Optimization: Doing the Chapter 3 Optimization: Doing the Best You Can

Chapter 3 Outline 3.1 Two Kinds of Optimization: A Matter of Focus 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 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.

Do you always make the best choice? Why not? 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.

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

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 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

Apartment Options 3.2 Optimization in Levels 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.

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

Apartment Options 3.2 Optimization in Levels 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 Looking at total costs, the Far apartment has the lowest costs.

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?

Apartment Options 3.2 Optimization in Levels 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

3.2 Optimization in Levels What’s Missing? Consider these items that might be close to the apartment

3.2 Optimization in Levels Optimizing in Levels Express all costs and benefits in the same unit (like $) Calculate total net benefit (benefits – costs) for each option 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.

A Comparison of the Apartments: 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 analysis, the best choice is the far apartment.

Optimizing in Differences 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. 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.

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.

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

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? 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?

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 their own experience that when there’s scarcity, price gets pushed up.