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# 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?
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?', 'How will I spend dollar number 24,388?'. Treating the problem in this matter 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 - An Example

Consider the decision on how many hours to work, as given 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 I earn 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 I value having that hour off. In this example it represents a marginal cost - what it costs me by working an additional hour. The increase in marginal costs is a common phenomenon; I do not mind working a few hours since there are 24 hours in a day. I still have plenty of time to do other things. However, as I start to work more hours it reduces the number of hours I have for other activities. I have to start giving up more and more valuable opportunities to work those extra hours.

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

By the same logic I should work the second and third hours as well. I will want to work until which time the marginal cost exceeds the marginal benefit. I will want to work the 10th hour as I receive a net benefit of #3 (marginal benefit of \$15, marginal cost of \$12). However, I 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.

Next Lesson: Market Distortions: Altering the Supply and Demand Equilibrium.
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