Budget equation

Recall the budget line from last section. We will look further into what the equation of this line, and changes that could affect the budget equations.

The Budget Equation

If all income has been used for the goods, then the budget line is expressed by the linear equation:

$xP_x+yP_y=I$
Where
x → quantity of good x
y → quantity of good y
$P_x$ → price of good x
$P_y$ → price of good y
I → income

Note: The slope and y-intercept of the budget equation can be found by putting the equation into the form y = mx + b.

$xP_x+yP_y=I$→$yP_y = -xP_x+1$
→$y=- \frac{P_x}{P_y}x+\frac{I}{P_y}$
Thus,
$Slope= - \frac{P_x}{P_y},y-intercept=\frac{I}{P_y}$

Changes to the Budget Equation

The budget equation can be changed in 6 basic ways.
Increase the price of good x: The consumer will buy less of good x, causing the budget line to be steeper.


Decrease the price of good x: The consumer will buy more of good x, causing the budget line to be less steep.


Increase the price of good y: The consumer will buy less of good y, causing the budget line to be less steep.


Decrease the price of good y: The consumer will buy more of good y, causing the budget line to be steeper.


Increase the Income: The consumer will buy more of both goods, causing the budget line to shift rightward. The slope stays the same.


Decrease the Income: The consumer will buy less of both goods, causing the budget line to shift leftward. The slope stays the same.