İktisada Giriş Theory of Consumer Choice Week 7: Theory of Consumer ’ s Choice In this chapter, we will propose a model of how consumers choose what to consume. There are four elements in this model of c onsumer c hoice : Consumer ’ s income, 1- Prices of goods, 2- Consumer ’ s tastes & preferences. These rank different bundles (combinations) 3- of goods according to the satisfaction (utility) they yield. The assumption that consumers pick the bundle that maximizes their utility 4- level. 7.1 Budget Constraint Consumer ’ s income and prices of goods together describe the consumer ’ s budget constraint. The budget constraint describes combinations of goods that the consumer can afford. Assume that you have an income of 100 YTL per week. Also, assume that there are only two goods that you need: lahmacun and baklavas. Supp ose one lahmacun (meal) costs 10 YTL and one baklava (kg) costs 20 YTL. This information is sufficient to draw a budget constraint. Let us put number of baklavas on the vertical axis and number of lahmacuns on the horizontal axis. The easiest way to draw a budget constraint is to consider the extreme points. If you choose to spend your money completely on food, you can buy 10 lahmacuns and zero baklavas. On the other extreme, if you spend your money completely on baklavas and do not eat (!), you can buy 5 b aklavas and zero lahmacuns. Now draw the points that the budget constraint crosses the axes. Then join these points and draw the budget line.L K 5 10 Q ty . of Baklava Qty of Lahmacun FIGURE 24 In between these two extreme points, there are other combinations of baklav as and lahmacuns that you are spending all of your income such as: 8 lahmacuns and one baklava, 6 lahmacuns and two baklavas, 4 lahmacuns and three baklavas, 2 lahmacuns and one four baklavas. These points are all on the budget line. How about a point suc h as L = (9, 3)? Point L is unaffordable, since it costs the consumer 150 YTL to buy it. How about a point such as K = (4,2) ? It is affordable, and costs only 80 YTL. But the consumer does not spend all of his income at K. We assume that there is no savin g in this model, so choosing this point does not make sense for the consumer. Notice the tradeoff between the two goods: if you want to consume more food, you have to buy less baklavas. This tradeoff is constant along the budget line: for every additional baklava, two lahmacuns have to be given up. Or in other words, for every additional lahmacun, half a baklava must be given up. This is called relative price. The relative price of baklavas in terms of lahmacuns is 2 lahmacuns per baklava. The relative pric e of lahmacuns in terms of baklavas is ½ baklavas per lahmacun. Relative price of lahmacuns in terms of baklavas is equal to the ratio of the price of a lahmacun divided by the price of a baklava, i.e. P M / P B . The relative price can also be found by the s lope of the budget line. The slope of a line is the change in the vertical distance divided by the change in the horizontal distance. As the qty. of baklavas increases, qty. of lahmacuns decreases, therefore slope of the budget line is negative. There is a close relationship between the slope of the budget line and relative price of goods. Slope of the budget line can be found by the negative of the relative price of lahmacuns in terms of baklavas. In our example, slope is -1/2. 7 .2 Tastes & Preferences T he budget constraint shows what the consumer can afford to buy given her income and prices of goods. Now, we will talk about how different consumers could have different preferences. This is the third element of our model of consumer choice: Consumer ’ s tas tes & preferences rank different bundles (combinations) of goods according to the satisfaction (utility) they yield. For example, some people like food more than other people. Some people may consume cigarettes while some others do not. We are trying to in corporate those preferences of consumers into our model. There are some simplifications that we make about preferences: 1- First, we assume that consumers are able to rank alternative bundles of goods according to the utility they provide , 2- While they do this ranking, we assume that consumers are consistent , they do not behave in a stupid way. For example, consider the three bundles: A = (3, 3), B = (2, 4) and C = (1, 5). If the consumer prefers A to B, and also prefers B to C, he must prefer A to C . 