1. Optimization: Doing the Best You Can
Chapter 3
Optimization: Doing the Best You Can
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2. 3.1 Two Kinds of Optimization: A Matter of Focus
3 Optimization: Doing the Best You Can
Chapter Outline
3.1 Two Kinds of Optimization: A Matter of Focus
3.2 Optimization in Levels
3.3 Optimization in Differences: Marginal Analysis
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3. 3 Optimization: Doing the Best You Can
Key Ideas
When an economic agent chooses the best feasible option, she is optimizing.
Optimization in levels calculates the total net benefit of different alternatives and then chooses the best alternative.
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4. 3 Optimization: Doing the Best You Can
Key Ideas
Optimization in differences calculates the change in net benefits when a person switches from one alternative to another, and then uses these marginal comparisons to choose the best alternative.
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5. Both optimization approaches lead to the same answer.
3 Optimization: Doing the Best You Can
Key Ideas
Both optimization approaches lead to the same answer.
Optimization in levels and optimization in differences give identical answers.
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6. Evidence-Based Economics:
3 Optimization: Doing the Best You Can
Evidence-Based Economics:
How does location affect the rental cost of housing?
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7. Do you always make the best choice? Why not?
3.1 A Matter of Focus
Do you always make the best choice?
Why not?
Ask students how many of them make the best choice in every situation. Ask them, why not?
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8. Sometimes it is difficult to make choices because
3.1 A Matter of Focus
Sometimes it is difficult to make choices because
Limited information
Sorting through information can be complicated
Inexperience
People have limited information available to them and information is costly to obtain. Sometimes there is so much information surrounding a choice that it’s difficult to know where to begin in sorting through it. And if you don’t have experience in dealing with a given situation, you may not be able to put whatever information you do have to good use.
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9. How to choose? (How to evaluate trade-offs?) Either
3.1 A Matter of Focus
How to choose? (How to evaluate trade-offs?)
Either
Optimization in levels = look at total benefit – total cost (net benefit) OR
Optimization in differences = look at the change in the net benefit of one option compared to another
Ask students to think about a choice they have made recently. How did they arrive at that choice? What kinds of factors did they think about? Try to categorize them into the “total” or “marginal” bucket.
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10. What value do you place on this?
3.1 A Matter of Focus
Demonstration:
What value do you place on this?
Follow the book in its set-up of the candy. Have small sizes of several kinds of candy bars—but only 4 different kinds, with one other kind available that some people would definitely not like, like one with coconut. For example, KitKat, Milky Way, Crunch and 3 Musketeers. Have a Mounds available for part 2 of this demonstration. Ask a student to come down to the front of the classroom and display the 4 candy bars. Ask, how much would you by willing to pay for this set of candy bars? Then ask the student to turn around and substitute the Mounds for one of the original candy bars. Ask the student to turn back around and ask how much he/she is willing to pay for this slightly different set. Then point out that really the only difference between the two sets is the first had a KitKat (or Milky Way or whatever one you picked) and the second one has a Mounds. Ask, of these two candy bars (the Mounds vs. the original one), which one do you prefer?
The candy bar preferred should correspond to the set that the student placed the higher value on. Repeat with a few more students. Then ask, what would have happened if I had increased the number of candy bars in the set? If there had been 8 different kinds or 12 or 15? If they don’t get there themselves, lead them to see that their answers based on totals might not be consistent with their marginal answers simply because the choice is now more complex. So when the alternatives are fewer, it’s more likely to be the case that the decision reached through total analysis is the same as that made through marginal analysis.
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11. Decision-making using totals: Where should I live?
3.2 Optimization in Levels
Decision-making using totals:
Where should I live?
Trade-off:
Cost vs. Distance
Tell students to imagine that they have just graduated from college and have accepted a job in the center of a large city. Now they need to decide where to live. There are four general apartment options, varying by how far away they are from your job and the cost.
