1.1 Intro and Consumer Theory - Preference and Utility-compressed fixed typopdf

EC201: Microeconomic Principles I
Welcome to the course!
Meet the EC201 Team
Dr Dimitra Petropoulou
d.petropoulou@lse.ac.uk
MT Lecturer
Professor Tim Besley
t.besley@lse.ac.uk
LT Lecturer
Ms Chiara Sotis
c.sotis@lse.ac.uk
Course Manager
As well as our lovely class teachers (Agnes, Andres, Diogo, Evgeniya, Jennifer,
Menna, Michelle, Ningyuan, Sowyma, Taka, Ufuk, Victor and Zarak)
A bit about me
• I did all my studies at LSE from BSc Economics to PhD Economics (with a stint
in Management as well)
• My research interest lies in International Trade (which you might be
surprised to hear is an applied microeconomics field)
• I worked at the Universities of Oxford, Sussex and Surrey, before returning to
LSE in September 2018
• My primary academic interest now is in economics teaching and learning
3
This term in a nutshell
Two big issues:
1. How do economic agents make decisions under constraints? How does
economic policy shape decisions? How can we assess welfare effects?
• Classical consumer theory; insights from behavioural economics
• Intertemporal choice; decisions under uncertainty; labour supply decisions
• Strategic decision-making
2. How do firms make decisions? How do firms interact in a market?
• Producer theory; market structure
• Game theory
• Applications to oligopoly
4
Key skills you will develop in EC201
• Analytical, logical and mathematical skills needed to understand
the models
• The ability to think critically about the models and their
relationship to the world
• The capacity to understand when/why a model is useful and its
limitations
• Employers value all these skills
5
EC201 Lectures and classes this term
• Lectures in weeks 1 – 11 (recorded, but attendance is better):
• Tuesdays 13:00 – 14:00 in PT
• Wednesdays 11:00 – 12:00 in PT
• Q&A sessions (unrecorded):
• Wednesday 12:00 – 12:30, weeks 4 and 8 in PT
• Ahead of Week 5 take home exam and Week 9 mock exam
• Classes weeks 2 – 11:
• Please stick to your allocated class group
• To (exceptionally) attend an alternative class, email both your teacher and
the teacher of the alternative class for permission, explaining the reason
6
Why are classes 2 hours?
• To give us more time to explore the material in greater depth
• Class content:
• Problem set (to be attempted in advance) – solutions will be
provided
• Some past exam questions
• Some discussion of questions relating to Reading
• Occasional classroom games
• Classes are key so prepare and engage to make the most of them!
7
EC201 Summative assessment
• 1 hour January examination (25% weight)
• 4 short questions spanning the MT syllabus (25 marks each)
• Readings will not be examined in January
• Each short question carries 25 marks (total 100)
• 3 hour Summer examination (75% weight)
• 2 long questions on MT syllabus (including readings)
• 4 short questions and 2 long questions on LT syllabus
• Short question carry 25 marks and long question 50 marks (total 300)
• 15 minutes reading time; no calculators permitted
• Please take steps to put in place an Inclusion Plan if you need one
8
EC201 Formative Assessment
• 2 individual pieces of work marked per term
• Michaelmas Term:
• Take home mock exam (long and short questions) due Week 5
• In-class mock exam (short questions only) in Week 9
• Lent Term: two in-class mock exams
• Why mock exams?
• To get a more realistic sense of performance
• Time management is key – the mocks will help you plan for the real thing
• Do them even if you didn’t revise as much as you hoped
9
What else will we do?
• Weekly Moodle image challenge!
• Send me images that relate to themes discussed in class each week
• It could be a photo you take or find (don’t violate copyright please)
• We will replace the image on the EC201 Moodle page with your photos
• Please ensure that anyone potentially identifiable (e.g. a student) is
happy to be on the EC201 Moodle page
• Design your own strategy competition (for the iterated Prisoners’
Dilemma) – more on this later on!
