budgetlinjer

A budget line, or budgetlinje, is a graphical representation of all combinations of two goods that a consumer can buy given a fixed income and prevailing prices. It shows the trade-offs the consumer faces when allocating limited resources.

In mathematical terms, if the prices are p1 and p2 for goods 1 and 2, and the consumer has income m, the budget line is p1 x1 + p2 x2 = m, where x1 and x2 are the quantities purchased. The line is bounded by nonnegativity constraints (x1 ≥ 0, x2 ≥ 0). The intercepts are x1 = m/p1 and x2 = m/p2, and the slope is -p1/p2, reflecting the opportunity cost of substituting one good for the other.

Changes in the budget line occur from income and price changes. A rise in income shifts the line outward (parallel shift), while a decrease shifts it inward. A change in the price of a good rotates the line around the remaining intercept, altering the slope. With more than two goods, the budget constraint becomes a hyperplane in higher-dimensional space.

The budget line is used in consumer theory to illustrate choice. Consumers maximize a utility function subject to the budget constraint, typically at the point where an indifference curve is tangent to the budget line, implying that the consumer’s marginal rate of substitution equals the price ratio. Budget lines also help explain concepts such as opportunity cost, normal and inferior goods, and the impact of policy changes on purchasing choices.