www.stuvia.com/user/TBKLeo
1. The Market
By a model, we mean a simplified representation of allocation is such that no Pareto improvements are
reality. possible, it is called Pareto efficient.
Two different variables:
exogeneous variables (determined by factors
not in the model)
endogenous variables (determined by forces in
the model)
Two simple principles:
optimization principle (people try to choose
the best patterns of consumption that they can
afford)
equilibrium principle (people adjust until the
amount that people demand of something is
equal to the amount that is supplied)
The reservation price is a person’s maximum
willingness to pay for something. In other words: the
reservation price is the highest price that a given person
will accept and still purchase the good.
A demand curve relates the quantity demanded to
price. The supply curve relates the quantity of goods
available to price.
In a competitive market, the price is the same for all
goods and is the highest the market will bear.
By drawing both the demand curve and supply curve on
the same graph, we can find out what the equilibrium
behaviour of the market is (equilibrium price). This
price is determined by the intersection of the supply and
demand curves.
Comparative statics involves comparing two “static”
equilibria without worrying about how the market moves
from one equilibrium to another (“what happens if?”).
A situation where a market is dominated by a single
seller of a product is known as a monopoly.
Other ways to allocate goods:
discriminating monopolist (auction to the
highest bidder, reservation price known)
ordinary monopolist (same price to maximize
profit, reservation price unknown)
rent control (fixed price is decided by an
external party, e.g. the government)
If we can find a way to make some people better off
without making anybody else worse off, we have a
Pareto improvement. If an allocation allows for a
Pareto improvement, it is called Pareto inefficient; if an
Page 1 of 35
, www.stuvia.com/user/TBKLeo
2. Budget Constraint
Consumption bundle (𝑥1 , 𝑥2 ) With lumpsum tax or subsidy. The government takes
Prices (𝑝1 , 𝑝2 ) away a fixed amount of money, regardless of the
Budget 𝑚 individual’s behaviour.
Budget constraint: Rationing: cannot consume more than a certain amount
of some good.
𝑝1 𝑥1 + 𝑝2 𝑥2 ≤ 𝑚
When defining the budget constraint like this:
𝑝1 𝑥1 + 𝑥2 ≤ 𝑚
We say that good 2 represents a composite good that
stands for everything else that the consumer might want
to consume other than good 1.
The budget line is the set of bundles that cost exactly
𝑚:
𝑝1 𝑥1 + 𝑝2 𝑥2 = 𝑚
These are the bundles of goods that just exhaust the
consumer’s income. We can rearrange the budget line to
give us the formula:
𝑚 𝑝1
𝑥2 = − 𝑥
𝑝2 𝑝2 1
This is the formula for a straight line with a vertical
intercept of 𝑚/𝑝2 and a slope of −𝑝1 /𝑝2 .
The formula tells us how many units of good 2 the
consumer needs to consume in order to satisfy the
budget constraint if she is consuming 𝑥1 units of good 1.
Economists sometimes say that the slope of the budget
line measures the opportunity cost of consuming good
1.
The budget line can change by shifting the prices
(slopes).
When we set one of the prices to 1, we often refer to that
price as the numeraire price. The numeraire price is the
price relative to which we are measuring the other price
and income.
If good 1 has a price of 𝑝1 but is subject to a sales tax at
rate 𝜏, then the actual price facing the consumer is
(1 + 𝜏)𝑝1 .
A subsidy is the opposite of a tax, reducing the price.
For example, the actual price of good 1 facing the
consumer with a subsidy 𝜎 is (1 − 𝜎)𝑝1 .
Page 2 of 35
, www.stuvia.com/user/TBKLeo
3. Preferences
Different preferences:
(𝑥1 , 𝑥2 ) ≻ (𝑦1 , 𝑦2 ) means the consumer strictly
prefers the 𝑥-bundle to the 𝑦-bundle
(𝑥1 , 𝑥2 ) ≽ (𝑦1 , 𝑦2 ) means the consumer weakly
prefers the 𝑥-bundle to the 𝑦-bundle, meaning
he either prefers the 𝑥-bundle or is indifferent
(𝑥1 , 𝑥2 ) ∼ (𝑦1 , 𝑦2 ) means the consumer is
indifferent between the 𝑥-bundle and the 𝑦-
bundle
These relations are not independent concepts, the
relations are themselves relates. For example:
(𝑥1 , 𝑥2 ) ≽ (y1 , y2 ) and (𝑦1 , 𝑦2 ) ≽ (𝑥1 , 𝑥2 )
then (𝑥1 , 𝑥2 ) ∼ (𝑦1 , 𝑦2 )
Three axioms about consumer preference:
complete: two bundles can be compared
A bad is a commodity that the consumer doesn’t like.
reflexive: any bundle is at least as good as
itself: (𝑥1 , 𝑥2 ) ≽ (𝑥1 , 𝑥2 )
transitive: if (𝑥1 , 𝑥2 ) ≽ (𝑦1 , 𝑦2 ) and (𝑦1 , 𝑦2 ) ≽
(𝑧1 , 𝑧2 ) then we assume that (𝑥1 , 𝑥2 ) ≽ (𝑧1 , 𝑧2 )
The indifference curve through a consumption bundle
consists of all bundles of goods that leave the consumer
indifferent to the given bundle. Indifference curves
representing distinct levels of preference cannot cross.
Two goods are perfect substitutes if the consumer is
willing to substitute one good for the other at a constant
rate. With perfect substitutes, the indifference curves
have a constant slope.
A good is a neutral good if the consumer doesn’t care
about it one way or the other.
Perfect complements are goods that are always
consumed together in fixed proportions.
