The consumer's optimum

A rational consumer chooses the most preferred bundle she can afford: the one giving her maximum satisfaction within her budget.

Where is it?

• It lies on the budget line, not below it. With monotonic preferences, a point below the line leaves money unspent that could buy more.
• It is at the point where the budget line just touches (is tangent to) the highest indifference curve it can reach.

At that point, the slope of the indifference curve equals the slope of the budget line:

MRS = p1 ÷ p2

In words: the rate at which she is willing to swap the goods equals the rate at which the market lets her swap them.

Why must this hold? Suppose at some point her MRS is 3 (she would give up 3 mangoes for a banana), but the price ratio is 1 (the market asks only 1 mango's worth of money for a banana). Then buying one more banana and one less mango makes her better off. So that point is not the optimum, and she keeps moving along the line until MRS equals the price ratio.