Chapter 2 BUDGET
CONSTRAINT
2.1 The Budget Constraint
Consumers choose the BEST bundle of goods
they can AFFORD.
 Budget set: affordability
 Consumption bundle: (x1, x2)

2.1 The Budget Constraint
The budget constraint
p1x1+p2x2≤m
 p1x1 : the amount of money the consumer is
spending on good 1.
 p2x2: the amount of money the consumer is
spending on good 2.
 m: the consumer’s income

2.2 Two Goods Are Often Enough

Composite good
good 2 represents a composite good that stands for
everything else that the consumer might want to
consume other than good 1.

The budget constraint will take the form:
p1x1+x2≤m
2.3 Properties of the Budget Set
p1x1+ p2x2 = m
p1(x1+Δx1) + p2(x2+Δx2) = m
 Subtracting the first equation from the second:
p1Δx1 + p2Δx2 = 0
Δx2/Δx1=-p1/p2
2.3 Properties of the Budget Set

Opportunity cost of
consuming good 1
 the
slope of the
budget line.
 In order to consume
more of good 1 one
has to give up some
consumption of good
2.
2.4 How the Budget Line Changes

Changes in income:
a parallel shift of the
budget line.
2.4 How the Budget Line Changes

Changes in
prices: increasing
price 1 while
holding price 2
and income fixed.
2.4 How the Budget Line Changes

Change the price of good 1 and good 2 at the
same time:
Multiplying both prices by t yields
tp1x1+tp2x2 = m
p1x1+p2x2 = m/t
2.5 The Numeraire

The budget line
p1x1+ p2x2 = m
is exactly the same budget line as
p1/p2x1+ x2 = m/p2
or
p1/mx1+ p2/mx2 = 1
2.6 Taxes, Subsidies, and Rationing

Quantity tax
t
dollars per unit of good 1,
 changes the price of good 1 from p1 to p1+t.

Quantity subsidy
s
dollars per unit of good 1,
 the price of good 1 would be p1-s.
2.6 Taxes, Subsidies, and Rationing

Value tax
a
sales tax at rate t,
 the actual price is (1+t)p1.

Ad valorem subsidy
 an
ad valorem subsidy at rate s,
 the actual price is (1-s)p1.
2.6 Taxes, Subsidies, and Rationing

Lump-sum tax
the budget line shifts inward.

Lump-sum subsidy
the budget line will shift outward.
2.6 Taxes, Subsidies, and Rationing

Rationing
Good 1 rationed.
2.6 Taxes, Subsidies, and Rationing

Sometimes taxes,
subsidies, and rationing
are combined.