Consumer Optimization

The way we make choices about what to buy depends on how our dreams, our wants, meet reality. We've covered thinking on the margin, budget constraints, and indifference curves. Now let's bring this all together to model how you decide what to purchase.

Remember, your budget constraint represents how the market values goods and what you can afford, given your income. Your indifference curves represent how you value goods based on your personal preferences. We all wish we could have more of everything. We would love to be way out here where we can consume as much as we want. But the reality is that we have limited resources and the prices of things force us to make tradeoffs. We want to get the best bang for our buck and that means finding that optimal combination of goods that brings together how the market values goods and our preferences. That's what this graph, illustrating your indifference curves and budget constraint, lets us better understand.

When you make a decision, you are effectively trying to be the happiest that you can, given the constraints that you face. You are, without knowing, solving a "constrained optimization" problem, where you are choosing the combination of goods that maximize your utility given the prices of goods and your income.

Let's go back to our pizza and coffee example. You have a budget of $50. Pizza costs $10. And each cup of coffee costs $5. Now, let's assume your indifference map looks like this. Making the best choice you can afford means you will spend your entire budget on the combination of pizzas and cups of coffee that make you the happiest. This means that your optimal consumption combination is on your budget line. Making the best choice you can afford also means that you will try to reach the indifference curve that represents the highest degree of satisfaction or utility. Because pizza and coffee are good things -- things that make you happy -- this will occur on the indifference curve that is the farthest away from the origin.

Why? Because the more pizza and coffee you have, the happier you are. What keeps you from reaching this indifference curve? If you thought prices and income, you are right! Your budget constraint determines what you can afford. So your optimal consumption combination will be where your budget constraint is tangent to the highest indifference curve.

To see why, let's go back to thinking about why you try to reach the indifference curve that is the farthest away from the origin. The best way to go about it is to look at a point where the budget line intersects one of your indifference curves. This particular combination of pizza and coffee -- it's affordable, because it's on your budget line. However, you are not the happiest you could be, now are you? Given your preferences, it's clear that you would be happier if you could buy this combination. It has more pizza, and just as many cups of coffee. But, hey, it's beyond your budget.

But now look at this. You are indifferent between this combination and this combination. Both are on the same indifference curve, and that means they provide you with the same utility. So, if you are trying to get the most utility you can, given what you can afford, you will never choose a combination of goods that intersects your budget constraint. You will choose one that is tangent to it. The point of tangency between the budget constraint and the indifference curve also means that at your optimal consumption combination, the market's relative price of the goods equals your willingness to substitute between them -- and that's your marginal rate of substitution.

Another way to see this is to recognize that at your best choice, the marginal utility per dollar of both goods is the same. Let's go back to thinking at the margin. At this point, would it make you happier to spend more money on pizza and less on coffee? Here, the marginal rate of substitution is 4, and that means you are willing to forego four cups of coffee to get one additional pizza. But pizza is only twice as expensive as coffee. So this is great news for you. The market is asking you to forego fewer cups of coffee than you are willing to. So you get that extra pizza.

Another way to think about this is to realize that at this point, your marginal utility per dollar of pizza is greater than your marginal utility per dollar from cups of coffee. Remember, as you get more pizzas, and are left with fewer cups of coffee, your marginal utility from pizzas is decreasing, and your marginal utility from cups of coffee is increasing. You will stop getting additional pizzas when your marginal utility per dollar from both goods is equal. Of course, very few of us calculate marginal utility or think of constrained optimization when we choose what to buy. But these concepts can help you understand your world and guide you how to make better decisions in the future.