Budget Line
The budget line is a graphical representation of the combinations of two goods that a consumer can afford given a fixed income and given prices. It defines the boundary of the consumer's feasible set and is a central tool in the analysis of consumer choice.
Definition
The budget line shows all combinations of two goods for which the consumer spends exactly their entire income. Its position depends on income and on the prices of the goods. An increase in income shifts the line outward, parallel to the original, while a change in the price of one good rotates the line, changing its slope.
The slope of the budget line equals the negative of the ratio of the prices of the two goods, which is the rate at which the consumer can trade one good for the other in the market. The intercepts show the maximum quantity of each good that can be purchased if all income is spent on that good.
Consumer Choice
The consumer's optimal choice is the point on the budget line that lies on the highest attainable indifference curve, where the budget line is tangent to the curve. At this point, the marginal rate of substitution between the goods equals the ratio of their prices, so that the rate at which the consumer is willing to trade equals the rate at which the market allows.
The solution to the consumer's problem yields the demand functions, which relate the quantities demanded to income and prices. The analysis of the budget line and indifference curves therefore provides the foundation for the theory of demand and for the analysis of the effects of changes in income and prices.
Shifts and Rotations
Changes in income shift the budget line. An increase in income moves the line outward, expanding the feasible set and allowing the consumer to reach a higher indifference curve, provided that both goods are normal. A decrease in income moves the line inward, reducing the feasible set.
Changes in prices rotate the budget line. A fall in the price of one good rotates the line outward along the axis of that good while leaving the intercept on the other axis unchanged, increasing the maximum affordable quantity. The rotation changes both the slope and the position of the line, altering the consumer's optimum.
Applications
The budget line is used to analyse a range of questions, including the effects of taxes and subsidies, the impact of rationing, and the choice between work and leisure. A tax on one good rotates or shifts the budget line, changing the consumer's optimum and generating a deadweight loss. A lump-sum transfer shifts the line outward without changing its slope.
The framework also extends to intertemporal choice, where the budget line represents the trade-off between consumption now and consumption in the future, and to the analysis of labour supply, where the budget line represents the trade-off between leisure and income. These applications illustrate the versatility of the budget line as a tool of economic analysis.
Income and Substitution Effects
Changes in prices affect consumer choices through two effects. The substitution effect reflects the change in relative prices, which encourages the consumer to substitute away from the good that has become relatively more expensive. The income effect reflects the change in real income, which alters the consumer's purchasing power.
The decomposition of the total effect into income and substitution effects provides insight into the nature of demand. For a normal good, the two effects work in the same direction, so that a price increase reduces demand. For an inferior good, the income effect works in the opposite direction, and in the case of a Giffen good, it dominates, so that demand rises when the price rises.
Revealed Preference
The theory of revealed preference provides an alternative foundation for demand theory, based on observed choices rather than on preferences. If a consumer chooses one bundle over another when both are affordable, the chosen bundle is revealed preferred, and the theory imposes consistency conditions on choices.
The approach avoids the need to specify a utility function and provides testable implications for consumer behaviour. It has been extended to the analysis of demand and to the measurement of welfare changes, and it informs the empirical analysis of consumer choice.
Rationing and Quantity Constraints
When consumers face quantity constraints, such as rationing or limits on purchases, the budget line framework must be modified. A binding constraint prevents the consumer from reaching the optimal bundle and creates a corner solution, in which the consumer purchases the maximum allowed of the rationed good.
The analysis of quantity constraints is relevant to the study of centrally planned economies, of rationing during emergencies, and of markets with quantity restrictions. It informs the assessment of the welfare effects of rationing and of the design of policies that impose constraints.
Intertemporal Choice
The budget line framework extends to intertemporal choice, in which the consumer allocates consumption over time subject to an intertemporal budget constraint. The slope of the constraint reflects the interest rate, which determines the rate at which the consumer can trade present for future consumption.
The analysis of intertemporal choice informs the study of saving, of borrowing, and of the effects of taxes and of interest rate changes on consumption over the life cycle. It provides the foundation for the life-cycle and permanent income hypotheses.