Indifference Curves and the Optimal Choice

Combinations That Give the Same Satisfaction

An indifference curve gathers all the combinations of two goods that give the consumer the same satisfaction. He or she is indifferent about which one to choose.

Points A, B, and C are on the same curve $U_1$: they give equal satisfaction. At A there are many sodas and few tacos; at C, the opposite.

Properties of the Curves

There are three properties worth remembering, each with its reason.

1. Negative slope. If you consume less of one good, you need more of the other to keep the same satisfaction.

2. Farther from the origin, more satisfaction. A curve that is higher or farther to the right has more of both goods and, since more is better, gives greater satisfaction.

3. They don't cross. If two curves intersected at a point, that point would have two different levels of satisfaction at the same time, which is impossible.

They are also usually convex (curved toward the origin): someone who already has many tacos will give up several of them for just one more soda, but if few tacos are left, he or she won't give them up as easily. This is the law of diminishing marginal utility seen on the graph.

What She Can Buy: The Budget

The curves show what Ximena wants; the budget shows what she can do. With $\$120$, tacos at $\$20$, and sodas at $\$15$, the constraint is:

where $x$ is tacos and $y$ is sodas. If she spends everything on tacos, she buys 6; if she spends everything on sodas, 8. The line joins those two points.

Points inside the triangle under the line are affordable but leave money over; those outside are unaffordable.

The Optimal Choice

Ximena wants to reach the highest possible curve without going over her budget. If a curve lies entirely outside the line, she can't afford it. If a curve cuts the line at two points, there is another, higher curve that is also affordable. The best point is where the curve just touches the line: the point of tangency.

• U₁ is affordable, but there are better options: it gives less satisfaction than the optimal point.

• U₂ touches the line at a single point: it is the best affordable curve.

• U₃ lies outside: she doesn't have enough money.

At the optimum, the budget is used up (the point is on the line) and the slope of the curve matches the slope of the line.

Go back to the beginning: Ximena chooses the combination where the highest indifference curve she can afford just touches her budget line.

Summary