EconS Preferences

Transcription

1 EconS Preferences Eric Dunaway Washington State University eric.dunaway@wsu.edu September 14, 2015 Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

2 Introduction So far, we have studied supply and demand and seen how they lead to market equilibrium. But how are they derived? This week, we re going to look at peoples preferences, utility functions, and budget constraints in order to get us ready to derive demand functions next week. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

3 Preferences At its essence, Economics is the study of choice, and pretty much everyone is willing to make a choice if they have the opportunity. Even if that choice is indi erence. As an example, if I were to show you an apple and an orange, you could probably tell me one of the three following things: "I prefer the apple over the orange." "I prefer the orange over the apple." "I like apples and oranges the same." Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

4 Preferences We use special notation for preferences. For example, the % is used to show preference. If I wrote Apples % Oranges, that would mean that I prefer apples at least as much as oranges. Apples Oranges would mean that I strictly prefer apples more than oranges (Think of it like a greater than symbol, but for preferences). Apples Oranges means that I am indi erent between apples and oranges, or that I just prefer them the same. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

5 Preferences Preferences allow us to develop indi erence curves, which we will look at next. However, there are a few properties of preferences that have to hold in order for people to make rational decisions. What do you mean by rational? Basically, there are a few logical paradoxes that can prevent us from analyzing a preference relationship mathematically, forming indi erence curves. Let s talk about them. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

6 Completeness Completeness means that given any two objects (or bundles of objects), I can compare them. For example, in our Apples and Oranges example, preferences satisfy completeness if and only if I can declare one or both of the following Apples % Oranges Oranges % Apples Note that if I say both of those choices, it just means that I am indi erent between Apples and Oranges (and that s ok!). The only way that completeness breaks down is if there are two objects that cannot be compared. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

7 Completeness When would we be unable to compare two objects? Usually, this is when we have no information or experience with a group of goods or similar goods. For example, I have never eaten borscht (a traditional Russian dish), or even beets before. If someone were to ask me to compare two di erent kinds of borschts without tasting them, I wouldn t even be able to form an opinion. Be careful, however, as the di erence between incomplete preferences and indi erent preferences is small, but very important. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

8 Transitivity Transitivity means that preferences are logically consistent. Let s add Bananas into the Apples and Oranges example. If I prefer apples to oranges, and oranges to bananas, then I have to prefer apples to bananas. If I don t, and actually prefer bananas to apples, a heartless microeconomist can take advantage of me. Let s look an example. You start with an apple and $5. You are willing to pay $1 in exchange for a fruit that you prefer more. Your preferences are as follows: Apples % Oranges Oranges % Bananas Bananas % Apples Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

9 Transitivity I ll play the role of a hearless microeconomist that has a bunch of fruit. First, I o er you a banana in exchange for your apple and $1. Since this is a good deal for you, you accept. You now have a banana and $4. Now, I o er you an orange in exchange for your banana and $1. Since this is also a good deal for you, you accept. You now have an orange and $3. Next, I o er you the same apple that you gave me at the beginning in exchange for your orange and $1. Once again, you see this as a good deal and accept. You now are back to your original apple and $2. I can repeat these steps over and over again until I have all of your money. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

10 Transitivity A great example of this happens in Sneetches on Beaches. At the climax of the story, the Sneetches prefer a star until they get one, then they prefer to not have a star. They pay money to a heartless microeconomist (Sylvester McMonkey McBean) over and over to add and remove the star until they nally run out of money. The moral of the story is to not have intransitive preferences. And don t discriminate. That s bad too. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

11 Preferences If preferences are both complete and transitive, we say that they are rational. Lastly, we need to talk about "goods" A good is somethings that we always want more of if we can have it. This is the opposite of a bad (like garbage), where we want as little of it as possible, and would even pay to have it go away. We need to have at least one good in order for our models to make sense. We aren t going to worry about bads in this class. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

12 More is Better Since we are using goods exclusively, we need one more property for our preference relations. More is better. If a person can have more of everything, they will be better o. It s important to note that it has to be more of everything, not just more of something. For example, under normal circumstances, is a person with one pair of shoes better o if they are given an additional left shoe? No, but if they get both an additional left shoe and an additional right shoe, they are better o for sure! That being said, if they only received an additional left shoe, they can t be worse o than they were before. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

13 Bundles We want to build preferences into something easier to analyze, so we group our goods into bundles. Keeping it simple, we will only consider two goods, apples and oranges. A bundle could consist of 3 apples and 1 orange, while another could consist of 1 apple and 3 oranges, and so on. The gure on the next slide shows several bundles. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

14 Bundles Apples E D 4 A C F G B H 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

15 Bundles Let s look at the properties we developed along with our new bundles. For completeness, since every bundle is somewhere on the gure, we can compare them in some way. We need more information to actually rank them in some cases. We can actually do a bit of ranking using transitivity and "more is better." Let s look at bundles B, F, and G. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

16 Bundles Apples 4 F G B 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

17 Bundles Bundle G has more of both goods than bundle F. Thus, bundle G must be preferred to bundle F, or G % F. Bundle F has more of both goods than bundle B. Thus, bundle F must be preferred to bundle B, or F % B. Since G is preferred to F and F is preferred to B, we also must have that bundle G is preferred to B, by transitivity. We could also establish this just through the "more is better" property. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

18 Bundles Since both apples and oranges are goods in our model, any bundle both up and to the right of another bundle must be strictly prefered. Because of this, we say that preferences increase as we move up and to the right. We can take all of the bundles for which we are indi erent and connect them with a line. This is called an indi erence curve. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