• Discussion forum to discuss class readings
10
Student support for EC201
• My MT office hours: Tuesdays 14:30 – 16:30, 32L 2.29 (from week 2)
• EC201 LSE LIFE Support Lab
•
•
•
•
Workspace 3, zone D on ground floor of the Library
Flyer on Moodle has full details
Many hours of support each week
Drop by to resolve your queries
• Moodle discussion forum for readings
• Revision discussion forum – leading up to the January exam
• Revision workshops – leading up to the Summer exam
• EC201 Course Reps
11
Reading for EC201
• No set textbook for this course
• Chapters from suitable intermediate textbooks are recommended
if you wish to consult a book (not necessary) – access the Reading
List via Moodle
• Readings will be discussed in weekly classes (examinable)
• Mathematics reading list (in case you need to brush up) on Moodle
12
EC201: Microeconomic Principles I
1.1 Consumer Theory: Preferences and Utility
The purpose of consumer theory
• To understand:
• What determines household behaviour: buying, selling,
working, saving and borrowing, accepting or alleviating risk
• How behavior is affected by changes in prices, income, wages,
interest rates, tax rates…
• How household welfare is affected by such changes
14
To analyse consumer theory we use models
• Models simplify and abstract from reality to focus on the most
salient aspects of an issue
• They leave out many things and distort others
• They have assumptions and definitions from which we use logical
argument to draw conclusions
• Conclusions help us understand the economy and design policy
15
How do we know if our model is any good?
• Models can be misleading…
• How suitable a model is depends on the context in which it is
being applied
• Important to understand limitations of models; contrast the
assumptions and conclusions of different models - we try and do
this in EC201
16
Question: Which is the best route from St Paul’s to Barbican?
Model: Tube Map
(a) Change at Bank & Moorgate?
(b) Change at Holborn & King’s Cross?
(c) Change at Liverpool street?
17
The tube map simplifies:
Regent’s
Park
TER
one
Great
Baker Portland
Street Street
ster
e
Hyde
Park
Green Park
Angel
A1
King’s Cross
St. Pancras
Russell
Square
Euston
Square
Goodge Street
Tottenham
Court Road
Leicester
Square
Piccadilly
Circus
Westminster
Cam
Hoxton
Euston
Regent’s Warren
Street
Park
Edgware
Oxford
Road
Bond Circus
Street
Marble Arch
King’s Cross
Farringdon
Holborn
Chancery
Lane
City
Thameslink
Temple
Charing
Cross
Blackfriars
Embankment
Covent
Garden
B
Old Street
Waterloo East
Barbican
St. Paul’s
Bank
Mansion
House
Cannon
Street
Shoreditch
High
Street
Moorgate
Liverpool
Street
Aldgate
Fenchurch St.
Tower
Hill
Monument
A10
John’s Wood
0
Mornington
Crescent
St.
Pancras
International
London Bridge
18
Our model gives:
19
But is there an even better model?
20
Back to consumer theory…
• Standard microeconomic models assume:
• Households maximize utility
• Firms maximize profits and minimize costs
• Do these models help us understand the world?
• Do we miss important things if we limit ourselves to these models?
• In EC201 we explore the standard models and complement them
with other approaches and behavioural economics
21
Standard critique
• Microeconomic models assume people make lightning
calculations, which they don’t
• …but perhaps they act as if they were
• Milton Friedman “Essays in positive Economics” (1953)
How do expert billiard players play?
“… not at all unreasonable that excellent predictions would be
yielded by the hypothesis that the billiard player made his shots as if
he knew the complicated mathematical formulae that would give
the optimal directions of travel ….”
22
How do we perform these
minor miracles?
Billiard players learn the
consequences of the laws of
physics even though they cannot
solve the equations…
23
How do we perform these minor miracles?
