Budget constraints and indifference curves
A graphical model shows how preferences and budgets combine to determine the best choice a consumer can afford.
The budget constraint
A budget constraint shows all combinations of two goods a consumer can afford: \(P_x X + P_y Y = I\), where I is income. On a graph, it is a straight line. Its slope is \(-P_x/P_y\), the rate at which the market lets you trade one good for the other.
Shifting the budget line
An increase in income shifts the budget line outward in parallel: more of everything is affordable. A change in one price rotates the line: if good X gets cheaper, the line pivots outward along the X axis, because more X can be bought with the same income.
Indifference curves
An indifference curve shows combinations of two goods that give the same satisfaction. Curves farther from the origin represent higher utility. They slope downward (to get more of one good while staying equally happy, you must give up some of the other) and usually bow inward toward the origin.
The marginal rate of substitution
The slope of an indifference curve is the marginal rate of substitution (MRS): how much of good Y you would give up for one more unit of X. Indifference curves bow inward because of a diminishing MRS: when you have lots of X, you will give up little Y for more.
The optimal choice
The best affordable bundle is where the budget line just touches the highest possible indifference curve, a point of tangency. There, the MRS equals the price ratio: the rate you are willing to trade equals the rate the market lets you trade. This is the graphical version of equalising marginal utility per dollar.
Income and substitution effects
When a price falls, two things happen. The substitution effect: the good is relatively cheaper, so you buy more of it instead of other goods. The income effect: your purchasing power rises, so you buy more of normal goods and less of inferior goods. Together they make up the total response.
Giffen goods
In theory, a very inferior good taking a large share of a poor household's budget could have an income effect strong enough to outweigh the substitution effect, so a price rise increases quantity demanded. These Giffen goods are rare; one study found rice in parts of China behaved this way among very poor households.
Worked example
Maria has 60 dollars to spend on books (15 dollars each) and films (5 dollars each). She could buy 4 books and no films, 12 films and no books, or combinations like 2 books and 6 films. The budget line's slope is -15/5 = -3: one book costs three films. Her best choice depends on her indifference curves.
Key takeaways
The budget line shows affordable bundles; its slope is minus the price ratio. Income changes shift it; price changes rotate it. Indifference curves show equal satisfaction and bow inward due to diminishing MRS. The optimum is where the budget line is tangent to the highest indifference curve, so MRS equals the price ratio. Price changes have substitution and income effects.
Flashcard
PxX + PyY = I
Check your understanding
If a consumer's income doubles and all prices double, what happens to the budget line?