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Chapter 1
Budget Constraint
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CONSUMER THEORY
Consumer theory: consumers choose the best bundle of goods they can afford.
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CONSUMER THEORY
Two parts to theory
1. “can afford”___ budget constraint
2. “best” ___ according to consumers’ preferences
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Budget Constraints
consumption bundle :
(x1, x2, …,xn) __ how much of each good is consumed
Commodity prices are p1, p2, … , pn.
m __ money the consumer has to spend
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Budget Constraints
A bundle (x1, … , xn) is affordable at prices p1, … , pn :
When p1x1 + … + pnxn mwhere m is the consumer’s (disposable) income.
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Budget Constraints
The consumer’s budget set is the set of all affordable bundles
The bundles that are only just affordable form the consumer’s budget line.
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Budget Set and Constraint for Two Commoditiesx2
x1
p1x1 + p2x2 = m is x2 = -(p1/p2)x1 + m/p2
so slope is -p1/p2.
m /p1
BudgetSet
m /p2
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Budget Constraints For n = 2 and x1 on the horizontal
axis, the constraint’s slope is -p1/p2. What does it mean?
xpp
xmp2
1
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2
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Budget Sets & Constraints; Income and Price Changes
The budget line and budget set depend upon prices and income. What happens as prices or income change?
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How do the budget set and budget constraint change as income m
increases?
Originalbudget set
x2
x1
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Higher income gives more choice
Originalbudget set
New affordable consumptionchoices
x2
x1
Original andnew budgetconstraints areparallel (sameslope).
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How do the budget set and budget constraint change as income m
decreases?
Originalbudget set
x2
x1
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How do the budget set and budget constraint change as income m
decreases?x2
x1
New, smallerbudget set
Consumption bundlesthat are no longeraffordable.Old and new
constraintsare parallel.
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Budget Constraints - Price Changes
What happens if just one price decreases?
Suppose p1 decreases.
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How do the budget set and budget constraint change as p1 decreases
from p1’ to p1”?
Originalbudget set
x2
x1
m/p2
m/p1’ m/p1”
-p1’/p2
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How do the budget set and budget constraint change as p1 decreases
from p1’ to p1”?
Originalbudget set
x2
x1
m/p2
m/p1’ m/p1”
New affordable choices
-p1’/p2
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How do the budget set and budget constraint change as p1 decreases
from p1’ to p1”?
Originalbudget set
x2
x1
m/p2
m/p1’ m/p1”
New affordable choices
Budget constraint pivots; slope flattens from -p1’/p2 to -p1”/p2
-p1’/p2
-p1”/p2
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Taxes, subsidies and rationing
1. Quantity tax ___ tax levied on units bought : p1 + t
2. Value tax ___ tax levied on rupees spent : p1 + αp1. Also known as ad valorem tax
3. Subsidies ___ opposite of a tax
a) p1 - s
b) p1 - µp1
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Taxes, subsidies and rationing
4. lump sum tax or subsidy __ amount of tax or subsidy independent of the consumer’s choices. Also called a head tax or a poll tax.
5. Rationing ___ can’t consume more than a certain amount of some good
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The Food Stamp Program
Food stamps are coupons that can be legally exchanged only for food.
How does a commodity-specific gift such as a food stamp alter a family’s budget constraint?
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The Food Stamp Program
Suppose m = $100, pF = $1 and the price of “other goods” is pG = $1.
The budget constraint is then F + G =100.
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The Food Stamp ProgramG
F100
100
F + G = 100; before stamps.
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The Food Stamp ProgramG
F100
100
F + G = 100: before stamps.
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The Food Stamp ProgramG
F100
100
F + G = 100: before stamps.
Budget set after 40 foodstamps issued.
14040
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The Food Stamp ProgramG
F100
100
F + G = 100: before stamps.
Budget set after 40 foodstamps issued.
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The family’s budgetset is enlarged.
40
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The Food Stamp Program
What if food stamps can be traded on a black market for $0.50 each?
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Shapes of Budget Constraints - Quantity Discounts
Suppose p2 is constant at $1 but that p1=$2 for 0 x1 20 and p1=$1 for x1>20.
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Shapes of Budget Constraints with a Quantity Discount
m = $100
50
100
20 80
x2
x1
Budget Set
Budget Constraint
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Shapes of Budget Constraints with a Quantity Penalty
x2
x1
Budget Set
Budget Constraint
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Shapes of Budget Constraints - One Price Negative
Commodity 1 is stinky garbage. You are paid $2 per unit to accept it; i.e. p1 = - $2. p2 = $1. Income, other than from accepting commodity 1, is m = $10.
constraint ?
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More General Choice Sets
Choices are usually constrained by more than a budget; e.g. time constraints and other resources constraints.
A bundle is available only if it meets every constraint.
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More General Choice Sets
Food
Other Stuff
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At least 10 units of foodmust be eaten to survive
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More General Choice Sets
Food
Other Stuff
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Budget Set
Choice is also budgetChoice is also budgetconstrained.constrained.
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More General Choice Sets
Food
Other Stuff
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Choice is further restricted by a time constraint.
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More General Choice Sets
So what is the choice set?So what is the choice set?
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More General Choice Sets
Food
Other Stuff
10
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More General Choice Sets
Food
Other Stuff
10
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More General Choice Sets
Food
Other Stuff
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The choice set is theintersection of all ofthe constraint sets.
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