19 Bundles Apples E D 4 A C F G B H 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

20 Bundles Apples I 1 I 2 I 3 I 4 E D 4 A C F G B H 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

21 Indi erence Curves Indi erence curves are a great tool for analyzing preferences. With one curve, we can see every point which is indi erent with one another and clearly see which bundles are more preferred. A few properties to note: While I only drew four indi erence curves on the last gure, there are actually an in nite number of them! Every single point has a place on an indi erence curve (even the points that I did not point out). Indi erence curves cannot cross one another. Indi erence curves are not "thick." Let s elaborate a little bit. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

22 Indi erence Curves Indi erence curves cannot cross one another. This property is implied by transitivity and the "more is better" property. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

23 Indi erence Curves Apples I 1 I 2 4 C F H 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

24 Indi erence Curves On the previous gure, indi erence curve 1 shows that bundles C and H are indi erent to one another. Indi erence curve 2 shows that bundles C and F are indi erent to eachother. Using transitivity, this must mean that bundles H and F are also indi erent. This can t be the case though, since by the de nition of a good, "more is better" and bundle F, having more of both apples and oranges than bundle H is strictly prefered. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

25 Indi erence Curves Indi erence curves are not "thick." See the next slide for an example. Again, this has to do with the "more is better" property. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

26 Indi erence Curves Apples I 1 4 A B 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

27 Indi erence Curves If an indi erence curve like in the previous slide existed, we could have both bundles A and B exist on the same curve, and they would be indi erent. However, like in the last example, bundle B has more of both goods than bundle A, and thus it must be strictly prefered. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

28 Indi erence Curves Perlo lists two more properties of indi erence curves in his book. Bundles on indi erence curves farther from the origin are preferred to those on indi erence curves closer to the origin. Indi erence curves slope downward. Both of these properties depend on both objects being goods. If we had a bad in our model, they would not hold. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

29 Marginal Rate of Substitution When a person is indi erent between two bundles, they are willing to trade between them without any external pressure. Basically, they don t have to be paid in order to swap one bundle for another. The amount that they are willing to trade away one unit of a good to receive the other is known as the marginal rate of substitution. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

30 Marginal Rate of Substitution Apples I D C H Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

31 Marginal Rate of Substitution If we started at bundle D, where we have 5 units of Apples and 2 units of oranges, and wanted to switch to bundle C, which has 3 units of apples and 3 units of oranges, the marginal rate of substitution can be calculated as MRS = Change in Oranges Change in Apples = = 1 2 = 1 2 What this means is that the consumer in this case is willing to give up 1 unit of apples in order to recieve half a unit of oranges. This makes sense, since the consumer did that twice - they gave up 2 units of apples to receive a full unit of oranges. We just always interpret it as giving up one unit of one good to receive the other. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

32 Marginal Rate of Substitution It s important to note that the marginal rate of substitution changes as we move to the atter part of the indi erence curve. This is because as we give up more apples, we have to be compensated with more and more oranges in order to remain indi erent. For example, if we start at bundle C, which has 3 units of apples and 3 units of oranges and want to move to bundle H, which has 1 unit of apples and 6 units of oranges, the marginal rate of substitution is MRS = Change in Oranges Change in Apples = = 3 2 = 3 2 Now, since I start with less apples than before, they are more valuable to me and I would have to be compensated with 1.5 units of oranges to get me to part with 1 unit of apples. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

33 More Indi erence Curves For the most part, we are going to see indi erence curves that look like the ones shown in the gures thus far. Meaning they will be bowed toward the origin and generally well behaved. The curvature of indi erence curves tells a lot about the relationship between the two goods. The less curved the indi erence curve is, the more substitutable goods are. The more curved the indi erence curve is, the more complementary the goods are. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

34 More Indi erence Curves The two extreme cases, as shown in the next gures, are perfect substitutes and perfect complements. With perfect substitutes, the marginal rate of substitution never changes as you move down the indi erence curve. A consumer is always willing to trade one good for the other at the same rate and remain indi erent. The indi erence curves are perfectly straight. (Pretty close) Example: Di erent types of bottled water. With perfect complements, the marginal rate of substitution does not have a value, as the consumer will only reach a higher indi erence curve by consuming items in the same proportion. The indi erence curves all have a 90 degree kink in them. Example: Left shoes and right shoes. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

35 More Indi erence Curves Apples E D 4 A C F G B H 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

36 More Indi erence Curves Apples E D 4 A C F G B H 0 4 Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

37 More Indi erence Curves Indi erence curves are a great tool for organizing preferences, but we still don t have a way to measure di erent "levels" of indi erence. It would be great if we could put numbers to all of this, and then we could start deriving some demand functions. That s why we have utility functions, which we ll talk about next time. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

38 Summary People use rational decision making in order to rank their preferred consumption bundles. The rules that the consumers develop for the basis for preference relations. Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

39 Preview for Tomorrow We re talking about Utility, i.e., why we like nice things. How can we take all of these preferences and put some math to it? Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

40 Assignment 4 1. Consider the gure given on the next slide. Indi erence curve I passes through points A, B, and C. a. Judging by the curvature of the indi erence curve, what type of preferences does this person have? b. What is the marginal rate of substitution from point A to point B? c. What is the marginal rate of substitution from point B to point C? d. What do the results from parts (b) and (c) imply about the marginal rate of substitution for this kind of preferences? Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41

41 Assignment 4 Apples 5 I A 3 2 B C Oranges Eric Dunaway (WSU) EconS Lecture 9 September 14, / 41