Lecture notes EC109. Microeconomics (EC109) - Score a First Too

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