• D. Kahneman “Thinking Fast and Slow” Penguin, 2011
• Modes of thinking:
• System 1 (fast, instinctive and emotional)
• System 2 (slow, deliberate, logical)
• Expert intuition is good in:
• an environment that is sufficiently regular to be predictable
• with an opportunity to learn regularities through prolonged
practice
• immediate and unambiguous feedback
• Applies to some decisions better than others
24
An (abridged) history of microeconomic theory
Alfred Marshall (1842-1924)
• 19th century orthodoxy
• University of Cambridge
• Father of neoclassical economics
• Principles of Economics, 1890
What did he achieve?
• Defined utility as the maximum one is willing to pay for a good
(when the alternative is no good); utility function and marginal utility
• the demand curve; consumer surplus
• elasticity
25
An (abridged) history of microeconomic theory
Where were the limitations?
• Lots of words, limited modelling
• No model of how the utilities of two goods
interact
• Does not examine (i) the effects of income or
changes in tastes on demand, or (ii) the effect
of changes in the price of other goods on
demand
What is utility and can it be measured in money?
• A big 19th century philosophical debate
26
An (abridged) history of microeconomic theory
John Hicks (1904 – 89)
• 20th century orthodoxy
• LSE from 1926 to 1935
• Nobel prize 1972
• Value & Capital, 1939
• Builds on Edgeworth (1881), Pareto (1909)
and Slutsky (1915)
What did he achieve?
• Dropped utility functions and started analysis with indifference curves
27
An (abridged) history of microeconomic theory
Hicks made two assumptions:
• Non-satiation (more is better)
• Decreasing Marginal Rate of Substitution (MRS)
Good 2
0
Good 1
28
Marginal Rate of Substitution (MRS)
• Hicks (and most textbooks) defines the MRS as minus the gradient of
indifference curve (at a particular point)
Good 2
●
●
●
0
Good 1
29
Marginal Rate of Substitution (MRS)
When moving from A and B:
2 scoops of ice cream given up
3 extra slices of pizza needed to attain the
same level of utility
Ice cream
3
●
1
A
− gradient of arc =
●
0
1
4
"
#
B
Pizza
30
Marginal Rate of Substitution (MRS)
When moving from A and B:
x2A - x2B = amount of good 2 given up
x1B - x1A = amount of extra good 1 needed
to attain the same level of utility
Good 2
x2A
●
A
x2B
0
x2A − x2B
= − gradient of arc
x1B − x1A
●
x1A
B
x1B
Good 1
31
Marginal Rate of Substitution (MRS)
As the change in good 2 becomes smaller,
the ratio becomes:
Good 2
x2A
●
x2A − x2B
=
−
gradient
of
tangent
line
=
MRS
x1B − x1A
A
●
●
0
x1A
●
Good 1
32
Back to Hicks…
• Indifference map but not a utility function
• Tells us whether the individual prefers one particular bundle of
goods over another… but not by how much
Good 2
● Bundle A
●
0
Bundle B
Good 1
33
In summary
• Marshall: utility from consumption of a single good
• Hicks: analysis with indifference curves
• Modern microeconomics: starts with preferences over consumption of
many goods
34
Modern assumptions on preferences and utility
• Utility depends on the quantities consumed of all goods
• Consuming !1, !2 … !& of goods 1,2 … & (a consumption bundle) gives
utility '(!1, !2 … . !&), which is a number
• From now on we focus on & = 2, without loss of generality
• Note:
• People are assumed to care only about their own consumption of goods
• In LT we extend to include other people’s consumption e.g. externalities
• This says nothing about where preferences come from
• Human relationships are not part of this theory – but can be included
35
Modern assumptions on preferences over
bundles of goods
1.
2.
3.
4.
5.
