In the preceding sections, we analyzed how a consumer’s preferences can be described by a utility function, why indifference curves are a convenient way to think about utility, and how the slope of the indifference curve—

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We start looking at the interactions of utility, income, and prices by making some assumptions. To keep things simple, we continue to focus on a model with only two goods.

Each good has a fixed price, and any consumer can buy as much of a good as she wants at that price if she has the income to pay for it. We can make this assumption because each consumer is only a small part of the market for a good, so her consumption decision will not affect the equilibrium market price.

The consumer has fixed income available to spend.

For now, the consumer cannot borrow or save. Without borrowing, she can’t spend more than her income in any given period. With no saving, it means that unspent money is lost forever, so it’s use it or lose it.

**budget constraint**

A curve that describes the entire set of consumption bundles a consumer can purchase when spending all income.

To incorporate prices and the consumer’s income into our model of consumer behavior, we use a budget constraint. This constraint describes the entire set of consumption bundles that a consumer can purchase by spending all of her money. For instance, let’s go back to the example of Sarah and her burritos and lattes. Suppose Sarah has an income of $50 to spend on burritos (which cost $10 each) and lattes ($5 each). Figure 4.14 shows the budget constraint corresponding to this example. The number of lattes is on the horizontal axis; the number of burritos is on the vertical axis. If Sarah spends her whole income on lattes, then she can consume 10 lattes (10 lattes at $5 each is $50) and no burritos. This combination is point *A* in the figure. If instead Sarah spends all her money on burritos, she can buy 5 burritos and no lattes, a combination shown at point *B*. Sarah can purchase any combination of burritos and lattes that lies on the straight line connecting these two points. For example, she could buy 3 burritos and 4 lattes. This is point *C*.

Figure 4.14: **Figure 4.14 The Budget Constraint**

Figure 4.14: The budget constraint demonstrates the options available to a consumer given her income and the prices of the two goods. The horizontal intercept is the quantity of lattes the consumer could afford if she spent all of her income (*I*) on lattes, *I*/*P*_{lattes}. The vertical intercept is the quantity of burritos she could afford if she spent all of her income on burritos, *I*/*P*_{burritos}. Given this, the slope of the budget constraint is the negative of the ratio of the two prices, –*P*_{lattes}/*P*_{burritos}.

The mathematical formula for a budget constraint is

Income = *P _{X}Q_{X}* +

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where *P _{X}* and

**feasible bundle**

A bundle that the consumer has the ability to purchase; lies on or below the consumer’s budget constraint.

**infeasible bundle**

A bundle that the consumer cannot afford to purchase; lies to the right and above a consumer’s budget constraint.

Any combination of goods on or below the budget constraint (i.e., any point between the origin on the graph and the budget constraint, including those on the constraint itself) is feasible**,** meaning that the consumer can afford to buy the bundle with her income. Any points above or to the right of the budget line are infeasible**.** These bundles are beyond the consumer’s reach even if she spends her entire income. Figure 4.14 shows the feasible and infeasible bundles for the budget constraint 50 = 5*Q*_{lattes} + 10*Q*_{burritos}.

The budget constraint in Figure 4.14 is straight, not curved, because we assumed Sarah can buy as much as she wants of a good at a set price per unit. Whether buying the first latte or the tenth, we assume the price is the same. As we see later, if the goods’ prices change with the number of units purchased, the budget line will change shape depending on the amount of the goods purchased. That’s an unusual case, though.