In this note, I show how indifference curves and budget constraints relate to . A demand curve captures the relationship between food choices. The budget line intersects with the point (2,2) along the pink indifference curve indicating that we can hire Chris for 2 hours and Sammy for 2. A simplified explanation of indifference curves and budget lines with choice of goods can also be shown with the Equi-marginal principle.
Then we can draw some conclusions about the choices a utility-maximizing consumer could be expected to make. Total spending for goods and services can fall short of the budget constraint but may not exceed it. Algebraically, we can write the budget constraint for two goods X and Y as: Suppose a college student, Janet Bain, enjoys skiing and horseback riding. For a consumer who buys only two goods, the budget constraint can be shown with a budget line.
A budget line shows graphically the combinations of two goods a consumer can buy with a given budget.
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The budget line shows all the combinations of skiing and horseback riding Ms. Combinations above and to the right of the budget line are beyond the reach of her budget. The vertical intercept of the budget line point D is given by the number of days of skiing per month that Ms.
Bain could enjoy, if she devoted all of her budget to skiing and none to horseback riding. If she spent the entire amount on skiing, she could ski 5 days per semester. She would be meeting her budget constraint, since: She could purchase 5 days of either skiing or horseback riding per semester.
Again, this is within her budget constraint, since: More generally, we find the slope of the budget line by finding the vertical and horizontal intercepts and then computing the slope between those two points.
The vertical intercept of the budget line is found by dividing Ms. The horizontal intercept is found by dividing B by the price of horseback riding, the good on the horizontal axis PH.
The slope is thus: It is easy to go awry on the issue of the slope of the budget line: It is the negative of the price of the good on the horizontal axis divided by the price of the good on the vertical axis.
But does not slope equal the change in the vertical axis divided by the change in the horizontal axis? The answer, of course, is that the definition of slope has not changed.
Notice that Equation 7. We then manipulated Equation 7.
Price is not the variable that is shown on the two axes. The axes show the quantities of the two goods. Indifference Curves Suppose Ms. Bain spends 2 days skiing and 3 days horseback riding per semester. She will derive some level of total utility from that combination of the two activities. There are other combinations of the two activities that would yield the same level of total utility.
Combinations of two goods that yield equal levels of utility are shown on an indifference curve. Because all points along an indifference curve generate the same level of utility, economists say that a consumer is indifferent between them. Point X marks Ms. The indifference curve shows that she could obtain the same level of utility by moving to point W, skiing for 7 days and going horseback riding for 1 day.
She could also get the same level of utility at point Y, skiing just 1 day and spending 5 days horseback riding. Bain is indifferent among combinations W, X, and Y. We assume that the two goods are divisible, so she is indifferent between any two points along an indifference curve.
Janet Bain is thus indifferent to which point on the curve she selects. Any point below and to the left of the indifference curve would produce a lower level of utility; any point above and to the right of the indifference curve would produce a higher level of utility. Now look at point T in Figure 7. It has the same amount of skiing as point X, but fewer days are spent horseback riding.
Bain would thus prefer point X to point T. Similarly, she prefers X to U. What about a choice between the combinations at point W and point T? Because combinations X and W are equally satisfactory, and because Ms. Bain prefers X to T, she must prefer W to T. In general, any combination of two goods that lies below and to the left of an indifference curve for those goods yields less utility than any combination on the indifference curve.
Such combinations are inferior to combinations on the indifference curve. Point Z, with 3 days of skiing and 4 days of horseback riding, provides more of both activities than point X; Z therefore yields a higher level of utility.
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It is also superior to point W. In general, any combination that lies above and to the right of an indifference curve is preferred to any point on the indifference curve. We can draw an indifference curve through any combination of two goods.
Indifference curve A from Figure 7. Bain prefers all the combinations on indifference curve B to those on curve A, and she regards each of the combinations on indifference curve C as inferior to those on curves A and B. Although only three indifference curves are shown in Figure 7. Different consumers will have different maps.
We have good reason to expect the indifference curves for all consumers to have the same basic shape as those shown here: They slope downward, and they become less steep as we travel down and to the right along them.
Curves that are higher and to the right are preferred to those that are lower and to the left. Here, indifference curve B is preferred to curve A, which is preferred to curve C. Bain is at point S, consuming 4 days of skiing and 1 day of horseback riding per semester. Suppose she spends another day horseback riding. This additional day of horseback riding does not affect her utility if she gives up 2 days of skiing, moving to point T.
She is thus willing to give up 2 days of skiing for a second day of horseback riding. The curve shows, however, that she would be willing to give up at most 1 day of skiing to obtain a third day of horseback riding shown by point U. It is the maximum amount of one good a consumer is willing to give up to obtain an additional unit of another. Here, it is the number of days of skiing Janet Bain would be willing to give up to obtain an additional day of horseback riding.
Notice that the marginal rate of substitution MRS declines as she consumes more and more days of horseback riding. The maximum amount of one good a consumer would be willing to give up in order to obtain an additional unit of another is called the marginal rate of substitution MRSwhich is equal to the absolute value of the slope of the indifference curve between two points. Bain devotes more and more time to horseback riding, the rate at which she is willing to give up days of skiing for additional days of horseback riding—her marginal rate of substitution—diminishes.
The Utility-Maximizing Solution We assume that each consumer seeks the highest indifference curve possible. The budget line gives the combinations of two goods that the consumer can purchase with a given budget.
Utility maximization is therefore a matter of selecting a combination of two goods that satisfies two conditions: In other words, the consumer would be indifferent to these different combinations. Example of choice of goods which give consumers the same utility Table plotted as indifference curve Diminishing marginal utility The indifference curve is convex because of diminishing marginal utility. When you have a certain number of bananas — that is all you want to eat in a week.
Extra bananas give very little utility, so you would give up a lot of bananas to get something else.
Indifference curve map We can also show different indifference curves. All choices on I2 give the same utility. But, it will be a higher net utility than indifference curve I1. I4 gives the highest net utility. Basically, I4 would require higher income than I1. Budget line A budget line shows the combination of goods that can be afforded with your current income.
IC3 is obtainable but gives less utility than the higher IC1 The optimal choice of goods can also be shown with the Equi-marginal principle Income-consumption curve As income rises, you can afford to consume on higher indifference curves. This optimal choice will shift to the right.
Indifference curves and budget lines
This we can plot consumption as income rises. The budget line shifts to the right With lower prices, we can now consume at a higher indifference curve of IC2, enabling more bananas and apples.
Income and substitution effect of a rise in price When the price of a good rises. People buy less for two reasons Income effect. This looks at the effect of a price increase on disposable income. If the price of a good increases, then consumers will have relatively lower disposable income.