We as consumers have to make choices every day. We are also very aware of our constraints, which are primarily time and income.
Therefore, how do we make the best choice to maximize our utility?
Our first key term, budget constraint, is defined as the graphical depiction of consumer income relative to the price of goods available.
Where the budget constraint touches the highest indifference curve available, the consumer is defined to be optimizing consumption, or getting the most utility.
IN CONTEXT
Suppose Kim has a budget of $100 to spend each month on "fun." She must choose between going to the movies or ordering Chinese takeout, her two designated "fun for the month" activities.
The movies will cost her $20 each time she goes, between the ticket and snacks at the concessions stand, whereas the Chinese takeout will cost her $10.
Kim's budget constraint will list all of the possible combinations she can afford if she spends all $100 on these two activities every month.
Let's look at the equation first. Again, her budget is $100, and we will call Chinese takeout "Good X," and the movies "Good Y":
Budget = $100
Good X (Chinese Takeout) = $10
Good Y (Movies) = $20
The budget constraint equation is fairly simple. We simply take the price of the first activity, Chinese takeout, times however many times she orders it, plus the price of the second activity, movies, times however many times she goes to the movies. The sum of these must equal $100.
$10X + $20Y = $100
For instance, if she orders Chinese takeout two times, then $10X would equal $20. Then, she could solve for Y to figure out how many times she can go to the movies and still stay within her budget of $100.
We will put trips to the movies on the y-axis and Chinese takeout on the x-axis.
Notice the extremes for each option, which indicate that she can afford either:
However, most people would probably prefer some combination.
Therefore, anywhere along this budget constraint would be her budget exactly, while anything in green is under her budget, or within her budget constraint.
If she purchases in this green area, she is saving money, by not spending all $100.
She does not have the money to do anything outside of her budget constraint.
However, this by itself doesn't really tell us what combination she should choose, because we don't know what she prefers. Does she prefer Chinese takeout? Does she prefer the movies? Let's explore this idea a bit further.
Now, if Kim is in fact going to strive for utility maximization, this means she is achieving the highest amount of satisfaction given her budget constraint.
It follows, then, that if she is getting the highest level of utility possible, she would be making the optimal choice. She would be purchasing the goods and services that are providing her with the highest level of utility or satisfaction.
Let's put it all together. Here we have the same budget constraint, but now we have added a series of indifference curves.
Notice, though, when you look at indifference curve two (with point B), indifference curve three (point C), and indifference curve four (point D), she gets more and more utility the further out her indifference curves go.
Indifference curve two would yield more utility than indifference curve one, and so on, which is going to help us figure out the ultimate point.
| Indifference Curve | Budget Constraint |
|---|---|
| Curve 1 - Point A | Inside budget constraint (can still increase utility) |
| Curve 2 - Point B | On budget constraint |
| Curve 3 - Point C | On budget constraint |
| Curve 4 - Point D | Outside budget constraint (cannot afford) |
Well, we can rule out her purchasing at point A because that is inside her budget constraint, so she can definitely still increase her utility by spending more money and potentially gaining more trips to the movies and more Chinese takeout.
We can also rule out point D because she can't spend that money--it's outside of her budget constraint.
Therefore, should she stay at point B or point C, because they are both on her budget constraint? In either case, she is spending exactly $100.
Well, the indifference curves help provide that answer, and it turns out that point C would yield the highest level of utility because that indifference curve is further out than the one containing point B.
So, by definition of indifference curves, Kim's utility is higher at any point along the third curve than along the second one.
C is within her budget and is also on the highest possible indifference curve that is within her budget, so is therefore the optimal choice for Kim.
Source: Adapted from Sophia instructor Kate Eskra.
