A budget line consists of all the consumption bundles that just exhaust the consumer's income. It is the boundary that separates all the affordable consumption bundles from all other bundles. Affordable choices that do not exhaust the consumer's income lie to the southwest of the budget line.
The slope of the budget line equals the price ratio times negative one, with the price of the good measured on the horizontal axis appearing in the numerator, and the price of the good measured on the vertical axis appearing in the denominator.
The budget line intersects the axis that measures the amount of any particular good, X, at the quantity M/PX, which is the amount of X the consumer can purchase by spending all income on X.
A change in income shifts the budget line—outward for an increase and inward for a decrease—without hanging its slope.
A change in the price of a good rotates the budget line—outward for a decrease and inward for an increase. The line pivots at the intercept for the good with the unchanged price.
Multiplying all prices by a single constant has the same effect on the budget line as dividing income by the same constant. Changing prices and income by the same proportion has no effect on the budget line.
Consumer choice
Assuming that more is better, the consumer's best choice lies on the budget line.
We can recognize best choices by applying the no-overlap rule.
Interior solutions always satisfy the tangency condition. Consequently, if a bundle that includes two goods, X and Y, is an interior solution, then MRSXY = PX/PYat that bundle.
When indifference curves have declining MRSs, any interior choice that satisfies the tangency condition is a best affordable choice.
Whenever the consumer purchases good X but not good Y, then MRSXY ≥ PX/PYat the chosen bundle.
Utility maximization
If a utility function represents a consumer's preference, then the affordable bundle that maximizes the utility function is the consumer's best choice.
At the best choice, a small amount of additional income generates the same increase in the consumer's utility value when spent on any good whose quantity is positive. That is, at the best choice, the ratio of marginal utility to price is the same for all goods. The increase in utility is at least as large as when the additional income is spent on any good whose quantity is zero.
Prices and demand
The price-consumption curve provides all the information necessary to draw an individual demand curve.
When the price of one good changes, the demand curve for another good may shift. The demand curve shifts to the left when the price of a complement rises and to the right when it decreases. When the price of a substitute changes, these effects are reversed.
Income and demand
We can determine how the consumption of a good varies with income, and whether it is normal or inferior, by examining the income-consumption curve.
At least one good must be normal starting from any particular income level.
No good can be inferior at all levels of income.
The income elasticity of demand is positive for normal goods and negative for inferior goods.
When a good is normal, the Engel curve slopes upward; when a good is inferior, it slopes downward.
An individual demand curve for a good shifts when income changes. When the good is normal, an increase in income shifts the demand curve to the right, and a decline in income shifts the demand curve to the left. When a good is inferior, these patterns are reversed.
How economists determine a consumer's preferences
If we can observe a sufficient number of consumer choices with sufficient variation in prices and income, we can trace the shape of a consumer's indifference curve. These choices reveal the consumer's preferences.
In practice, economists have few opportunities to observe a single consumer make a large number of choices. Instead, they usually combine data on the choices of many individuals, using statistical procedures to allow for differences in individual preferences.
