1. Chapter 3 Microeconomics Optimization: Doing the Best You Can
Second Edition
Chapter 3
Optimization:
Doing the
Best You Can
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2. Learning Objectives
3.1 Optimization: Choosing the Best Feasible Option 3.2 Optimization Application: Renting the Optimal Apartment 3.3 Optimization Using Marginal Analysis

3. Key Ideas (1 of 3)
When an economic agent chooses the best feasible option, she is optimizing.
Optimization using total value calculates the total value of each feasible option and then picks the option with the highest total value.

4. Key Ideas (2 of 3)
Optimization using marginal analysis calculates the change in total value when a person switches from one feasible option to another, and then uses these marginal comparisons to choose the option with the highest total value.

5. Key Ideas (3 of 3)
Optimization using total value and optimization using marginal analysis give identical answers.

6. Evidence-Based Economics
How does location affect the rental cost of housing?

7. Optimization: Choosing the Best Feasible Option (1 of 4)
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?

8. Optimization: Choosing the Best Feasible Option (2 of 4)
Sometimes it is difficult to make choices because
You have limited information
Sorting through information can be complicated
You are inexperienced in dealing with a given situation
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.

9. Optimization: Choosing the Best Feasible Option (3 of 4)
Optimization can be implemented using many different techniques. We explore how to optimize using two techniques, which yield identical answers.

10. Optimization: Choosing the Best Feasible Option (4 of 4)
Two Optimization Techniques 1. Total Value total benefit – total cost (net benefit) OR 2. Marginal Analysis 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.

11. Optimization Application: Renting the Optimal Apartment (1 of 12)
Exhibit 3.1 Apartments on Your Short List, Which Differ Only on Commuting Time and Rent and Are Otherwise Identical
Trade-off: Cost vs. Distance Decision-making using totals: Where should I live?
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.

12. Optimization Application: Renting the Optimal Apartment (2 of 12)
Optimization using total value
Translate all costs and benefits into common units, like dollars per month.
Calculate the total net benefit of each alternative.
Pick the alternative with the highest net benefit
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.

13. Optimization Application: Renting the Optimal Apartment (3 of 12)
Exhibit 3.1 Apartments on Your Short List, Which Differ Only with Regard to Commuting Time and Rent and Are Otherwise Identical
Apartment Options
Apartment
Commuting Time
(hours/month)
Rent
($/month)
Very Close
5 hours
$1,180
Close
10 hours
$1,090
Far
15 hours
$1,030
Very Far
20 hours
$1,000
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.

14. Optimization Application: Renting the Optimal Apartment (4 of 12)
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.

15. Optimization Application: Renting the Optimal Apartment (5 of 12)
Exhibit 3.2 Commuting Cost and Rental Cost Expressed in Common Units, Assuming an Opportunity Cost of Time of $10/hour
Apartment Options
Apartment
Commuting
Time (hours/month)
Commuting Cost
($/month)
Rent
Total Cost: Rent + Commuting
Very Close
5 hours
$50
$1,180
$1,230
Close
10 hours
$100
$1,090
$1,190
Far
15 hours
$150
$1,030
Very Far
20 hours
$200
$1,000
$1,200
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…

16. Optimization Application: Renting the Optimal Apartment (6 of 12)
If the round-trip commute takes 20 hours/month (very far) and the opportunity cost of time is $10/hour, then the dollar cost of that commute is ( 20 hours month )( $10 hour ) = ( $200 month )
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.

17. Optimization Application: Renting the Optimal Apartment (7 of 12)
Exhibit 3.3 Total Cost Including Both Rent and Commuting Cost, Assuming an Opportunity Cost of Time of $10/hour
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.

18. Optimization Application: Renting the Optimal Apartment (8 of 12)
Before and After Comparisons: What if the opportunity cost of commuting changes?
What could change the opportunity cost of our time? Increased wages? Changes in our life circumstances?
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 get married and have children. You might place a higher value on an hour of time given up for commuting than before, because you have another, more fulfilling 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.

19. Optimization Application: Renting the Optimal Apartment (9 of 12)
Exhibit 3.4 Commuting Cost and Rental Cost Expressed in Common Units, Assuming an Opportunity Cost of Time of $15/hour
Apartment Options
Apartment
Commuting Time
(hours/month)
Commuting Cost
($/month)
Rent
Total Cost: Rent + Commuting
Very Close
5 hours
$75
$1,180
$1,255
Close
15 hours
$225
$1,030
Far
Very Far
20 hours
$300
$1,000
$1,300
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…

20. Optimization Application: Renting the Optimal Apartment (10 of 12)
Exhibit 3.6 Total Cost Curves with the Opportunity Cost of Time Equal to $10/hour and $15/hour

21. Optimization Application: Renting the Optimal Apartment (11 of 12)
What’s Missing?
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.

22. Optimization Application: Renting the Optimal Apartment (12 of 12)
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?

23. Optimization Using Marginal Analysis (1 of 6)
Marginal Analysis: 1. Translate all costs and benefits into common units, like dollars per month. 2. Calculate the marginal consequences of moving between alternatives. 3. Choose the best alternative with the property that moving to it makes you better off and moving away from it makes you worse off.

24. Optimization Using Marginal Analysis (2 of 6)
Exhibit 3.7 Relationship Between Levels and Differences (Margins), Assuming a $10/hour Opportunity Cost of Time
A Comparison of the Apartments:
Apartment
Commuting Cost
Marginal
Rental Cost
Total Cost
Very Close
$50
$1,180
$1,230
−$90
−$40
Close
$100
$1,090
$1,190
−$60
−$10
Far
$150
$1,030
−$30
$20
Very Far
$200
$1,000
$1,200
Tell students that the focus in marginal analysis is “how much more (or less) this option costs, 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 you 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 you would save $30 on rent, so no—you would be losing $20.
As in the total analysis, the best choice is the far apartment.

25. Optimization Using Marginal Analysis (3 of 6)
A Comparison of the Apartments:
Animated slide provided as a supplement. To hide, right click on the slide thumbnail and select “Hide Slide”
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.

26. Optimization Using Marginal Analysis (4 of 6)
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.

27. Optimization Using Marginal Analysis (5 of 6)
Exhibit 3.8 Total Cost of Each Apartment and the Marginal Cost of Moving Between Apartments, Assuming an Opportunity Cost of $10/hour
Point out to students that regardless of which approach is used—optimization in levels or in differences—it leads to the same outcome.

28. Optimization Using Marginal Analysis (6 of 6)
Exhibit 3.8 Total Cost of Each Apartment and the Marginal Cost of Moving Between Apartments, Assuming an Opportunity Cost of $10/hour
Animated slide provided as a supplement. To hide, right click on the slide thumbnail and select “Hide Slide”
Point out to students that regardless of which approach is used—optimization in levels or in differences—it leads to the same outcome.

29. Evidence-Based Economics (1 of 3)
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

30. Evidence-Based Economics (2 of 3)
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?

31. Evidence-Based Economics (3 of 3)
Exhibit 3.9 Apartment Rent in Portland, Oregon, Depends on Distance from the City Center
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.

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