3- More is better. Consumers prefer larger quantities of goods to smaller quantities. For example, if A = (3, 3) and C = ( 4 , 4), then C must be preferred to A. We need more info . in order to know the ranking between A = (3,3) and B = (3,4) or A and F . Let us show the implication of this assumption on Figure 25. B A 5 10 Q ty . of Baklava Qty of Lahmacun C D E F Preferred to A A is preferred to here FIGURE 25 For a given point A, the northeast region of A is preferred to A. The southwest region is worse than A, so A is preferred to this region. To rank the north west and southeast regions, we need to have more detailed information on preferences. Marginal Rate of Substitution Keeping total utility (satisfaction) constant, how many baklavas would you give up in order to get one more lahmacun? This amount is the marginal rate of substitution (MRS) of lahmacun s for baklava s. L H Q ty . of Baklava Qty. of Lahmacun 10 5 A K U2 U2 U3 U3 FIGURE 2 6 Of course, this depends on your initial position: how many lahmacuns and baklavas you already have. If you are really hungry, let us say you did not eat for two days, then you will give up a lot of baklavas for one lahmacun right? Then, on Figure 26, if you are at a position that has very little lahmacuns such as point K = (1, 4), then you are ready to give up a lot of baklavas. Let us say you are ready to give up exactly two baklavas for one lahmacun. So you come to point H = (2, 2). Point K and point H gives you equal satisfaction. Notice that between points K and H, marginal rate of substitution of lahmacun s for baklava s is two baklava s for one lahmacun . At point H, if you think of having one more lahmacun, you do not want to give up two baklavas anymore. In fact, you think that you can give up one more baklava only if you can get three more lahmacuns. That is, you are equally satisfied if you come to a point such as L = (5, 1). Notice that your marginal rate of substitution between H and L is 1/3 baklava s for one lahmacun . So MRS has declined sharply as we move towards more lahmacuns and less baklavas. This is commonsense because consumers prefer more ba lanced combinations of goods instead of getting only one good. This property is called diminishing marginal rate of substitution propert y and is an important element of our model: 4- Preferences exhibit diminishing marginal rate of substitution . That is, consumers prefer more balanced combinations of goods to more extreme combinations. Indifference Curves Notice that points K, H and L gives the consumer the same total utility. Assuming all the points on the curve that connects these points also yield the same utility, we call this curve an indifference curve. The consumer is indifferent to all the points on an indifference curve. She has the same satisfaction levels at all points on the curve. Let us name this curve U 2 U 2 . There is a special relationshi p between MRS and the slope of the indifference curve. In particular, the slope of the indifference curve is the absolute value of the MRS of lahmacun s for baklava s . For example, between points K and H, slope of the indifference curve is -2. Between points H and L, slope of the indifference curve is - 1/3. These numbers are just the negatives of the MRS ’ s of lahmacuns for baklavas. Properties of I ndifference C urves: Notice that one can draw other indifference curves that represent a smaller or a larger sati sfaction level. Consider a bundle such as A = (3, 3) on the graph. This bundle includes more of both lahmacuns and baklavas than point H. Therefore it must be on a higher indifference curve such as U 3 U 3 . Consider bundle S = (1, 1). This bundle must be on a lower indifference curve because it includes less of both lahmacuns and baklavas. Can indifference curves be positively sloped? No, because if they were, we would be saying that as we increase both goods, utility stays constant. This cannot be true. Ther efore, indifference curves are always negatively sloped. Can indifference curves CROSS each other? Let us suppose they can. Z Q ty . of Baklava Qty. of Lahmacun 10 5 X Y U U ’ U U ’ FIGURE 27. CAN INDIFFERENCE CURVES CROSS EACH OTHER? Is there a problem here? Let us think about it. B undles X and Y are on the same indifference curve, so they must yield the same level of utility . Also, bundles Y and Z are on the same indifference curve, so they also must yield the same utility . But then, X and Z must yield the same level of utility. But there is a problem here: We have assumed that more is better. If more is better, bundle Z must have a greater utility than bundle X because bundle Z has a greater number of lahmacuns and baklava