Just as production possibilities frontiers limit society s ability to produce and consume, each individual family is constrained by its income in choosing among consumption alternatives. A consumer s budget line is usually straight because the purchasing pattern a family chooses seldom affects market prices.

A budget line (or constraint) depicts the choices available to a consumer who faces constant prices and who has a given income.

Figure 5 shows budget lines for two levels of income using the assumption that asparagus (A) and a proxy for all other goods, called shmoo (B), each cost $1 per pound. Any point in the AB space represents a specific combination of asparagus and shmoo and would require a certain level of income.

We can write the family s budget constraint as equal to

where Pa and Pb are the prices of asparagus and shmoo, respectively, and all family income (Y) is spent on either asparagus (A) or shmoo (B).

Because income is limited, asparagus can be traded for shmoos as long as the family stays within its income constraint. Subtracting PaA from each side yields

Finally, we can solve for the amounts of B, given certain purchases of A, if we divide this equation by Pb:

This equation defines the budget line for the family in Figure 5.

 

Because both asparagus and shmoo cost $1 per pound (Pa = Pb), point v represents the situation where the family has $600 per week, all of which is spent on shmoo. Note that Y/Pb = $600/$1 = 600 pounds of shmoo. Point z represents just the opposite: all income is spent on asparagus, nothing is spent on shmoo.

 

The slope of the budget line equals  Pa/Pb, which equals  1, because shmoo and asparagus are priced identically. Thus, as income changes, the family s budget line moves in or out, but as long as the ratio of the two prices remains the same, the slope of the budget line will not change.

 

The budget line pivots if asparagus prices double to $2 a pound. A consumer with a $600 weekly income could now buy a maximum of only 300 pounds of asparagus, but could still buy as much as 600 pounds of shmoo. Alternatively, if the price of asparagus fell to $0.50 a pound, up to 1,200 pounds of asparagus might be purchased from a $600 income. Budget lines reflecting various possible prices for asparagus, with the price of shmoo still at $1 a pound and with a $600 weekly budget, are shown in Figure 6.