
Return on Investment
45
Risk Averse vs. Risk Loving
Total Utility
Risk Loving
Return on Investment
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