Exhibit 3.1 Apartments on Your Short List, Which Differ Only on Commuting Time and Rent and Are Otherwise Identical
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12. Apartment Options 3.2 Optimization in Levels
Ask students which one they would pick. They should answer that they don’t have enough information yet, and they don’t. Ask what information is missing for them to make a good choice. They should say that they don’t know how much it costs to commute. They will probably also say that they need to know how much income they have. Tell them to assume that all 4 apartments are affordable—now we are just focused on costs. They might also say they don’t know enough about where the apartments are located, amenities, etc. Again, tell them that for right now, we’re just focused on costs.
Exhibit 3.1 Apartments on Your Short List, Which Differ Only on Commuting Time and Rent and Are Otherwise Identical
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13. What does it cost to commute? Availability of public transportation
3.2 Optimization in Levels
What does it cost to commute?
Availability of public transportation
Gasoline
Parking
Wear and tear on car
Opportunity cost of time
Before showing students the list, ask them to identify the costs of commuting. Tell them that you’re going to focus on one—the opportunity cost of the time involved in commuting. This is how much they would have to be paid to spend an hour commuting rather than doing something else with that hour. Solicit what their opportunity cost would be. Ask them why some students have a lower opportunity cost than others do.
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14. Apartment Options 3.2 Optimization in Levels
Tell them you’re now ready to present the total costs of each apartment option. Looking at total costs, the Far apartment has the lowest costs.
The same information can be presented in a graph…
Exhibit 3.2 Commuting Cost and Rental Cost Expressed in Common Units, Assuming an Opportunity Cost of Time of $10/hour
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15. 3.2 Optimization in Levels
This is the same information as in the previous slide, just presented graphically instead of in a table. We are looking for the apartment with the lowest cost.
Exhibit 3.3 Total Cost Including Both Rent and Commuting Cost, Assuming an Opportunity Cost of Time of $10/hour
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16. 3.2 Optimization in Levels
Comparative Statics: What if the opportunity cost of commuting changes?
Tell students that one of the most powerful things about economics is its ability to predict how economic agents’ behavior changes when circumstances change. For instance, what if you discovered that you have an artist inside of you, desperate to come out, and you take up painting as a hobby. You might place a higher value on an hour of time given up for commuting than before, because you have another, more exciting use for your time. Assume the opportunity cost of your time goes up to $15/hour. Does that change the optimal choice? Ask them to predict what will happen in terms of the choice of apartments.
NOTE: using an example that does not have an actual dollar amount attached to it (like getting some increase in income) drives home the point that opportunity cost refers to all kinds of other uses, not just those that can be directly monetized.
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17. Apartment Options 3.2 Optimization in Levels
Because time is more valuable, the commute becomes more expensive. Therefore, the apartment that’s a little closer is the optimal choice.
Again, shown graphically…
Exhibit 3.4 Commuting Cost and Rental Cost Expressed in Common Units, Assuming an Opportunity Cost of Time of $15/hour
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18. 3.2 Optimization in Levels
Exhibit 3.6 Total Cost Curves with the Opportunity Cost of Time Equal to $10/hour and $15/hour
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19. What’s Missing? 3.2 Optimization in Levels
This example is one using total net benefit to evaluate options, but it doesn’t present any benefits, just costs. Ask students to brainstorm other factors that should be considered when making a choice such as this—categorize as a benefit or cost. Point out that not everyone would have the same list—some people might consider a nearby park a benefit, others wouldn’t care. Summarize that the goal is not to come up with “the” right answer, but to present a framework for making a decision that leads to an optimal answer for an individual.
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20. Express all costs and benefits in the same unit (like $)
3.2 Optimization in Levels
Optimizing in Levels
Express all costs and benefits in the same unit (like $)
Calculate total net benefit (benefit – costs) for each option
Choose the option with the highest net benefit
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21. How many servings do you want?
3.3 Optimization in Differences: Marginal Analysis
Decision-Making Using Marginal Analysis:
What’s the net benefit of one more?
Tell students that sometimes it’s difficult to know what the “total” is going to be, so it’s hard to make a decision based on it.
