where:
I = income
PX = price ofgood X
X = quantity purchased of good X
PY = price ofgood Y
Y = quality purchased of good Y.
The above relationship, our budget constraint, is shown diagrammatically as a budget
line in Figure 4.6.
A budget line shows the maximum combinations of X and Y that can be purchased
with a given income and the prices of the two goods. The budget line goes through every
combination of the two goods that can be purchased when all income is expended. For
example, if the consumer spent all their income on Y, they could purchase I/PY units of Y
and no units of X. This combination is shown at point A, the intercept of the budget
constraint with the Y axis. Point B shows the intercept with the X axis, a consumption
bundle of all X and no Y. Combinations of X and Y are contained along the budget line.
The budget line has a negative slope showing that more X can only be purchased by
reducing the consumption of Y. Geometrically, the slope of the budget line in Figure 4.6 is