Introduction to Utility Maximization

As consumers, we make choices every day about what and how much to buy and use. In order to model how consumers make these decisions, economists (reasonably) assume that people make choices that maximize their levels of happiness. Economists even have their own word for happiness:

• utility: the amount of happiness gained from consuming a good or service

This concept of economic utility has some specific properties that are important to keep in mind:

• sign matters: positive utility numbers (i.e. numbers greater than zero) indicate that consuming a good makes the consumer happier. Conversely, negative utility numbers (i.e. numbers less than zero) indicate that consuming a good makes the consumer less happy.
• bigger is better: The greater the utility number, the more happiness the consumer receives from consuming an item. (Note that this is consistent with the first point, since large negative numbers are smaller, i.e. less than, small negative numbers.)
• ordinal but not cardinal properties: Utility numbers can be compared, but it doesn't necessarily make sense to perform calculations with them. In other words, while it is the case that a utility of 6 is better than a utility of 3, it is not necessarily the case that a utility of 6 is twice as good as a utility of 3. Similarly, it's not necessarily the case that a utility of 2 and a utility of 3 would add to a utility of 5.

Economists use this concept of utility to model consumers' preferences, since it stands to reason that consumers prefer items that give them higher levels of utility. The consumer's decision regarding what to consume, therefore, boils down to answering the question "What affordable combination of goods and services gives me the most happiness?"

In the utility maximization model, the "affordable" part of the question is represented by a budget constraint and the "happiness" part is represented by what are known as indifference curves. We will examine each of these in turn and then put them together to arrive at the consumer's optimal consumption.