The Budget Line | Econ Academy

Before we can figure out what a consumer wants to buy, we need to know what they can buy. The budget line (also called the budget constraint) shows every combination of two goods a consumer can afford given their income and the prices of those goods. Anything on or below the line is affordable; anything above it is out of reach.

Key Term

Budget Line

The budget line is the set of all bundles $(X, Y)$ that exactly exhaust a consumer’s income. The equation is $P_{X} X + P_{Y} Y = I$ , where $P_{X}$ and $P_{Y}$ are prices and $I$ is income. Points below the line are affordable but leave money unspent; points above the line are unaffordable.

Budget line in slope-intercept form. The vertical intercept is $I / P_{Y}$ and the slope is $- P_{X} / P_{Y}$ .

Interactive — Building the budget line: 60 dollars on coffee and sandwiches

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5-step walk through finding intercepts, slope, and an affordable bundle on the line.

The slope of the budget line is $- P_{X} / P_{Y}$ , the negative of the price ratio. This tells you the opportunity cost of one more unit of good $X$ in terms of good $Y$ . If a pizza costs 10 dollars and a movie costs 20 dollars, the slope is $- 10/20 = - 0.5$ : every extra pizza costs you half a movie.

The intercepts are easy to find. If you spend all your income on good $X$ , you can buy $I / P_{X}$ units. If you spend everything on good $Y$ , you get $I / P_{Y}$ units. Connect these two intercept points and you have the budget line. The budget set is the entire triangle below and including the line — every bundle the consumer can afford.

Check yourself · no marks

A student has 120 dollars to spend on books (30 dollars each) and meals (10 dollars each). What is the slope of the budget line (with meals on the horizontal axis)?

Commit to one first. Guessing and being wrong beats reading the answer cold.

Worked Example

You have 60 dollars per week to split between coffee (4 dollars per cup) and sandwiches (6 dollars each). Write the budget line equation, find the intercepts, and determine the slope.

Practice · 1 / 4

No penalty for a wrong answer

Apply the budget line concepts:

Income = 200 dollars, price of X = 10 dollars, price of Y = 20 dollars. What is the maximum amount of Y you can buy?

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