Completeness
Transitivity
Continuity
Non-satiation
Convexity
36
1. Completeness
As utility is a number, then for any two bundles of goods ("1$, "2$) and
("1(, "2() it follows that one of these relationships must hold:
• )("1$, "2$) > )("1(, "2(): the consumer prefers bundle ("1$, "2$) to
("1(, "2()
• )("1$, "2$) = )("1(, "2(): the consumer is indifferent between
bundles ("1$, "2$) and ("1(, "2()
• )("1$, "2$) < )("1(, "2(): the consumer prefers bundle ("1(, "2() to
("1$, "2$)
37
1. Completeness
• Diagrammatically, if a consumer is choosing between any two bundles A
and B then either:
(i) A is preferred to B
Good 2
Good 2
● Bundle A
●
0
(iii) indifferent between A
and B
(ii) B is preferred to A
Good 2
●
● Bundle A
Bundle A
● Bundle B
● Bundle B
Bundle B
Good 1
0
Good 1
0
Good 1
38
1. Completeness
• Key implication: the consumer can make choices over the entire range
of possibilities
• Is this realistic? What could go wrong?
si-gua
jay-lan
mao-gua
39
1. Completeness
• Key implication: the consumer can make choices over the entire range
of possibilities
• Is this realistic? What could go wrong?
• Consumers may find it impossible to rank some options
• Decision-making takes time and effort (e.g. grocery shopping), and
we are often unsure of what a product is and does
• We are subject to systematic biases
• The standard model is not based on psychological research;
behavioural economics is
40
2. Transitivity
As utility is a number, then for any three bundles of goods ("1$, "2$),
"1(, "2( and ("1) , "2) ):
• If +("1$, "2$) > +("1(, "2() and +("1(, "2() > +("1) , "2) ), then it
follows that +("1$, "2$) > +("1) , "2) )
• If bundle A is preferred to bundle B, and bundle B is preferred to bundle
C, then it follows that bundle A is preferred to bundle C
41
2. Transitivity
While transitivity may seem obvious, be careful…not all relationships are
necessarily transitive.
Example 1: Is height transitive?
Example 2: Is winning at tennis transitive?
42
3. Continuity
• If bundle A is preferred to bundle B and bundle C is close to bundle B,
then bundle A is preferred to bundle C
• This can be stated far more precisely but beyond the scope of EC201
Good 2
● Bundle A
●
● Bundle C
Bundle B
0
Good 1
43
Implications of assumptions 1-3:
• Completeness, transitivity and continuity imply:
• Preferences can be represented by a utility function and indifference
curves
• Utility is ordinal i.e. different utility functions can represent the
same preferences
• You will have to take this on trust. Proving it requires mathematics
beyond the scope of EC201
44
Ordinal Utility
• Utility functions assign numbers to indifference curves
• The ordering of these numbers reflects preferences over different
bundles
• But the numbers themselves are not material, provided the ordering is
preserved
• Key implication: different utility functions can reflect the same
preferences, if ordering is preserved
45
Ordinal Utility
Example 1: Does replacing 1, 2, 3
x2
with 1, 4, 9 change preferences?
u(x1, x2) = 2
Example 2: Does replacing 1, 2, 3
by 1, 30, 14 change preferences?
u(x1, x2) = 3
u(x1, x2) = 1
0
x1
46
Ordinal Utility
• Let preferences of a consumer be represented by the utility function
! "1, "2 = "1¾ "2½ (Cobb-Douglas)
• If "1 > 0 and "2 > 0, then ! > 0
• ! 1,1 = 1
• ! 1,4 = 2
• ! 1,9 = 3
• Hence bundle (1,9) is preferred to (1,4), which is preferred to (1,1)
• Now consider function .("1, "2) = [!("1, "2)
• .(1,1) = 1
• .(1,4) = 4
• .(1,9) = 9
]2
4⁄
5
= "1
"2
• Again bundle (1,9) is preferred to (1,4), which is preferred to (1,1)
47
Ordinal Utility
• If follows that !(#1, #2) represents the same preferences as
((#1, #2) - this means consumer decisions would be the same!
• This is because the ordering of numbers attached to the indifference
curves does not change
• A monotonic transformation is a way of transforming a set of
numbers into another set that preserves the order of the original set
• So any function !(#1, #2) that is a monotonic transformation of
((#1, #2) will reflect the same preferences
• Can you think of examples of monotonic transformations?
