Ch3 Lecture Notes - Microeconomics- Pallab Ghosh PDF

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Microeconomics- Pallab Ghosh...

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ECN 1123 Principles of Microeconomics Microeconomics by Acemoglu, Laibson and List Chapter 3: Optimization: Doing the Best You Can Professor Pallab Ghosh

Q: How does location affect the rental cost of housing?

Suppose you have just landed a job near the center of New York City and you now need to decide where to live. If you live close to the Manhattan city center, your round-trip commute will be 15 minutes. If you live in the distant suburbs, your round-trip commute will be 60 minutes. If there are lots of workers like you who work downtown, where will be the apartments be relatively less expensive? How should you make the best decision given the trade-offs you face? In this chapter we will dig into the concept of optimization- choosing the best feasible option. You will learn how to optimize by using cost-benefit analysis. And we will apply this knowledge to a single example that we revisit throughout the chapter- choosing an apartment.

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Chapter 3: Microeconomics by Acemoglu, Laibson and List

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Professor Pallab Ghosh

Two Kinds of Optimization: A Matter of Focus

Economists believe that optimization describes most of the choices that people, households, businesses, and governments make. To an economist, seemingly unrelated decisions- for example, where a college student will travel in spring break, which apartment a worker will rent, or what price Appel charges for iPhone- all are connected by the unifying principle of optimization. Whatever choices people face, economists believe that they are likely to try to choose optimally. We do not assume that people will always successfully optimize, but we do believe that people try to optimize and usually do a pretty good job with whatever information they have.

People are not perfect optimizers because optimization is usually not easy, and it is often quite complex. To illustrate this complexity, consider the choice of an apartment. In large cities there are hundreds of thousands of rental apartments. And each apartment has many different characteristics to consider such as location, views, and neighbourhood amenities. At the heart of the complexity is the trade offs. For example, how do you compare two apartments, one of which has the virtue of lower rent and one of which has virtue of shorter distance? How would you determine which apartment is better choice for you? Note that the choice of apartment is just one illustration of the general concept of optimization. Optimization can be implemented using many different techniques. However, we explore how to optimize using two techniques, which yield identical answers. 1. Optimization in Levels: we calculate the net benefit (= total benefit - total cost) of different alternatives, and then chooses the best alternative. 2. Optimization in Differences: we calculate the change in net benefits when a person switches from one alternative to another and then use these marginal comparisons to choose 2

Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

the best alternative.

1.1

Optimization in Levels

Let’s explore optimization in levels in more depth. Imagine that you have narrowed your choices to four leading candidates. The below figure summarizes the short list, including two key pieces of information for ach apartment- the monthly rent and the amount of commuting time per month. As shown, rents fall the farther you are from your work. You might wonder what about other differences among these apartments, like the distance of near by park, hospitals, fire-stations, etc.

To keep things simple, we omit other factors for not, even though they are important in practice. Also note that we are focusing only on costs in this example- the cost of commuting time and the cost of rent. We are assuming that the benefits from these apartments are the same- for instance, proximity of shopping or public transportation. This implies that cost-benefits analysis simplifies 3

Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

to finding the alternative which has the lowest cost. To find out the total cost, we first need to decide on a common unit of account. Let’s pick dollars per month because rent is already expressed in dollars per month. Now we need to translate the indirect cost- commuting time into the same unit of measurement. Let’s assume that the opportunity cost of commuting time is $10/hour. This is the hourly value of commuting. If the round trip commute takes 20 hours per month and the opportunity cost of time is $10/hour, then the dollar cost of that commute is 

20 hours month



×



$10 hour



=



$200 month



Using this calculation we can calculate the total cost of living in the apartment which is the sum of rent and commuting cost. The below table shows the total cost in dollars for all four apartments.

The above table gives us the answer to our optimization problem. Apartment Far is the best apartment for a consumer with an opportunity cost of time of $10/hour. This apartment has the lowest cost $11,180-taking into account both direct rent costs and indirect time cost of commuting.

