Topic 07 Lecture Notes PDF

Chapter 7 Consumer behaviour 7.1 Introduction In this section, we will theoretically derive a behavioural function called the de- mand function, which maps the price of a product to the intended purchase quant- ity of a consumer. Our objective is to identify the factors that affect the shape o...

Chapter 7 Consumer behaviour 7.1 Introduction In this section, we will theoretically derive a behavioural function called the de- mand function, which maps the price of a product to the intended purchase quant- ity of a consumer. Our objective is to identify the factors that affect the shape of this function. The plan: 1. Define “better”: This defines consumer’s preferences, or the objective func- tion. 2. Define “affordable”. This defines the budget constraint. 3. Solve the following problem: Choose the “best” option from those that are “affordable”. Comparative statics: how does the result in point 3 change when “best” or “af- fordable” is changed? 86 7.2. PREFERENCES 87 7.2 Preferences Economists assume that individuals have preferences. Rather than speculate on what should be preferred, we accept these preferences as given (non-paternalism). This section explains how economists describe preferences and the typical condi- tions they satisfy. 7.2.1 Preferences: Basic definitions and assumptions A ≿ B means that A is at least as good as B (or weakly better). A ∼ B means that A and B are equally good (or indifferent). A ≻ B means that A is strictly better than B. Assumption 1. Consumer’s preferences are rational. Preferences are rational if they are Complete: any two alternatives A and B can be compared and either A ≿ B or B ≿ A. Transitive: if A ≿ B and B ≿ C, then A ≿ C. Additionally, assume that preferences are stable. The term rational has a specific meaning in this context which is different that in common English. Rationality does not imply that behaviour is Conscious: Preferences revealed through actions, rather than stated inten- tions, are what economists focus on. For example, one might claim to prefer a safer car but choose a faster one. 7.2. PREFERENCES 88 Typical: Preferences can be rational but very unusual. Objectively correct: Rational individuals can have incorrect beliefs, such as thinking that flying is more dangerous than driving. Egoistic: Rationality does not exclude altruism or other-regarding prefer- ences such as snobbery, status-seeking, etc. In essence, rational consumers are goal-oriented. For convenience, from now on, we assume egoistic preferences. Assumption 2. Monotonicity: More of a good or service is always preferred to less 7.2.2 Utility Utility is a numerical index associated with each bundle that indicates which bundles are better (it is sometimes interpreted as satisfaction or happiness, but this already assumes more than is needed). The statement “A ≻ B” is equivalent to “A yields a strictly higher utility than B”. A utility function tells us what is the level of utility for any given allocation or outcome. Suppose one has utility √ √ u (x1 , x2 ) = x1 + x2 , where x1 is quantity of the first good, etc. Then we can state that bundle (16, 1) is strictly preferred to (4, 4), which we can write as (16, 1) ≻ (4, 4) because utility u (16, 1) > u (4, 4). Utility could be understood as an objective measure of satisfaction, such as a monetary payoff, but it can also be a description of subjective desires or preferences unrelated to money. Ordinal utility: Captures only the ranking (but not intensity) of outcomes according to one’s preferences. 7.2. PREFERENCES 89 Cardinal utility: Its level is treated as an ethically or behaviourally significant quantity. For example, consider three different formulations 1. a cup of coffee gives me utility 2 and a cup of tea gives me utility 3. 2. a cup of coffee gives me utility 19,999 and a cup of tea gives utility 20,000. 3. a cup of coffee gives me utility −28 and a cup of tea gives me utility −10. In the ordinal approach, all three specifications mean exactly the same; they in- dicate that I prefer tea to coffee, and the numbers themselves are meaningless. In the cardinal approach, the three specifications may mean different things. They still covey the same ordinal preference (that I prefer tea to coffee), but they may contain additional information depending on how these numbers are interpreted. Furthermore, cardinal utility may or may not be transferable. It is transferable if a unit of utility can be costlessly transferred to another person. For example, if utility is the same as monetary wealth, then transferring one unit of utility from Alice to Bob is possible by simply transferring £1. 7.2.3 Indifference curve and Marginal Rate of Substitution It is possible to derive some conclusions in a model with one good only, but in order to talk about interdependence between goods and fundamental concepts of substitution and complementarity, we need a model with at least two goods. This presents us with a difficulty—we will need a way to trace a 3D object on a 2D paper. The three dimensions are the quantity of good 1, the quantity of good 2, and the utility level that each such bundle generates. The solution is to use the same method as in topographic maps, namely the ‘level curves’. 