than bundle X. Therefore, indifference curves cannot inters ect. 7 .3 Consumer Choose s the Bundle That Maximizes Her UtilityIn this part, we combine the two sides of this problem: the budget constraint and preferences. Which point does the consumer choose? First, consider the fact that the consumer will choose a po int ON the budget line. Let us show why this is the case on the graph : With an income of 100 YTL and price of a lahmacun is 10 YTL and price of a baklava is 20 YTL, the budget constraint is the same as before. Let us draw this budget line. L B 5 10 Q ty . of Baklava Qty of Lahmacun U1 U1 U3 U3 U2 U2 C FIGURE 28 Not interior of the budget set, because this leaves some income unspent. Not a point outside of the budget, because those points are unaffordable. The consumer makes the best possible choice on the budget line. But there are many p oints on the budget line. Which point does the consumer choose on the budget line? She chooses the point that gives her maximum possible utility. How do we know which point is that? We draw indifference curves. Add TWO indifference curves on the above gra ph. U1U1 passes below the budget line, U3U3 passes above the budget set. Ask them if the consumer chooses U3U3 because it gives highest utility. What is the problem? Since the consumer will choose a point ON the budget line, this could be on U1U1. Consider a point such as B on U1U1. It is affordable. But does the consumer maximize her utility at B? Is there a higher indifference curve that gives better utility? YES, we can draw higher indifference curves. Draw another indifference curve that is higher than U1U1 but still not tangent. Show that still utility can be increased by drawing another one. Do this until they are convinced that it is the highest affordable curve that is tangent to the budget line. Ask yourself if you can show another point that is bet ter than C and still affordable? Give a little time. Point C = (4, 3) is the point chosen. What is interesting at this point? At this point, the slope of the indifference curve is equal to the slope of the budget constraint. Recall that the slope of the i ndifference curve shows the consumer ’ s preferences: it is equal to the MRS of lahmacuns for baklavas. It shows how many baklavas this consumer would give up for one additional lahmacun. This depends on where the consumer is on the analytical space. On the other hand, the slope of the budget constraint shows the relative price of lahmacuns in terms of baklavas. Since prices are constant, this is always equal to ½. The optimal choice happens at a point where MRS of lahmacuns for baklavas (1/2 at point C) is equal to the relative price of baklavas in terms of lahmacuns (1/2 everywhere). 7 .4 Applications of the Model 1- When Preferences are DifferentConsider the following application to see how this model produces different choices when preferences are diff erent. Consider Joseph who likes lahmacun and Iris who likes baklava. Joseph ’ s preferences look like following: Preferences of Joseph Lahm acun Baklava FIGURE 29 Joseph is willing to give up a lot of baklavas to get one more lahmacun through most of each indiffere nce curve. Illustrate slope on these curves. High slope implies MRS of lahmacuns for baklavas is high. What sort of a consumption pattern do you expect Joseph to choose? Is he more likely to demand more lahmacuns or more baklavas? Now consider the prefere nces of Iris, a baklava lover:Preferences of Iris FIGURE 30 Above preferences show a small MRS of lahmacuns for baklavas. Small number of baklavas is given up to get additional lahmacuns. This is because relative value of lahmacuns is smaller th an the value of baklavas for IRIS. We expect Iris to choose a bundle with a lot of baklavas and few lahmacuns. Now we will see how these differences in tastes lead these consumers to choose different bundles. Assume they have the same budget. See Figure 31 and 32. Lahm acun BaklavaL B 5 10 Q ty . of Baklava Qty of Lahmacun C Joseph ’ s choice Figure 31 L B 5 10 Q ty . of Baklava Qty of Lahmacun C İ ris ’ s choice Figure 32 Having the same budget means that the relative price of baklavas in terms of lahmacuns is the same for both consumers. How about their MRS ’ s? Notice that Joseph choo ses a point that is far to the right, in order to make his MRS equal to ½. Because his indifference curves are steep, we need to go rightwards to allow it to flatten. This means she chooses a point with a large number of lahmacuns and a small number of bak lavas. This is consistent with Joseph ’ s preferences. Now check Iris ’ s choice. She has flat indifference curves. This means we need to go leftwards to get her MRS equal to ½. This means Iris chooses a point with a large number of baklavas and a small number of lahmacuns. This is consistent with Iris ’ s preferences. SO OUR MODEL IS ABLE TO TRANSLATE DIFFERENT PREFERENCES INTO DIFFERENT CHOICES. 