Page 3 of 35
1. The Market
By a model, we mean a simplified representation of allocation is such that no Pareto improvements are
reality. possible, it is called Pareto efficient.
Two different variables:
exogeneous variables (determined by factors
not in the model)
endogenous variables (determined by forces in
the model)
Two simple principles:
optimization principle (people try to choose
the best patterns of consumption that they can
afford)
equilibrium principle (people adjust until the
amount that people demand of something is
equal to the amount that is supplied)
The reservation price is a person’s maximum
willingness to pay for something. In other words: the
reservation price is the highest price that a given person
will accept and still purchase the good.
A demand curve relates the quantity demanded to
price. The supply curve relates the quantity of goods
available to price.
In a competitive market, the price is the same for all
goods and is the highest the market will bear.
By drawing both the demand curve and supply curve on
the same graph, we can find out what the equilibrium
behaviour of the market is (equilibrium price). This
price is determined by the intersection of the supply and
demand curves.
Comparative statics involves comparing two “static”
equilibria without worrying about how the market moves
from one equilibrium to another (“what happens if?”).
A situation where a market is dominated by a single
seller of a product is known as a monopoly.
Other ways to allocate goods:
discriminating monopolist (auction to the
highest bidder, reservation price known)
ordinary monopolist (same price to maximize
profit, reservation price unknown)
rent control (fixed price is decided by an
external party, e.g. the government)
If we can find a way to make some people better off
without making anybody else worse off, we have a
Pareto improvement. If an allocation allows for a
Pareto improvement, it is called Pareto inefficient; if an
Page 1 of 35
, www.stuvia.com/user/TBKLeo
2. Budget Constraint
Consumption bundle (𝑥1 , 𝑥2 ) With lumpsum tax or subsidy. The government takes
Prices (𝑝1 , 𝑝2 ) away a fixed amount of money, regardless of the
Budget 𝑚 individual’s behaviour.
Budget constraint: Rationing: cannot consume more than a certain amount
of some good.
𝑝1 𝑥1 + 𝑝2 𝑥2 ≤ 𝑚
When defining the budget constraint like this:
𝑝1 𝑥1 + 𝑥2 ≤ 𝑚
We say that good 2 represents a composite good that
stands for everything else that the consumer might want
to consume other than good 1.
The budget line is the set of bundles that cost exactly
𝑚:
𝑝1 𝑥1 + 𝑝2 𝑥2 = 𝑚
These are the bundles of goods that just exhaust the
consumer’s income. We can rearrange the budget line to
give us the formula:
𝑚 𝑝1
𝑥2 = − 𝑥
𝑝2 𝑝2 1
This is the formula for a straight line with a vertical
intercept of 𝑚/𝑝2 and a slope of −𝑝1 /𝑝2 .
The formula tells us how many units of good 2 the
consumer needs to consume in order to satisfy the
budget constraint if she is consuming 𝑥1 units of good 1.
Economists sometimes say that the slope of the budget
line measures the opportunity cost of consuming good
1.
The budget line can change by shifting the prices
(slopes).
When we set one of the prices to 1, we often refer to that
price as the numeraire price. The numeraire price is the
price relative to which we are measuring the other price
and income.
If good 1 has a price of 𝑝1 but is subject to a sales tax at
rate 𝜏, then the actual price facing the consumer is
(1 + 𝜏)𝑝1 .
A subsidy is the opposite of a tax, reducing the price.
For example, the actual price of good 1 facing the
consumer with a subsidy 𝜎 is (1 − 𝜎)𝑝1 .
Page 2 of 35
, www.stuvia.com/user/TBKLeo
3. Preferences
Different preferences:
(𝑥1 , 𝑥2 ) ≻ (𝑦1 , 𝑦2 ) means the consumer strictly
prefers the 𝑥-bundle to the 𝑦-bundle
(𝑥1 , 𝑥2 ) ≽ (𝑦1 , 𝑦2 ) means the consumer weakly
prefers the 𝑥-bundle to the 𝑦-bundle, meaning
he either prefers the 𝑥-bundle or is indifferent
(𝑥1 , 𝑥2 ) ∼ (𝑦1 , 𝑦2 ) means the consumer is
indifferent between the 𝑥-bundle and the 𝑦-
bundle
These relations are not independent concepts, the
relations are themselves relates. For example:
(𝑥1 , 𝑥2 ) ≽ (y1 , y2 ) and (𝑦1 , 𝑦2 ) ≽ (𝑥1 , 𝑥2 )
then (𝑥1 , 𝑥2 ) ∼ (𝑦1 , 𝑦2 )
Three axioms about consumer preference:
complete: two bundles can be compared
A bad is a commodity that the consumer doesn’t like.
reflexive: any bundle is at least as good as
itself: (𝑥1 , 𝑥2 ) ≽ (𝑥1 , 𝑥2 )
transitive: if (𝑥1 , 𝑥2 ) ≽ (𝑦1 , 𝑦2 ) and (𝑦1 , 𝑦2 ) ≽
(𝑧1 , 𝑧2 ) then we assume that (𝑥1 , 𝑥2 ) ≽ (𝑧1 , 𝑧2 )
The indifference curve through a consumption bundle
consists of all bundles of goods that leave the consumer
indifferent to the given bundle. Indifference curves
representing distinct levels of preference cannot cross.
Two goods are perfect substitutes if the consumer is
willing to substitute one good for the other at a constant
rate. With perfect substitutes, the indifference curves
have a constant slope.
A good is a neutral good if the consumer doesn’t care
about it one way or the other.
Perfect complements are goods that are always
consumed together in fixed proportions.
Page 3 of 35
