## Factors That Affect the Budget Constraint’s Position

Because relative prices determine the slope of the budget constraint, changes in relative prices will change its slope. Figure 4.15a demonstrates what happens to our example budget constraint if the price of lattes doubles to \$10. The budget constraint rotates clockwise around the vertical axis. Because PX doubles, PX/PY doubles, and the budget constraint becomes twice as steep. If Sarah spends all her money on lattes, then the doubling of the price of lattes means she can buy only half as many lattes with the same income (the 5 lattes shown at A′, rather than 10 lattes as before). If, on the other hand, she spends all her money on burritos (point B), then the change in the price of a latte doesn’t affect the bundle she can consume. That’s because the price of burritos is still the same (\$10). Notice that after the price increase, the set of feasible consumption bundles is smaller: There are now fewer combinations of goods that Sarah can afford with her income.

Figure 4.15: Figure 4.15 Effects of Price or Income Changes on the Budget Constraint
Figure 4.15: (a) When the price of lattes increases, the horizontal intercept (I/Plattes) falls, the slope (–Plattes/Pburritos) gets steeper, the budget constraint rotates toward the origin, and the consumer (Sarah) has a smaller set of latte and burrito combinations from which to choose. The higher price for lattes means that she can buy fewer lattes, or if she purchases the same number of lattes, she has less money remaining to buy burritos.
(b) When the price of burritos increases, the vertical intercept (I/Pburritos) falls, the slope (–Plattes/Pburritos) gets flatter, the budget constraint rotates toward the origin, and again, Sarah has a smaller choice set. The higher price for burritos means that she can buy fewer burritos or, for a given purchase of burritos, she has less money available to buy lattes.
(c) When Sarah’s income is reduced, both the horizontal and vertical intercepts fall and the budget constraint shifts in. The horizontal intercept is lower because income I falls; thus, (I/Plattes) falls. The same holds for the vertical axis. Because the movement along both axes is caused by the change in income (the reduction in I is the same along both axes), the new budget constraint is parallel to the initial budget constraint. Given a reduction in income, Sarah’s choice set is reduced.

If, instead, the price of a burritos doubles to \$20, but lattes remain at their original \$5 price (as in Figure 4.15b), the budget constraint’s movement is reversed: It rotates counterclockwise around the horizontal axis, becoming half as steep. If Sarah wanted to buy only lattes, this wouldn’t affect the number of lattes she could buy. If she wants only burritos, now she can obtain only half as many (if you could buy a half a burrito; we’ll assume you can for now), at bundle B′. Notice that this price increase also shrinks the feasible set of bundles just as the lattes’ price increase did. Always remember that when the price rises, the budget constraint rotates toward the origin. When the price falls, it rotates away from the origin.

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Now suppose prices are stable but Sarah’s income falls by half (to \$25). With only half the income, Sarah can buy only half as many lattes and burritos as she could before. If she spends everything on lattes, she can now buy only 5. If she buys only burritos, she can afford 2.5. But because relative prices haven’t changed, the tradeoffs between the goods haven’t changed. To buy 1 more burrito, Sarah still has to give up 2 lattes. Thus, the slope of the budget constraint remains the same. This new budget constraint is shown in Figure 4.15c.

Note that had both prices doubled while income stayed the same, the budget constraint would be identical to the new one shown in Figure 4.15c. We can see this more clearly if we plug in 2PX and 2PY for the prices in the slope-intercept format of the budget constraint:

In both the figure and the equation, this type of change in prices decreases the purchasing power of the consumer’s income, shifting the budget constraint inward. The same set of consumption bundles is feasible in either case. If Sarah’s income had increased rather than decreased as in our example (or the prices of both goods had fallen in the same proportion), the budget constraint would have shifted out rather than in. Its slope would remain the same, though, because the relative prices of burritos and lattes would not have changed.

We’ve now considered what happens to the budget constraint in two situations: when income changes while prices stay constant and when prices change, holding income constant. If prices and income both go up proportionally (e.g., all prices double and income doubles), then the budget constraint doesn’t change at all. You have double the money but everything costs twice as much, so you can only afford the same bundles you could before. You can see this mathematically in the equation for the budget constraint above: If you multiply all prices and income by any positive number (call it k), all the ks will cancel out, leaving you with the original equation.

### figure it out 4.3

Braden has \$20 per week that he can spend on video game rentals (R), priced at \$5 per game, and candy bars (C), priced at \$1 each.

1. Write an equation for Braden’s budget constraint and draw it on a graph that has video game rentals on the horizontal axis. Be sure to show both intercepts and the slope of the budget constraint.

2. Assuming he spends the entire \$20, how many candy bars does Braden purchase if he chooses to rent 3 video games?

3. Suppose that the price of a video game rental falls from \$5 to \$4. Draw Braden’s new budget line (indicating intercepts and the slope).

Solution:

1. The budget constraint represents the feasible combinations of video game rentals (R) and candy bars (C) that Braden can purchase given the current prices and his income. The general form of the budget constraint would be Income = PRR + PCC. Substituting in the actual prices and income, we get 20 = 5R + 1C.

To diagram the budget constraint (see the next page), first find the horizontal and vertical intercepts. The horizontal intercept is the point on Braden’s budget constraint where he spends all of his \$20 on video game rentals. The x-intercept is at 4 rentals (\$20/\$5), point A on his budget constraint. The vertical intercept represents the point where Braden has used his entire budget to purchase candy bars. He could purchase 20 candy bars (\$20/\$1) as shown at point B. Because the prices of candy bars and video game rentals are the same no matter how many Braden buys, the budget constraint is a straight line that connects these two points.

The slope of the budget constraint can be measured by the rise over the run. Therefore, it is equal to We can check our work by recalling that the slope of the budget constraint is equal to the negative of the ratio of the two prices or Remember that the slope of the budget constraint shows the rate at which Braden is able to exchange candy bars for video game rentals.

2. If Braden currently purchases 3 video game rentals, that means he spends \$15 (= \$5 × 3) on them. This leaves \$5 (= \$20 – \$15) for purchasing candy bars. At a price of \$1 each, Braden purchases 5 candy bars.

3. When the price of a video game rental falls to \$4, the vertical intercept is unaffected. If Braden chooses to spend his \$20 on candy bars, at a price of \$1, he can still afford to buy 20 of them. Thus, point B will also be on his new budget constraint. However, the horizontal intercept increases from 4 to 5. At a price of \$4 per rental, Braden can now afford 5 rentals if he chooses to allocate his entire budget to rentals (point C). His new budget constraint joins points B and C.

The slope of the budget constraint is Note that this equals the inverse price ratio of the two goods

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