48
Checking whether two utility functions reflect the same
preferences
• Method 1: eyeballing…sometimes you can see one utility function is a
positive monotonic transformation of the other
• Example: ! "1, "2 = "1¾ "2½ and )("1, "2) = ¾ ,-"1 + ½,-"2
• Method 2: checking the MRS
• If / is a strictly increasing function ) "1, "2 = / ! "1, "2 then
! and ) represent the same preferences
• The same preferences imply the same indifference curves, which
imply the same MRS
• Check whether the two utility functions have the same MRS to see
whether they represent the same preferences!
49
Back to the Marginal Rate of Substitution
Good 2
"2!
0
%&' = − gradient of tangent line
●
!
"1!
./%*+
."+
=
=
%*, ./.",
Good 1
50
Back to the Marginal Rate of Substitution
• Let ! "1, "2 = ' ( "1, "2
• For ( "1, "2 , the )*+ =
-.,
-/0
-.,
-/1
• For ! "1, "2 , the )*+ =
-2,
-/0
-2,
-/1
=
34
3.
34
3.
-.
-/0
-.
-/1
=
-.,
-/0
-.,
-/1
• Hence they reflect the same preferences
51
Example: Cobb-Douglas preferences
(⁄
)
• Let ! "1, "2 = "1
*⁄
)
"2
and + "1, "2 = ,⁄- ./ "1 + 1⁄- ./"2
• For ! "1, "2 , the 234 =
675
689
675
68(
• For + "1, "2 , the 234 =
6=5
689
6=5
68(
=
(⁄ : <*5) : *5)
) ;
,
(
<(
5)
*⁄ : 5) :
) ;
,
=
(⁄ 95
) 89
*⁄ 95
) 8(
=
,:,
1:;
,:,
= 1:
;
• Hence they reflect the same preferences
52
4. Non-satiation
• More is better
• A consumer prefers having more of either good to having less:
• If x1B > x1A then (x1B,x2A) is preferred to (x1A,x2A)
• If x2B > x2A then (x1A,x2B) is preferred to (x1A,x2A)
• If "#!"$% > 0 and "#!"$( > 0 then increasing )1 and/or )2 increases
utility and non-satiation is satisfied
53
Example: Cobb-Douglas preferences
(⁄
)
• Consider ! "1, "2 = "1
•
,-
+,./ =
• ,-+,.( =
0⁄ " 2*⁄) " *⁄)
2
1 1
5⁄ " (⁄) " 2(⁄)
2
1 1
*⁄
)
"2
> 0 for positive values of "1 and "2
> 0 for positive values of "1 and "2
• So the non-satiation assumption is satisfied
54
4. Non-satiation
• Key implication: indifference curve slope downwards and the preferred
set is above the indifference curve
55
4. Non-satiation
• Question: Is non-satiation satisfied for this consumer?
x2
preferred set
0
x1
56
Are these people satiated?
• Bill Gates, Queen Elizabeth II, Melinda Gates
57
5. Convexity
• Non-satiation implies the
indifference curve is downward
sloping and the preferred set lies
above it
• Given non-satiation, convexity is
satisfied if the indifference curve
is convex
• A set is convex if the straight line
joining any two points in the set
lies in the set
58
5. Convexity
• Key implication: Convexity means a preference for averages
• C is the average of A and B and is preferred to either A or B
●C
59
Non-convex preferences?
• Example: tea and coffee in the same cup!
• Key implication: A preference for extremes rather than averages
x2
A
●
preferred
set
B●
0
x1
60
Checking for convexity
• If non-satiation is satisfied then the following method allows you to
check convexity
• Rearrange the formula for the utility function to get x2 as a function
of x1 and u
• Find the second derivative of this function with respect to x1
• If the second derivative is positive the convexity assumption is
satisfied!
