We are going to see the consumer s decision theory that you have seen in ECON 111 in another way.

Transcription

1 2 Demand We are going to see the consumer s decision theory that you have seen in ECON 111 in another way. 2.1 The budget line Whenever one makes a decision one needs to know two things: what one wants to do and what one can do. When talking about consumption decisions, what one can do is limited by two things: one s income and the prices of the goods that one is considering. These prices are usually takes as given; i.e., as a general rule one does not have much influence on these prices. Suppose that your monthly income is $30 and you are deciding between two goods: pop and movies. The price of pop is $3 for a six-pack and the price of movies is $6. If you spent all your income in pop (y-axis) you can buy 10 packs (and no movies). This is one possibility. If you spend all your income in movies, you can go to the movies 5 times a month but you cannot buy any pop. This is another possibility. You can also go 2 times to the movies and buy 6 packs; etc. The budget line can be represented by an equation p m q m + q p = I. The budget line tells you which combinations of goods are affordable and which ones are non-affordable, what you can and cannot do. You can also afford anything below the budget line but, assuming that there is no future and you do not want money for the sake of money, you are not going to be below the budget line because you can afford to be in the budget line which will give you more satisfaction. We usually represent a line like that y = a + b x, where a is the intercept and b is the slope. Let us rewrite the budget equation In our example, q p = I p m q m. q p =10 2 q m. What is the economic meaning of the intercept and the slope? The intercept is the real income (or purchasing power) income expressed in units of a good. The slope is the relative price price of one good divided by the price of another. It represents the opportunity cost of the good in the x-axis in terms of the good in the y-axisorhowmanyunitsofthegoodinthey-axisoneneedstogiveup in order to get one more unit of the good in the x-axis. Definition 4 The budget line describes the limits to a household s consumption choices. 3

2 2.1.1 Questions 1. How does your budget line change if your income increases? Do you have more or fewer choices? Does the slope of the budget line change? 2. How does your budget line change if the price of one of the goods you are considering buying decreases? Do you have more or fewer choices? Does the slope of the budget line change? 2.2 Preferences Once you know what you can do, you need to know what you want to do, your preferences, what you like and dislike. Here we are going to introduce a concept that is going to sound strange, very strange indeed. Economists measure the satisfaction that you obtain from consuming, from fulfilling your wants and needs. We call it utility. Utility is a way of talking about preferences. Definition 5 (Total) utility is the (total) satisfaction that a person obtains from consumption. The idea of measuring satisfaction may sound strange but, if you think about it, there is nothing intrinsically different between measuring satisfaction and anything else that is not countable. Counting heads is intuitive. Measuring the temperature is not. However we, ingenious human beings, have devised ways of measuring the temperature. Or length or weight. And we have been doing it for so long that it seems intuitive to you now. If I say it is 30 o Cyou know it is pretty hot and if I say it is -40 o C you know it is really cold. But because it is not so intuitive we have many different ways of measuring the same things. We can measure temperature in Celsius or Fahrenheit. We can measure length in kilometers or miles. Or we can measure weight in kilos or pounds. But you (especially you Canadians Europeans or Americans are not so good at this) know how to translate from one to the other. Mathematically, we would say that these different ways of measuring are monotonic transformations of each other. This means that if one increases, the other does too; and viceversa. If I say that today is 30 o C and yesterday was 20 o C, I am saying that today is hotter than yesterday was. So if I use Fahrenheit, the number for today should be higher than the number for yesterday: 86 instead of 68. Units are not so important as long as we all use the same so we understand each other. If I say that today is 30 o I need to tell you if 30 o Cor30 o Fsoyou know weather it is very warm or fairly cold. Likewise with the utility. If I say that the utility I receive from going to the movies is 50 and the utility I receive from watching the same movie at home is 25, you know that I prefer going to a theatre. But if I say that the utility I obtain from going to the movies is 100 and the utility I obtain from watching the same movie at home is 50, you also know that I prefer going to a theatre. The units are irrelevant. 4

3 By the end of this topic, it should be more or less clear that, in some way, we reveal our preferences, we vote with our dollars. Because of this, somehow, we can measure utility in dollars in Canada. And in pounds in Britain and in euros in Spain. And, with some reservations, we can make comparisons. Here, instead of using the marginal utility approach, we are going to see something called indifference curves. It is the same thing. We can graphically represent preferences using a bunch of curves. An indifference curve shows combinations of goods among which the consumer is indifferent (the consumer obtains the same satisfaction). Suppose that you are indifferent between consuming 2 movies a month and 6 packs of pop or consuming 2 packs of pop and 6 movies. An indifference curve will go through these two points. Indifference curves (usually) have three properties: 1. they are downward sloping: because for most goods we prefer more to less, to be indifferent between bundle A and bundle B it must be that, if bundle A includes more pop, then bundle B should include more movies and vice-versa. If bundle B includes more pop and movies, one usually prefers B. 2. The further they are from the origin, the higher the level of satisfaction. Because the point B in curve 2 includes more of both goods, it should be preferred. 3. They cannot cross. Suppose that one is indifferent between A and C and between B and C but one prefers A to B. This is a contradiction. Now, suppose you are indifferent between consuming 2 movies a month and 6 packs of pop (point A) or 3 movies and 4 packs. You are willing to exchange two packs for one movie. This is called the marginal rate of substitution (MRS): the rate at which a person will give up the good measured on the y-axis to obtain one more unit of the good measured in the x-axis in order to remain indifferent. As you can see the MRS is the (arc) slope of the indifference curve. You also know that the limit of the arc slope is the slope at a point. So the MRS at point A can be measured at the slope of a tangent to the indifference curve at point A. This is a curve, not a line. So the slope at point A is not the same at the slope at point B. The MRS is not the same along an indifference curve: as you remember from ECON 111, because of the diminishing marginal utility, the moremoviesoneenjoysthelessonecaresforanextramovieandthelessone iswillingtogiveupforanextramovie. 2.3 The choice So now we have what we can do on one hand the budget line, and what we want to do in the other utility. It is time to look at the way we, consumers, take consumption decisions. Remember that economists think that we, as consumers, optimize or make the best of our resources. We maximize our utility, our satisfaction. And how do we do that? 5

