The budget set and budget line

A consumer cannot buy everything: she is limited by her income (M) and the prices of the goods (p1 and p2).

The budget set is all the bundles she can afford: p1x1 + p2x2 ≤ M.

The budget line is the bundles that cost exactly her income: p1x1 + p2x2 = M.

• If she spends everything on good 1, she gets M ÷ p1 (where the line meets the x1 axis); on good 2 only, M ÷ p2.
• The slope of the line is −p1 ÷ p2: the rate at which the market lets her swap good 2 for good 1.

Example: income ₹30, prices ₹5 and ₹3. Budget line: 5x1 + 3x2 = 30; she can buy at most 6 of good 1 or 10 of good 2; slope = −5/3. Points above the line are not affordable.

Changes:

• A change in income shifts the line parallel: outward if income rises, inward if it falls.
• A change in the price of good 1 pivots the line around its intercept on the good 2 axis. If p1 rises, she can buy less of good 1, and the line becomes steeper.

If both prices and income change in the same proportion (say, all double), the budget set does not change.