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Optimal Choice

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Source: Image of Budget Constraint Graph created by Kate Eskra, Image of Preference Map created by Kate Eskra

Hi. Welcome to economics. This is Kate. This tutorial is called Optimal Choice. As always, my key terms are in red and my examples are in green.

In this tutorial, we'll be looking at the budget constraint. You'll see an equation for the budget constraint, as well as what it looks like on a graph. You'll be able to read and interpret indifference curves, and specifically in this tutorial, you'll understand how indifference curves work together with the budget constraint to help us maximize our utility to make the best choice.

So we know that we all have to make choices every day. We also are very familiar with the fact that we are constrained by our time and our money. So the whole point of all of this, when it all comes together, we'll be looking at, how do we make the best choice to help us maximize our utility? Remember, utility is satisfaction. It's what we get out of something.

So here it is as your key term, the budget constraint. It's 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, that's where the consumer is going to be optimizing consumption, or getting the most utility.

So let's say that Kim has a budget for herself of $100 to spend every month on "fun," and let's simplify it. Let's say that there are two things that she's looking at doing for fun, going to the movies or ordering Chinese takeout. The movies are going to cost her about $20 every time she goes between the ticket and snacks at the concessions stand, whereas Chinese takeout is going to cost her $10. So Kim's budget constraint is going to list for us all of the possible combinations she can afford if, in fact, she spends all $100 on these two activities every month.

Let's look at the equation first. So again, her budget is $100. We'll call Chinese takeout good x, and we'll call the movies good y, and there are the prices. So the equation's really pretty simple. You just take the price of whatever the first one is, so $10 times however many times she orders Chinese takeout. 20 plus $20 times however many times she goes to the movies has to equal $100. If she orders Chinese takeout two times, that would be $20 here. How many times can she go to the movies? We would solve for y and figure that out. That's what the equation looks like.

Now, if we graph that equation, it's going to look something like this. Kim's budget constraint for the month, where her budget's $100, we put trips to the movies on the y-axis and Chinese takeout on the x-axis. This right here is showing that at the extremes, she can either afford five trips to the movies-- because again, if she gets Chinese takeout 0 times, 5 times 20 gives her her $100 budget-- or the other extreme, if she goes to the movies not at all, she can order Chinese takeout 10 times because 10 times $10 gives her her $100 budget.

But most people recognize that we would probably prefer some combination. Anywhere along this budget constraint would be within her budget, or would be her budget exactly. Anything in green is under her budget. It's totally within her budget constraint. If she actually purchases in here, she's saving money. She's not spending all $100. Anything out here, she does not have the money to do it because it's outside of her budget constraint.

But this by itself doesn't really tell us what combination she should choose. We don't know what she prefers. Does she prefer Chinese takeout? Does she prefer the movies? Well, let's go a little bit further.

If she is in fact going to maximize her utility, that means that she's achieving the highest amount of satisfaction within her budget. And if she is, in fact, 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.

So let's put it all together. So we have that budget constraint, nothing changed with that, but now I've added a series of indifference curves. So remember, an indifference curve, just one of these-- let's look at this first one right here-- tells us any point along that indifference curve Kim would be indifferent to. She doesn't prefer any one point along that curve to the next. She would like this as much she would like this as much as she would like this.

But indifference curve two, indifference curve three, indifference curve four, she gets more and more utility the further out her indifference curves go. Indifference curve two here would yield more utility than indifference curve one. That's going to help us figure out the ultimate point.

Well, we can rule out her purchasing at point A because that's inside her budget constraint, so she can definitely still increase her utility by spending more money and gaining more trips to the movies and more Chinese takeout, potentially. We can rule out point D because she can't spend that money. It's outside of her budget constraint. So that leaves us with should she stay at point B or should she be at point C, because they're both on her budget constraint? She's spending exactly $100.

Well, the indifference curves help give us that answer, and it turns out that C would yield the highest level of utility because that indifference curve is further out than this indifference curve. So by definition of indifference curves, her utility is higher at any point along this third curve than along this one. So C is within our budget and it's on the highest possible indifference curve that is within her budget, so that would be the best choice for Kim.

So what did you learn in this tutorial? You looked at a budget constraint. We talked about the equation of it and we looked at a graph of it. It all really comes together when we saw that last graph where we put the indifference curves together with the budget constraint to show us the combinations that are possible, but also the combinations that maximize our utility and help us to optimize our choices. Thank you so much for listening. Have a wonderful day.

*Budget Constraint*

*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.*

**Utility Maximization**

*Achieving the highest amount of satisfaction given a consumer's budget constraint.*

**Optimal Choice**

*Goods and services purchased by a consumer that provides the highest level of utility possible.*