A Few Applications of Review MaterialBudget Constraints

Isocosts

Utility Functions

Production Functions

Deriving the Budget Constraint

A consumer consumes goods X and Y, which have prices Px and Py with income I

Expenditures are:

PxX + PyY

Along the budget constraint, all income is spent:

PxX + PyY = I

Budget Constraint algebraIYPXP YX XPIYP XY

XP

P

P

IY

Y

X

Y

Intercept:

Slope:

YP

I

Y

X

P

P

Budget Constraint

X

Y

Not affordable

Affordable

I/Px

I/Py

Slope = -Px/PY

The affordable bundles are together known at the Opportunity Set or Budget Set

Budget Constraint for Three Commodities

x2

x1

x3

I /p2

I /p1

I/p3

p1x1 + p2x2 + p3x3 = IThis is a plane instead of a line.

Change in income: pay raise

YP

I

XP

I

IYPXP YX

X

Y

XP

P

P

IY

Y

X

Y

Change in price: X gets cheap

YP

I

XP

I

IYPXP YX

X

Y

XP

P

P

IY

Y

X

Y

Example: The Food Stamp Program

Consider the two good example where consumers purchase food (F) and all other goods are lumped into one category (G).

Suppose I = $100, pF = $1 and the price of “other goods” is pG = $1.

The budget constraint is then F + G =100.

Example: The Food Stamp Program

G

F100

100F + G = 100: before stamps.

Example: The Food Stamp Program Now assume that the government offers each

family food stamps worth $40.

Draw the new budget constraint of a typical family.

Example: The Food Stamp Program

G

F100

100 Budget set after 40 foodstamps issued.

140

The family’s budgetset is enlarged.

40