EC 109: Microeconomics
Topic 1: Consumer Theory
- Differences in behaviour emerge from
Tastes
Circumstances
- We optimise based on our constraints
Budget Constraint
- We have different bundles of goods we want to buy
- Income and prices affect the quantity of consumer demand
- Income can be determined in 2 ways:
Exogenously: an amount M determined outside the model
Endogenously: determined by endowments from inside model
- In a model where you can buy 2 goods, A at price p A and B at price p B, with exogenous
income M
M
If you only bought A , M =x A × p A so the maximum quantity ( x A ) you could buy is
pA
M
If you only bought B, M =x B × p B so the maximum quantity ( x B ) you could buy is
pB
- BUT we may want a combination of the goods, and we may not spend all of the income
THEN M ≥ x A × p A + x B × pB
n
For more goods, this sum becomes M ≥ ∑ pi xi where pi and x i are the price and
i=1
quantity of each good
M pA
- If we plot A on the y-axis, this can be rearranged to x B ≤ − ×xA
pB p B
M −p A
This tells us the y-intercept and the slope
pB pB
- Feasible Set: all possible combinations of the two goods given our budget M
- Plotting this gives us the feasible set of combinations of the two goods
Affordable: any bundle of goods below the budget constraint
Just Affordable: any bundle of goods on the budget constraint
- The slope tells us the rate the market substitutes good A for good B — the opportunity cost
, To consume one more good A (∆ x A ), how much good B must be sacrificed (∆ x B )?
- If we spend all our money:
M =x A × p A + x B × pB
There will also be some equation satisfying
M =( x ¿ ¿ A +∆ x A )× p A +( x ¿ ¿ B+ ∆ x B)× p B ¿ ¿
- Solving this system gives p A × ∆ x A + p B × ∆ x B=0
∆ x B −p A
THUS =
∆ xA pB
- This makes sense since if the price ratio changes, ceteris paribus, the rate of substitution
(slope) will change
If both prices change by equal amounts, the slope stays constant but the budget
constraint shifts
- If income falls, the budget constraint is translated inwards
Kinked Budget Constraint
- The price of good y is constant but the price of a good x varies with amount bought
P x= 1
{
P when 0 ≤ x ≤ a
P2 when x > a
- SO, opportunity cost different at different amounts bought = the slope different:
{
P1
P1 when 0 ≤ x ≤ a
Py
=
Py P2
when x> a
Py
M M
- Vertical intercept and horizontal intercept are normal ( and ) when0 ≤ x ≤ a
Py Px
M −a P1
- Horizontal intercept is a+ when x >a
P2
Preferences
- Budget constraints tell us the possible combinations of goods a consumer can buy
BUT preferences can tell us what they actually want to buy
- Assume that consumers choose what they want most
- For instance, compare two bundles ( x 1 , x 2) and ( y 1 , y 2 ) to determine preference ordering:
Strict preference (≻): would choose one good over another every time
Weak preference (≽): one good is at least as good than the other, but it can be better
Indifference ( ): like both goods equally
- Only consider ordinal relations (which good do you prefer, not how much more you prefer it)
- Preferences have several assumed properties:
3 properties give us rational consumer behaviour:
o Completeness: can always rank bundles X , Y (either X ≻ Y , Y ≻ X or X Y )
o Transitivity: if X ≽Y and Y ≽ Z , then X ≽ Z
o Continuous: If bundle X ≽Y , and bundle Z very similar to Y introduced (within
small radius of Y ), X ≽ Y SO small changes in bundles don’t affect preference
ordering
, 2 properties are not needed for rational behaviour but give well-behaved preferences:
o Monotonicity (non-satiation): since talking about goods, not bads, more is better so
if bundle Y ( y 1 , y 2) has as much of both goods and more of one as X ( x1 , x2 ), Y ≻Z
o Convexity: strong convexity states that averages better than extremes; weak
convexity — that averages at least not worse than extremes
SO, for two extreme bundles where ( x 1 , x 2 ) ( y 1 , y 2 ), for 0<t <1, an average:
z=(t x 1+ ( 1−t ) x 2 ,t x 2−(1−t ) x 1) ≽(x 1 , x 2 )
- If we plot different preferences on a preference plan, we can choose one bundle, X , to
compare and treat it as the origin
Any bundle in Quadrant I relative to it, is better due to the monotonicity assumption
Any bundle in Quadrant III relative to it, is worse due to the monotonicity assumption
- BUT monotonicity alone cannot compare X to bundles in Quadrants II and IV relative to it
Indifference Curves
- Indifference curve: models which bundles that provide the same utility to a consumer
Continuous
Convex shape as joining two extreme bundles on indifference curve in straight line cord
gives average bundles which are preferred and thus not on the same indifference curve
Cannot cross as then two points with same x-value both indifferent to bundle at
intersection SO indifferent to each other due to transitivity, but one has more good y ,
violating monotonicity
Downward sloping as only way to retain utility by consuming more of one good is to
reduce the other
- Indifference map: plots several indifference curves
Due to monotonicity argument, curves to the right provide more utility
- SO, consumers would like the highest indifference curve under their budget constraint
- BUT the shape depends on types of goods as assumptions change:
Perfect substitutes: goods with constant rate of substitution
Perfect complements: goods that are always consumed together
Bads: good that is disliked by consumers
o Would not be downward sloping, since to consume more bads and utility to remain
the same, more of the other good must be consumed
Neutral goods: goods you do not care about
Satiation: overall best bundle, where any bundle of more or less is worse
, Utility
Utility function, u( x , y) : describe preferences, assigning higher number to preferred bundles
Still only ordinal relation, not cardinal (which bundle is preferred, not by how much)
- The further from the origin, the higher the utility
Utility has to be the same for all bundles on the same indifference curve but a higher
indifference curve will give a higher utility
- Bundle ( x 1 , x 2 ) ≻ ( y 1 , y 2 ) ⟺u ( x 1 , x 2 ) >u ( y 1 , y 2 )
- Utility functions will look different for different types of goods
Perfect substitutes: only care about total sum of the two goods A and B:
U ( A , B )=aA +bB where a and b tell us about the ratio the goods are in
Perfect complements: only get utility when amount of good A = amount of good B
U ( A , B )=min {aA , bB }
Cobb-Douglas functions: between these extremes, this gives well-behaved preferences:
where the simplest form is U ( x 1 , x 2 )=x 1 x 2
a 1−a
U ( x 1 , x 2 )=x 1 x 2
Monotonic Transformations
Monotonic transformation: transforming one utility function into another describing same
preferences
Can do this since utility functions are ordinal
- Transforms a set of numbers into another while maintaining the order and MRS
- Examples include:
U ( x 1 , x 2 ) +k , k ∈ R
aU ( x 1 , x 2 ) , a ∈ R
log (U (x 1 , x 2))
n
U ( x 1 , x 2 ) ,n ∈ R
- You can optimise a utility function to find optimal demand, but can’t work back from optimal
demand to generate a utility function since there is not a unique solution
Behavioural Insights
- Different factors affect utility:
Psychological attitudes
Peer pressure (e.g. when someone sells lots of shares, others follow)
Personal experiences
Culture (e.g. environmental concern)
- Ceteris paribus: we only consider choices among quantifiable options, while only changing
one factor at a time
- Do economic axioms actually hold true? Are consumers rational?
Too many choices reduce sales
Prospect Theory: how choices are framed
Loss Aversion: disutility of giving up something greater than utility of receiving it
Default option
Marketing and product placement in shops
Sunk cost fallacy
Bounded rationality: behaviour influenced by environment and information we have
Poor feedback restricts information
