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Budget line & utility

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Budget Line and Utility

The budget line shows every combination of two goods a consumer can afford given income and prices; utility measures the satisfaction those goods provide. Learn the budget line equation and slope, total and marginal utility, the law of diminishing marginal utility, and how the two combine in consumer choice.

The budget line

A budget line (or budget constraint) shows every combination of two goods a consumer can just afford, given a fixed income and the prices of the goods. If income is M and the goods cost PX and PY, the line is PXx + PYy = M. Any point on the line spends the whole budget; points below it are affordable but leave money unspent.

The budget line A budget line drawn on axes for good X and good Y. It meets the vertical axis at income divided by the price of Y and the horizontal axis at income divided by the price of X. The affordable combinations lie in the shaded triangle below the line, and the slope equals minus the price of X over the price of Y. Good Y Good X M / PY M / PX Affordable Budget line slope = −PX / PY
The budget line joins the most of each good you can afford; the shaded region is affordable.

The line meets each axis where all income goes to one good, and its slope is −PX/PY — the rate at which the market lets you trade one good for the other. A change in income shifts the line; a change in one price rotates it, a setup studied further with the budget equation.

Utility is the satisfaction a consumer gets from goods. Total utility is the overall satisfaction from all units consumed, while marginal utility is the extra satisfaction from one more unit.

The law of diminishing marginal utility says that as you consume more of a good, each extra unit adds less satisfaction than the one before. The first slice of pizza is worth a lot; the fourth much less.

Diminishing marginal utility A bar chart of marginal utility for units one through five. The bars get shorter from left to right, showing that each additional unit consumed adds less extra satisfaction than the unit before it. Marginalutility Units consumed 1 2 3 4 5
Marginal utility falls with each additional unit consumed.

The budget line sets what is affordable; utility sets what is desirable. A consumer does best by choosing the affordable combination that reaches the highest utility, which leads into utility maximizing and the way economists model tastes with preferences and indifference curves.

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