Budgetlinjen

Budgetlinjen, the Danish term for the budget line, is a fundamental concept in consumer choice theory. It represents all combinations of two goods that a consumer can afford given their income and the prices of the goods. Graphically, it is a straight line in the plane defined by the quantities of the two goods.

For goods X and Y with prices p_x and p_y and income I, the budget line satisfies p_x x + p_y y = I. The intercepts are x = I/p_x when y = 0 and y = I/p_y when x = 0. The slope is -p_x/p_y, which shows the rate at which the consumer can trade off one good for the other while keeping expenditure constant. The line assumes goods are divisible and that prices and income are known and fixed.

Changes in income shift the budget line outward (increased income) or inward (decreased income) while preserving its slope. Changes in prices rotate the line around an intercept, altering the slope. The consumer’s optimal choice is typically at the point where the budget line is tangent to the highest attainable indifference curve; if the tangency cannot be achieved due to constraints, the optimum may lie at a corner of the budget set.

In multi-good contexts, the concept generalizes to a budget plane or hyperplane in higher dimensions. The budget line is a simplification that aids analysis of how price changes, income, and preferences shape consumption choices.