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Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

We can also see the result by plotting the total costs. The above figure plots the total cost of each of the four apartments. It is easy to see that Apartment Far is the best. Economists call the best feasible choice the optimum, which is labeled on the total cost curve. To sum up our discussion so far, optimization in levels has three steps: 1. Translate all costs and benefits into common units, like dollars per month 2. Calculate the total net benefit of each alternative 3. Pick the alternative with highest net benefit

1.2

Comparative Statics

Economic models predict how a person’s choice change when something in the environment changes. Comparative statics is the comparison of economic outcomes before and after some economic variable is changed. For example, some consumers will choose to drive more expensive cars if their wealth increases, In this example, the car choice is the economic behavior that changes when the variable of consumer wealth changes, We now return to the example in the previous subsection yo conduct a comparative statics analysis. Specifically, we ask what happens when the opportunity cost of time is changed. Let’s assume that the opportunity cost of time increases from $10/hour to $15/hour. Why might opportunity cost to rise? For example, you might got a promotion and hence your hourly wage rose. Q: How does this increase in opportunity cost of time change the predicted behavior? Try to intuitively answer how would a change in the value of time affect the optimal decision of where to live? Should commuters with a higher value of time move closer to where they work or farther away? To answer this question, we again need to translate the indirect cost- commuting time into the same unit as the direct cost of rent, which is dollars per month. Accordingly we show the calculation of total cost for all the four apartments in the below table:

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Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

The above table provides the answer to our optimization problem. The best apartment for a consumer with an opportunity cost of time of $15/hour now shifts to Apartment close from Far. Apartment Close has the lowest total cost $1,240 by taking into account both direct and indirect time costs of commuting.

In the above figure, the purple line represents the total cost curve for the commuter with an opportunity cost of $10/hour. The orange line represents the total cost curve for the commuter with an opportunity cost of $15/hour. The key properties are visible in the above figure: 1. The $10/hour cost curve lies below the $15/hour cost curve. The $10/curve has lower commuting costs for each apartment, so the total cost, which takes into account both the direct cost of rent and the indirect cost of commuting, is lower for all apartments. 2. The $10/hour curve has a minimum value for Apartment Far, while the $15/hour curve has a minimum value for Apartment Close.

1.3

Optimization if Differences: Marginal Analysis

Until now, we have studied the apartment-hunting problem by calculating the total cost of each apartment. As explained above, we call that approach optimization in levels. We are now going to discuss an alternative optimization technique: optimization in differences. Optimization in differences is faster to implement than optimization in levels, because optimization in differences focuses only on the way that alternatives differ. Optimization in differences breaks an optimization problem down by thinking about how costs and benefits change as you hypothetically move from one alternative to another. For example, consider two alternative vacations at the same hotel in Miami: a four-day trip versus a five day 6

Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

trip. Suppose that you are choosing between these two options. If you optimize in levels, you would evaluate the total net benefit of a four day trip and compare it to the total net benefit of a five day trip. Alternatively, you could think about only the differences between the two trips. In other words, you could think about only the costs and benefits of the extra day. An optimizer will take the five day vacation if the benefit of vacation for the fifth day exceeds the cost of the fifth day. Economists use the word marginal to indicate the difference between alternatives, usually a difference that represents one “step” or “unit” more. The fifth day of vacation is the difference or margin, between a four-day vacation and a five-day vacation. Marginal Analysis will never change the ultimate answer to the question “what is optimal?” but it will change the way that you think about optimizing. Marginal analysis forces us to focus on what is changing when we compare alternatives. Marginal analysis is the way that we implement optimization in differences.

1.4

Marginal Costs

When we studied the problem of choosing an apartment, we did not use marginal analysis. Instead, we solved the problem by calculating and comparing the total cost. We will now solve the same apartment-selection problem using marginal analysis. The optimum won’t change, we will confirm that below but the way you think about the problem will. Again, consider the commuter with a $10/hour opportunity cost of time. Instead of thinking about each of the apartments in isolation, let’s now think about the apartments comparatively. Specifically, let’s focus on what changes as we hypothetically “move” from one apartment to the next, stepping further away from the city center. What is the difference between each pair of apartments? The below table will help us to think this way.