61
Example: Cobb-Douglas preferences
(⁄
)
• Consider ! "1, "2 = "1
*⁄
)
"2
• We have already shown that non-satiation is satisfied
(⁄
)
• Rearrange: ! = "1
•
12(
0123 =
*⁄
)
"2
)⁄
/)⁄
*
− ⁄. ! "1 *
,
⇒! =
"1- "2.
< 0 and
1 ( 2(
⇒ "2 = !
0123( =
)⁄
*
/(⁄
*
"1
78⁄ ! )⁄* " /:⁄*
9
1
>0
• As non-satiation is satisfied a positive second derivative implies that
the preferred set is convex
62
Implications of assumptions 1-5
• We have already seen utility is ordinal and indifference curves
downward sloping and convex (preference for averages)
• The assumptions further imply that indifference curves cannot cross
(see Problem Set 1)
• Moreover, we cannot compare different people’s utility!
• This is important for the study of welfare economics and we will
revisit this in LT
63
Ordinal utility vs Cardinal utility
• Utility is ordinal so no single utility function represents a person’s preferences
• Yet in some contexts we treat utility as if it were cardinal…
• For example, when it comes to the analysing the welfare of society as a whole
• Also when we come to studying decision-making under uncertainty in a few
weeks
64
Ordinal utility and social welfare
• Example: under Utilitarianism the objective of society is to maximize the sum
of utility of all members of society
• In a society with two people A and B a Utilitarian would maximise:
!"($1", $2") + !*($1*, $2*)
• But if we replace !"($1", $2") by, say, 2!"($1", $2") and maximize
2!"($1", $2") + !*($1*, $2*) the social optimum will change!
65
Preferences we will work with regularly
• Cobb-Douglas: ! "1, "2 = "1' "2( (and in logarithmic form)
• Quasi-linear:
! "1, "2 = "1 + *("2) or ! "1, "2 = *("1) + "2
• Perfect substitutes: ! "1, "2 = ,"1 + -"2
• Perfect complements: ! "1, "2 = min[,"1, -"2], where , and - are
positive constants
• These have particular properties and implications for consumer choice and
welfare effects, which we will explore (including in Problem Set 1)
66
Final food for thought
• Where do preferences come from and how do they change?
• Who is the consumer? What determines ‘household preferences’ in a
household with several members?
• What is the relationship between utility and happiness or life satisfaction?
• What is the effect of other consumers on our utility?
67
Review checklist:
1. What is the purpose of a model? What determines its suitability?
2. What are the fundamental differences between the approach of
Marshall, Hicks and modern microeconomics?
3. Explain how preferences can be represented by a utility function.
4. What do the assumptions completeness, transitivity and continuity
imply?
5. What do we mean when we say utility is ordinal? What are the
implications of ordinality?
6. Which assumption would be violated if indifference curves were to
cross?
7. What do non-satiation and convexity imply about consumer
preferences?
68
Mathematical Appendix – Concavity and convexity
Concave functions
• A function is concave if any line joining two points on its graph lies
entirely on or below the graph.
f(x)
0
x
70
Concave functions
For functions with first and second derivatives:
• Concave functions are functions with decreasing first derivatives
• Concave functions are functions with negative second derivatives
f(x)
0
x
71
Concave functions
• If a function is concave and its derivative is 0 at x0 then x0
maximizes the function.
f(x)
0
x0
x
72
!"
Recall
is
!#
decreasing
0
x0
>0
<0
f(x)
increasing
At x0
x
f(x)
decreasing
= 0 thus x0 maximizes f(x).
73
Convex functions
• A function is convex if any line joining two points on its graph lies
entirely on or above the graph
x2
0
x1
74
Convex functions
For functions with first and second derivatives
• Convex functions are functions with increasing first derivatives
• Convex functions are functions with positive second derivatives
f(x)
0
x
75
A convex set
• Mathematically a set is convex if any straight line joining two
points in the set lies in the set
• For example:
not convex
convex
A
B
C
D
convex
not convex
76