Tell them to imagine that they sit down at the dinner table and a large bowl of their favorite food is there. Ask them if they will want 3 servings. You will probably be met with blank stares. Then tell them that often, decisions are made sequentially, not as a total. From 0—having none of their favorite food—how many will want one serving? They all should say that they want one. Talk about how they made that decision—they weighed the benefits and costs and decided that the benefits of one serving outweighed the costs. Then ask if they want a second serving. Some will and some won’t. Point out that they are again weighing the costs and benefits, but it’s of the second serving after they have consumed the first. Then ask about a third serving, pointing out the same relationships. The overall point to be made is that sometimes trying to make a decision using totals is difficult because you don’t have enough information. Students don’t know if they’ll want a second or third serving until they have information about how they feel after the first one or two. Sometimes decisions are made on the basis of one more—at the margin.
How many servings do you want?
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22. A Comparison of the Apartments:
3.3 Optimization in Differences: Marginal Analysis
A Comparison of the Apartments:
Tell students that the focus in marginal analysis is “how much more (or less) does this option cost, compared to another one”.
From the table above, the marginal cost of the commute is going to be the same: how much more does it cost me to commute from a close apartment, compared to a very close apartment? $50 How much more does it cost to commute from a far apartment compared to a close apartment? $50.
Looking at the net benefits, then:
Should your choice change from a very close, to a close apartment? It would cost $50 more in commuting, but you would save $90 on rent, so yes—you would save $40.
Should your choice change from a close apartment to a far apartment? It would cost $50 more in commuting, but would save $60 on rent, so yes again—you would save $10
Should your choice change from a far apartment to a very far apartment? It would cost $50 more in commuting, but would save $30 on rent, so no—you would be losing $20.
As in the total analysis, the best choice is the far apartment.
Exhibit 3.7 Relationship Between Levels and Differences (Margins), Assuming a $10/hour Opportunity Cost of Time
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23. Principle of Optimization at the Margin
3.3 Optimization in Differences: Marginal Analysis
Principle of Optimization at the Margin
If an option is the best choice, you will be made better off as you move toward it, and worse off as you move away from it.
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24. Optimizing in Differences:
3.2 Optimization in Differences: Marginal Analysis
Optimizing in Differences:
Express all costs and benefits in the same unit
Calculate how the costs and benefits change as you move from one option to another
Apply the Principle of Optimization at the Margin—choose the option that makes you better off by moving toward it, and worse off by moving away from it.
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25. 3.2 Optimization in Differences: Marginal Analysis
Point out to students that regardless of which approach is used—optimization in levels or in differences—it leads to the same outcome.
Exhibit 3.8 Total Cost of Each Apartment and the Marginal Cost of Moving Between Apartments, Assuming an Opportunity Cost of $10/hour
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26. Evidence-Based Economics:
3 Optimization: Doing the Best You Can
Evidence-Based Economics:
How does location affect the rental cost of housing?
Point out that we have been assuming that the closer the apartment is to the center of the city, the more expensive it is. Is that true?
Remind students that apartments vary in quality, so in order to answer the question, we need to hold everything else about apartments constant and only look at how location affects rental costs.
Look at one city in particular—Portland, OR
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27. Evidence-Based Economics:
3 Optimization: Doing the Best You Can
Evidence-Based Economics:
How does location affect the rental cost of housing?
Note that Portland has a highway system that rings the city. Ask what the effect of that system will be on commuting time. Ask for predictions about rental costs near the system vs. some distance away. What if Portland didn’t have that ring of highways? Would that change rental costs?
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28. 3 Optimization: Doing the Best You Can
Point out that their predictions are correct—rental costs are highest in the central city, and then decrease. But they flatten at the distance of the highway ring, then continue to fall.
But why do we observe these data? What causes the price of apartments in the center city to be so much higher? If they don’t get there on their own, lead them to understand that there is limited space in the center city for apartments. Even though the concept of supply hasn’t been introduced yet, they know from their own experience that when there’s scarcity, price gets pushed up.
Exhibit 3.9 Apartment Rent in Portland, Oregon, Depends on Distance from the City Center
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