# Introduction to the Use of Marginal Analysis

## Thinking at the Margin

From an economist's perspective, making choices involves making decisions 'at the margin' -- that is, making decisions based on small changes in resources:

• How should I spend the next hour?
• How should I spend the next dollar?

In fact, economist Greg Mankiw lists under the "10 principles of economics" in his popular economics textbook the notion that "rational people think at the margin." On the surface, this seems like a strange way of considering the choices made by people and firms. It is rare that someone would consciously ask themselves -- "How will I spend dollar number 24,387?" or "How will I spend dollar number 24,388?" The idea of marginal analysis doesn't require that people explicitly think in this way, just that their actions are consistent with what they would do if they did think in this way.

Approaching decision making from a marginal analysis perspective does have some distinct advantages:

• Doing so leads to the optimal decisions being made, subject to preferences, resources and informational constraints.
• It makes the problem less messy from an analytic point of view, as we are not trying to analyze a million decisions at once.
• While this does not exactly mimic conscious decision-making processes, it does provide results similar to the decisions people actually make. That is, people may not think using this method, but the decisions they make are as if they do.

Marginal analysis can be applied to both individual and firm decision making. For firms, profit maximization is achieved by weighing marginal revenue versus marginal cost. For individuals, utility maximization is achieved by weighing the marginal benefit versus marginal cost. Note, however, that in both contexts the decision maker is performing an incremental form of cost-benefit analysis.

## Marginal Analysis: An Example

To gain some more insight, consider the decision regarding how many hours to work, where the benefits and costs of working are designated by the following chart:

Hour - Hourly Wage - Value of Time
Hour 1: \$10 - \$2
Hour 2: \$10 - \$2
Hour 3: \$10 - \$3
Hour 4: \$10 - \$3
Hour 5: \$10 - \$4
Hour 6: \$10 - \$5
Hour 7: \$10 - \$6
Hour 8: \$10 - \$8
Hour 9: \$15 - \$9
Hour 10: \$15 - \$12
Hour 11: \$15 - \$18
Hour 12: \$15 - \$20

The hourly wage represents what one earns for working an extra hour - it is the marginal gain or the marginal benefit.

The value of time is essentially an opportunity cost -- it is how much one values having that hour off. In this example, it represents a marginal cost -- what it costs an individual to work an additional hour. The increase in marginal costs is a common phenomenon; one usually doesn't mind working a few hours since there are 24 hours in a day. She still has plenty of time to do other things. However, as an individual starts to work more hours, it reduces the number of hours she has for other activities. She has to start giving up more and more valuable opportunities to work those extra hours.

It is clear that she should work the first hour, as she gains \$10 in marginal benefits and loses only \$2 in marginal costs, for a net gain of \$8.

By the same logic, she should work the second and third hours as well. She will want to work until the time at which the marginal cost exceeds the marginal benefit. She will also want to work the 10th hour as she receives a net benefit of #3 (marginal benefit of \$15, marginal cost of \$12). However, she will not want to work the 11th hour, as the marginal cost (\$18) exceeds the marginal benefit (\$15) by three dollars.

Thus marginal analysis suggests that rational maximizing behavior is to work for 10 hours. More generally, optimal outcomes are achieved by examining marginal benefit and marginal cost for each incremental action and performing all of the actions where marginal benefit exceeds the marginal cost and none of the actions where marginal cost exceeds the marginal benefit. Because marginal benefits tend to decrease as one does more of an activity but marginal costs tend to increase, the marginal analysis will usually define a unique optimal level of activity.