4 We know that we are going to choose a point in the line (we do not want the points below and the ones above are not affordable). We are not going to choose point A because point B is in a higher indifference curve. For the same reason we are not going to choose point B. The point that we are going to choose is the one at which the indifference curve is tangent at the budget line. We cannot do better than that. As this point the indifference curve has the same slope than the budget line. So one maximizes when the MRS equals the relative price. MRS = p m. (1) Intuitively, if you are at any other point, you can obtain more for one of the goods that what you need to keep the same level of satisfaction. Then you should exchange some of this good for the other and you will be better off. Let us say that the relative price is one. You are at a point in which, if you give up a unit of good x, you only need 1/2 unit of good y to keep the same level of satisfaction (your MRS is 1/2). Then you should consume one less unit of good x and one more unit of good y and your total utility will increase by whatever amount of satisfaction 1/2 unit of good y brings you. In ECON 111 you have seen that the utility is maximized when the marginal utility per dollar spent is equal for all goods. What is marginal utility? Marginal utility is the increase in utility derived from the last unit consumed. Marginal utility per dollar spent is marginal utility divided by price. Thus MU m p m = MU p. (2) Intuitively, if the marginal utility that you obtain from the last dollar spent in both goods is not the same, you should shift spending from one good to the other. Let us say that the last dollar spent on pop gives you 5 utils (units of satisfaction) and the last dollar spent on movies only gives you 3 utils. If you spent one dollar less on movies and one dollar more on pop, your total utility increases by 2 units. To show that condition (1) and condition (2) are equivalent, notice that we can rearrange condition (2), by using cross-multiplication, to read MU m MU p = p m. (3) Equation (1) and equation (3) are equivalent because it can be shown (although I am not going to do it) that MRS = MU m MU p. Therefore, condition (1) and condition (2) are equivalent. 6

5 2.4 Criticisms of the marginal utility theory OK. So now you are going to tell me that you do not make consumption decisions in this way. Let me tell you a story. This summer I stopped by a boutique and looked at some jeans priced at $40. I thought: With $40 I can go five times to the movies and I have lots of summer stuff and I did not buy the jeans. Now, here comes winter and I do not have pants (I do not wear dresses in winter); so, I go and buy the same jeans even if it means that I cannot go to the movies for a while. Does it sound familiar? Let me put the same story in economic jargon. In the summer, I had lots of clothing so the marginal utility of an extra pair of pants was low. (Remember that the marginal utility depends of the amount of the good you already have/enjoy.) The marginal utility of an extra piece of clothing was not five times the marginal utility of going to the movies, so I did not buy the jeans. Here comes winter and I do not have enough clothing. Then, the marginal utility of an extra pair of pants (remember the diminishing marginal utility law?) is as high as five times the marginal utility of going to the movies, and I buy the jeans. Do you still think that we do not take decisions in this way? Oh, I know that you do not make calculations in your head. But when you throw a ball in baseball you are not making calculations about the law of gravity, the curvature, the relation between weight and impulse,... And it does not mean that you are not using all of these things. Instead of thinking in this way, your parents taught you to throw a ball when you were a child. You learned by repetition and got a feeling for it. In the same way, your parents gave you an allowance when you were a child so you learned, little by little, how to make these kind of decisions. If this did not convince you, let me tell you that this little model of consumer s behaviour predicts well, as we are going to see. A model is a simplified version of reality in which we forget about certain things, not important at this point, and focus in others, important at this point. The model of a house by an architect does not show the plumbing because it is not important to him/her. The plumber has a model of the same house that, basically, only shows the plumbing the important thing to her/him. Economists are pragmatic and for most of us (not all) the accuracy of the predictions is more important than the veracity (truthfulness) of the assumptions. If a model predicts well, it is useful. A model is not going to predict well if the assumptions are completely crazy but the assumptions do not need to be 100% true (it is a simplified version of reality, so they are never going to be 100% true). References [1] Pindyck, Robert S. and Daniel L. Rubinfeld. Microeconomics. Upper Saddle River, Prentice Hall, (Chapter 3) 7

6 [2] Varian, Hal R. Intermediate Microeconomics. New York, W.W. Norton and Co., (Chapter 2-5) 8