Note that the marginal cost is the extra cost generated by moving from one feasible alternative to the next feasible alternative. Therefore, it is the difference between the total cost of two successive

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Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

units. We can also calculate the marginal cost by using the following expression: Marginal Total Cost = Marginal Commuting Cost + Marginal Rental Cost The last column marginal cost contains all the information we need to optimize. Start at the top of the column and think about how each move away from the city center affects the worker. 1. The first move, from Very Close to Close, has a marginal cost of -$40 per month, so it is cost cutting. That move is worth it. 2. The second move, from Close to Far, has a marginal cost of -$10 per month. That move is also cost cutting and consequently it is also worth taking. 3. The Third move, from Far to Very Far, has a marginal cost of $20 per month. So that move is not worth taking, because it represents an increase in costs. To sum up, the first two moves paid themselves and the final move did not. Therefore, Far is the best option among the 4 candidates. Note that an optimizer’s goal is to make himself as well off as possible. An optimum is the point at which the optimizer cannot do any better. The apartment that is better than all its feasible alternatives is also the apartment that minimizes total costs. This is an example of the Principle of Optimization at the Margin, which states that an optimal feasible alternative has the property that moving to it makes you better off and moving away from it makes you worse off.

The above figure helps to visualize these ideas. In the figure we plot the total cost of each apartment and the marginal cost of moving one apartment at a time farther away from the city center of town. For instance, moving from Very Close to Close lowers total cost by $40. The dashed red line shows a change of -$40 between the total cost of Very Close and the total cost of Close. 8

Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

Since optimization in levels and optimization in differences pick out the same optimum, you can use whichever method is easier for the particular problem that you are analyzing. However, it is important to understand why economists mostly use optimization in differences, that is optimization at the margin. Optimization at the margin is simple because you can ignore everything about two alternatives that are being compared except the particular attributes that are different. Marginal analysis reminds you not to analyze information that will turn out to be irrelevant to your decision. To sum up, optimization in differences has three steps: 1. Translate all costs and benefits into common units, like dollars per month 2. Calculate the marginal consequences of moving between alternatives 3. Apply the Principle of Optimization at the Margin by choosing the best alternative with the property that moving to it makes you better off and moving away from it makes you worse off.

1.5

Evidence-Based Economics

Q: How does location affect the rental cost of housing? Answer: Throughout this chapter, we have been assuming that rental prices are higher near the city center, holding the quality of the apartment fixed. You may have wondered whether we had our facts right. People often imagine dingy apartments downtown and nice houses out in the country. If we want to isolate the effect of location, we need to hold apartment quality constant and vary only location.

Economists Beth Wilson and James Frew assembled a database that contains information on many apartments that were available for rent in Portland, Oregon. They used statistical techniques to effectively compare apartments near the city center similar apartments that are farther away. 9

Chapter 3: Microeconomics by Acemoglu, Laibson and List

Professor Pallab Ghosh

Such analysis reveals a strong negative relationship between distance and rent, which is shown in the above figure. The plot shows the apartments that all have the following features- one bedroom, one bathroom, laundry unit in the apartment, covered parking, cable, and air-conditioning. The analysis compares the rent of these apartments, holding all of their features constant except for the distance to the city center. The above figure confirms that proximity to the city center raises rents. The closer you get to the city, the higher the rent goes. For example, at a distance of 6 miles from the city center, the typical rent for an apartment with the specified features is nearly $1,000. For an apartment that is 1 mile from the city center, the rent for the same apartment is $1,500. We also note that a noticeable flattening around 12 miles from the city center. Q: Can you guess why rents stop changing in this region?

The answer follows from considerations about the opportunity cost of time and structure of Portland’s highway system. Like most large cities, Portland has a ring of fast highways- a “ring road”- about 12 miles from the center of the city. People who live within a few miles of the ring road have the advantage of being near a highway system that speeds up travel time. Because of the ring roads, commute times change relatively little as you go from 9 miles to 14 miles away from the city center.

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