Transcript Budget Set - Claremont McKenna College

Intermediate Microeconomics
Budget Sets
1
Consumer Theory

First part of class we want to understand “demand”.



We want to do so from “first principles”.
Consumer Theory - a model to describe how individuals behave.

How do individuals choose what to consume?

How do these decisions respond to changes in the environment?

How can we use this model to describe market demand for goods?
How should we start?
2
Budget Set

How do you know what goods you can choose to
consume at any one time?
3
Budget Set

Suppose you are endowed with $10 and only
goods you consume are peanuts and beer.



Peanuts cost $0.10/oz (i.e. pp = 0.10)
Beer costs $0.20/oz (i.e. pb = 0.20)
How can we fully describe what combinations of
peanuts and beer you can consume?

Analytically?

Graphically?
4
Budget Set

Consumption Bundle – A list of numbers indicating how much of
each good an individual is consuming: {q1, q2, …., qn}

Budget Set – the set of consumption bundles of goods a person can
afford to consume.

Generally can be expressed by equation of form:
p1q1 + p 2q2 + … + p3q3 ≤ m
5
Budget Set

Ex: Suppose there are two goods, peanuts and beer.




{50, 20} is a consumption bundle containing 50 oz. of peanuts and 20
oz of beer,
{0,50} is a consumption bundle containing 0 oz. of peanuts and 50 oz
of beer,
{10,50} is a consumption bundle containing 10 oz. of peanuts and 50
oz of beer.
If pp = 0.10, pb = 0.20, and m = 10, the budget set is
0.10qp + 0.20qb ≤ 10


Is the bundle {50, 20} in your budget set? How about {0,50}? How
about {10,50} ?
What does it mean when the budget equation holds with inequality as
opposed to equality?
6
Budget Set

Interpreting prices
 As we will see, prices will play a big role in our
analysis of consumer behavior.
 In our previous example, what was the price of
beer?

How do you interpret the slope of budget set?

What if you lived in London, were endowed with
5 pounds, and Peanuts cost 0.5 pence/oz and Beer
costs 0.10 pence/oz . What would your budget set
look like? Are prices the same in London or
different?
7
Graphing Budget Sets
q2
m/p2
p1/p2
-1
m/p1 q1

So slope of budget constraint is rise/run or
simply negative of price ratio (-p1/p2).

Interpretation of slope: relative cost of good 1
in terms of good 2.
8
Graphing Budget Sets

What happens when relative prices change?

(original) m = 10, pp = 0.10 and pb = 0.20

m = 10, pp = 0.20, and pb = 0.20

m = 10, pp = 0.10 and pb = 0.10
9
Graphing Budget Sets

What happens when endowment changes but
relative prices don’t?

(original) m = 10, pp = 0.10 and pb = 0.20

m = 20, pp = 0.10, and pb = 0.20

m = 4, pp = 0.10 and pb = 0.20
10
Budget Sets and Taxes

Suppose m = $10, pp = 0.10, and pb = 0.20

How would budget set change if a 25% sales
tax were imposed on beer?

How about if a 25% sales tax were imposed on
all goods?

How about if a 25% tax were imposed on each
person’s endowment?
11
Is two-good framework sufficient?

With two goods, we could write a budget set as :
p1q1 + p2q2 ≤ m

Suppose we are interested in analyzing good 1,
but there are two other goods that a consumer can
also spend money on.


Analyze good 1 compared to a composite good which is
just the amount of money spent on all other goods (i.e.
goods 2 and 3).
Denoting “dollars” of composite good as qc we can write
budget set as:
1.
q c + p1 q 1 ≤ m
2.
p 2 q 2 + p 3 q 3 ≤ qc

If we are only interested in analyzing good 1, we can
ignore equation 2, and we are back in two-good
framework.

How would we draw this? What is slope?
12
More Complicated Budget Constraints

Budget constraints seem pretty simple,
why do we make them so complicated?

Consider more complicated pricing
schemes.

Bulk Pricing
 Hamburger is $2/lb for first 3lbs, but
only $1/lb for each additional amount
past 3lbs.
13
More Complicated Budget Constraints

Government policy can also often make
budget constraints more complicated

Food Stamps


pre-1979 – qualifying poor households
could get “50% off coupons” for up to
$200 worth of food per month.

post-1979 - qualifying poor households
given $100 in food vouchers.
How do budget sets differ across two
programs for a person earning $300/mo.?
14
More Complicated Budget Constraints

Public housing





Suppose a person is given a take-it-or-leaveit offer of a free apartment
Further suppose this apartment would rent
for $300/month in the marketplace.
If person had $500/mo. in income, what
would budget constraint look like?
What if instead of this “in-kind” benefit,
person was given $300 in cash.
 What would budget constraint look like?
So why don’t we always give cash
benefits?
15
Budget Constraints more broadly

Suppose you work for Doctors without Borders.




Your funds are enough to have twenty “beds” in your clinic.
Each malaria patient you treat needs one week in your clinic for full
treatment.
Each tuberculosis patient you treat needs two weeks in your clinic for
full treatment.
What is monthly “budget constraint”? What is the “cost/price” of
treating a tuberculosis patient?
16