Chapter 3
Optimization:
Doing the
Best You Can
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CHAPTER 3 - Optimization: Doing the Best You Can
Chapter 3 Outline
3.1 Two Kinds of Optimization: A Matter of Focus
3.2 Optimization in Levels
3.3 Optimization in Differences: Marginal Analysis
Key Ideas
1.
2.
3.
4.
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.
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.
Optimization in levels and optimization in differences give
identical answers.
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3.1 A Matter of Focus
Do you always make the best choice?
Why not?
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
Idea: 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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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
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3.2 Optimization in Levels
Decision-making using totals: Where should I live?
Trade-off: Cost vs. Distance
You 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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3.2 Optimization in Levels
Apartment Options
Exhibit 3.1 Apartments on Your Short List, Which Differ Only on Commuting Time and
Rent and Are Otherwise Identical
You have just graduated and got a job in a city. You have the income to pay the rent.
Tell them to assume that all 4 apartments are affordable—now you 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.
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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
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3.2 Optimization in Levels
Apartment Options
Exhibit 3.2 Commuting Cost and Rental Cost Expressed in Common Units, Assuming an
Opportunity Cost of Time of $10/hour
Looking at total costs, the Far apartment has the lowest costs.
Exhibit 3.3 Total Cost
Including Both Rent and
Commuting Cost, Assuming
an Opportunity Cost of Time
of $10/hour
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3.2 Optimization in Levels
Comparative Statics: What if the opportunity cost of commuting
changes?
Change of circumstances – interest in painting so there is higher value
on an hour of time given up for commuting than before. For example,
the opportunity of your time is now $15/hour
Question: what happens in terms of the choice of apartments?
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3.2 Optimization in Levels
Apartment Options
Exhibit 3.4 Commuting Cost and Rental Cost Expressed in Common Units, Assuming an
Opportunity Cost of Time of $15/hour
Because time is more valuable, the commute becomes more expensive. Therefore, the
apartment that’s a little closer is the optimal choice.
Exhibit 3.6 Total Cost Curves with the Opportunity Cost of Time Equal to $10/hour
and $15/hour
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3.2 Optimization in Levels
What’s Missing? Consider these items that might be close to the apartment
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3.2 Optimization in Levels
Optimizing in Levels
1. Express all costs and benefits in the same unit (like $)
2. Calculate total net benefit (benefits – costs) for each option
3. Choose the option with the highest net benefit
Decision-Making Using Marginal Analysis:
What’s the net benefit of one more?
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.
Often people 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.
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3.3 Optimization in Differences: Marginal Analysis
A Comparison of the Apartments:
Exhibit 3.7 Relationship Between Levels and Differences (Margins), Assuming a $10/hour
Opportunity Cost of Time
The focus in marginal analysis is “how much more (or less) this option costs, compared
to another one.” The marginal cost (MC) of the commute is going to be the same =$50.00
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
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analysis, the best choice is the far apartment.
3.3 Optimization in Differences: Marginal Analysis
Principle of Optimization at the Margin

1.
2.
3.
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.
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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3.2 Optimization in Differences: Marginal Analysis
Exhibit 3.8 Total Cost of Each Apartment and the Marginal Cost of Moving Between
Apartments, Assuming an Opportunity Cost of $10/hour
Note: Approach—optimization in Levels or in Differences—it leads to the same
outcome.
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3 Optimization: Doing the Best You Can
Evidence-Based Economics:
How does location affect the rental cost of housing?
Assuming that the closer the apartment is
to the center of the city, the more
expensive it is. Is that true?
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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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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3 Optimization: Doing the Best You Can
Exhibit 3.9 Apartment Rent in Portland, Oregon, Depends on Distance from the City
Center
 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.
 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
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their own experience that when there’s scarcity, price gets pushed up.