2- When Income Changes Here we analyze how a consumer changes her consumption if her income increases or decreases. C onsider the case where consumer ’ s income increases from 100 YTL to 160 YTL per week. Commonsense suggests that the consumer would buy more lahmacuns and more baklavas if both goods are normal (remember inferior goods). Let us see what our model would say. Then we must draw a new budget line. This crosses the Lahmacuns axis at 16 and the Baklavas axis at 8. This means that she affords MORE bundles: her budget set expanded. L 10 20 Q ty . of Baklava Qty of Lahmacun U1 U3 U3 D 2 8 10 5 C FIGURE 33 Notice that the relative price of lahmacuns in terms of baklavas did not change. This is because the prices and hence the price ratio did not change. Consequently, slope of the budget line also did not change. This is a PARALLEL SHIFT of the budget line outwards. Does the consumer still choose point C when she has more money? Of course no. She can jump to a higher utility indifference curve. Show the effect on a graph. She now chooses point D. Point D gives her both more lahmacuns and more baklavas. Assume C=(4, 3) and D = (5, 6). Show this on the gr aph. Then what is the income elasticity of demand (IED) for lahmacuns? % change in income is 60%. % change in qty of lahmacuns demanded is (1/6)*100 = 16.7%. Then, I.E.D. for lahmacuns is 16.7/60 = 0.28. Are lahmacuns income elastic or inelastic? Lahmacuns are a necessity good because their IED is smaller than one. This means that consumers ’ demand for lahmacun increases when their income goes up, but not as fast as their income.What is the IED for baklavas? % change in qty of baklavas demanded is (3/3)*10 0 = 100%. Then, IED becomes 100/60 = 1.67. Therefore, baklavas are income elastic. We can consider baklava as a luxury good. 3- When Prices Change Law of demand says that other things equal, if the price of a good increases, qty demanded of the good decrea ses. Does our model verify this law or this law is just an empirical observation that happens to hold most of the time? Let us check. Assume that the price of lahmacuns increase to 20 YTL instead of 10 YTL. Law of demand says that qty of lahmacuns demande d should decrease. What does our model say? To know the answer, we need to draw a new budget line that reflects the price change. Notice that the budget line would rotate . It now crosses the Lahmacuns axis at 5 instead of 10. This shrinks the budget set, the consumer cannot buy bundles that she was able to buy with her previous budget. In particular, she cannot buy the previous optimal point C = (4, 3). See Figure 34. L E 5 10 Q ty . of Baklava Qty of Lahmacun U3 U3 U2 C 5 D H H A BFIGURE 34 Consumer ’ s new optimal choice is E = (3, 2). It i ncludes less of both Lahmacuns and Baklavas. The move from C to E can be decomposed into two distinct effects. These two effects are the substitution effect and income effect. Substitution effect is shown by the move from C to D. Income effect is shown by the move from D to E. Substitution effect is the adjustment of demand to the relative price change alone, keeping utility level constant. We can draw this effect by drawing a hypothetical budget line HH parallel to the new budget line but giving the same utility as C. The consumer responds to the new relative price of 1/1 Baklava/Lahmacun instead of the old ½ Baklava/Lahmacun by buying less Lahmacun and more Baklava. This is because Lahmacun has become relatively more expensive and Baklava has become relat ively cheaper. At point D, consumer can enjoy the same utility level as C, but takes into account that Lahmacun is relatively more expensive now than before. Income effect is the adjustment of demand to a change in real income alone, keeping relative pric es constant. Notice that when price of Lahmacun is 20 liras instead of 10, the purchasing power (real income) of the same 100 liras has decreased. The income effect isolates this reduction in purchasing power. The income effect is shown by the parallel shi ft of the budget line from HH to AB. If we keep relative prices of Lahmacun and Baklava constant at 1/1 but only reduce real income, we move from D to E.