Title: Utility Theory
1Utility Theory
- First Cardinal
- Second Ordinal
- Third Cardinal
2In Essence the Principle of Utility has two routes
3Jeremy 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.
4Jeremy 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.
5Jeremy 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
6Jeremy 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.
7Jeremy Bentham
8Jeremy 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.
9Jeremy 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.
10Extract 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.
11Extract 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 .
12Jeremy 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)
13Natural 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
14Benthams 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)
15Moral 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
16The 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
17The 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
18Measure 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
19Measure 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
20Measure 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.
21Measure 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
22Finals 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
23Arsine-JulesEmile-Juvenal Dupuit
- 1804-1866
- Born in Fossano, Italy which at the time was
under French domination
24Jules 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
25Dupuits 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.
26Marginal 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
27King-Davenants Law of Demand
28Marginal 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
29Dupuit 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
30Dupuits Argument
MU Price
p1
p2
q1
q2
Quantity of Water
31Dupuits Consumer Surplus
Quantity
Thus, if price is p1 consumer pays Or1p1 and the
consumer surplus is r1p1P
r1
r2
p
p1
p2
O
Price
32Consumers 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
33William Stanley Jevons
- 1835-1882
- (drowned just short of 47)
34W. 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
35W. 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
36W. 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
37Graphical Analysis
TU
Units of X
MU
Units of X
38Utility
- The Equimarginal Principle
- MuX MUY
- The only difference with the Equimarginal
Principle is that it assumes the PX PY 1
39Theory of Exchange
MU Beef
MU Corn
MU Beef
MU Corn
40Theory 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
41Ordinal Utility
U
2
U
x1
0
x2
42Expected 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
43Risk Averse vs. Risk Loving
Total Utility
Risk Neutral
Return on Investment
44Risk Averse vs. Risk Loving
Total Utility
Risk Averse
Return on Investment
45Risk Averse vs. Risk Loving
Total Utility
Risk Loving
Return on Investment