1. Utility Theory
First: Cardinal
Second: Ordinal
Third: Cardinal

2. In Essence the Principle of
Utility has two routes
A d a m S m it h
N a t u r a l I d e n t it y
J e r e m y B e n t h a m
A r t ific ia l I d e n t it y
P r in c ip le o f
U t ilit y

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. 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)”

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 ⇒ Pleasure
– Pain ⇒ Pain

17. 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

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. 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.

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-Davenant’s Law of
Demand
Defect Above the
Common 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

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. Dupuit’s Argument
Quantity of Water
MU=
Price
p1
q1
p2
q2

31. Dupuit’s Consumer Surplus
O Price
Quantity
p
r1
p1
r2
p2
Thus, if price is p1 consumer pays
Or1p1 and the consumer surplus is
r1p1P

32. Consumers’ Surplus, Monopoly, and Discrimination
Tariff # of Passengers Utility
Yield of the Toll
Gross Net
0
1
2
3
4
5
6
7
8
9
10
11
12
100
80
63
50
41
33
26
20
14
9
6
3
0
445
425
391
352
316
276
234
192
144
99
69
36
0
:2 f @
0 -200
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
MU
Units of X
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 Corn
MU Corn
MU Beef
MU Beef

40. Theory of Labor
Pleasure
Pain
Real Wages
or Amount of
Product
Degree of Utility of Real Wages
Net Pain of Labor Curve
At Arrows have same
amount

41. Ordinal Utility
x1
x2
U
0
2
U

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 LovingTotalUtility
Return on Investment
Risk Neutral

44. Risk Averse vs. Risk LovingTotalUtility
Return on Investment
Risk Averse

45. Risk Averse vs. Risk LovingTotalUtility
Return on Investment
Risk Loving