7.2. PREFERENCES 90 Figure 7.1: Representing 3D on a 2D surface (source: reddit) 7.2. PREFERENCES 91 Food Food Non-monotonic preferences C≻A∼B C A B A B Water Water Figure 7.2: Indifference curves Consider a space where one can substitute one good for another, for example, units of water on x-axis and units of food on y-axis. An indifference curve is a set of bundles that the consumer views as equally good. In other words, an indifference curve is a ‘level curve’ of the ‘utility hill’. Assumptions made so far lead us to a few observations (see Figure 7.2): 1. Indifference curves are downward sloping. If they were not, it would contra- dict the assumption of monotonicity. 2. Indifference curves farther from the origin depict better bundles, which is true by monotonicity. Moreover, indifference curves cannot be ‘thick’. 7.2. PREFERENCES 92 Food A B C Water Food A ∆f B D ∆w C Water Figure 7.3: Shape of indifference curves 7.2. PREFERENCES 93 3. Distinct indifference curves cannot cross. If they did, it would imply that the intersection point would would give two different utility levels, which is impossible. 4. For any point, there is an indifference curve passing through it. It is just that we do not draw all of them. Subjective substitution between goods Consider a change depicted on Figure 7.3: move from A to B, then to C. In both cases, we give the consumer one unit of water and take away some units of food to keep them just indifferent. On the left, as water becomes more plentiful and food becomes scarce, water is valued more in terms of food. On the right, as water becomes more plentiful and food becomes scarce, water is valued less in terms of food. The indifference curve on the right seems to describe our typical preferences better. The Marginal Rate of Substitution of water for food, M RSwf , indicates how much food has to be given up when the consumer receives one more unit of water, so that they remain as well off as before. M RSwf = ∆f /∆w|the same i.c. approximates the slope of a smooth indifference curve. Assumption 3. M RS is diminishing (along a smooth indifference curve, moving to the right, in absolute terms). Alternatively, we say that preferences are convex. Another way to say this: the Marginal Rate of Substitution of water for food is the consumer’s value of an extra unit of water expressed in units of food. Assump- tion 3 simply says that the Marginal Value of water decreases as the consumer obtains more of water. 7.2. PREFERENCES 94 Number of apples Utility Marginal Utility, M Uapple 0 101 1 110 9 2 114 4 3 116 2 4 117 1 5 116 −1 Table 7.1: Marginal utility 7.2.4 Marginal utility Marginal Utility, denoted as M Ugood is extra utility generated by an extra unit of the good. Consider again Figure 7.3. The slope of a smooth indifference curve is M RSwf = ∆f /∆w|same i.c.. However, the move from A to B can be decomposed into two steps, A → D → B. 1. If A → D, then utility goes down roughly by ∆f × M Uf. 2. If D → B, then utility goes up roughly by ∆w × M Uw. 3. To stay on the same indifference curve, the total utility must not change. Hence, these two changes must cancel each other out, −∆f × M Uf = ∆w × M Uw , or ∆f M Uw =− ∆w same i.c. M Uf Since the left hand side is M RSwf , we conclude that the Marginal Rate of Substi- tution can be easily expressed in terms of Marginal Utilities. 7.3. BUDGET CONSTRAINT 95 Economists often assume diminishing marginal utilities, meaning that while each additional unit of a commodity increases utility, these increment decrease with each additional unit. This assumption leads to a diminishing MRS, thereby implying Assumption 3. 7.2.5 Conclusions It is a mathematical fact that if preferences are rational (plus a technical assump- tion called continuity), then there is some utility function that captures these preferences. The overall conclusion is that preferences over consumption bundles can be represented by specifying any of the following. Ordinal preference relation, ≿ A picture of indifference curves Utility function, u (.) Marginal Utilities, M U (.) Marginal Rate of Substitution, M RS (.) 7.3 Budget constraint Budget constraint states that expenditures are limited by income. Let pw and pf be prices of water and food, respectively, and Y be the income. These are exogenous to the consumer. The budget constraint can be written as pw w + pf f ≤ Y. The budget line, where this condition holds with equality, can be written as f = (Y /pf ) − (pw /pf ) w. One can see that this line has a slope of (−pw /pf ) and 7.4. CHOICE 96 Food - pw/pf S Intercept Y/pf R P Y/pw Water Figure 7.4: Budget constraint an intercept of Y /pf. Bundles such as P and R are affordable, while S is not. The bundle R requires all the income. 7.4 Choice Given her preferences (in the form of either M Uf and M Uw , indifference curves, utility, or M RS), and market conditions (in the form of pw , pf and Y ), the con- sumer chooses the best bundle from those that are affordable. The first observation is that the consumer must spend all her money,so that the budget constraint is satisfied with equality, pw w + pf f = Y. This is not surprising in a model without a future, as leaving money unspent is pointless. There are models with multiple periods, in which consumers take decisions about savings. The optimal choice of a consumer is represented by point D. Points like A, B and C are affordable but there are better affordable options; point E is not affordable. An interior point like D must satisfy the tangency condition: 7.4. CHOICE 97 Food D E A C B Y/pw Water Figure 7.5: Optimal choice Slope of indifference curve = Slope of budget line pw M RSwf = − pf In other words, the consumer continues to adjust her bundle along the budget line until her subjective rate of substitution between two goods (M RS) is equal to the market rate of substitution (price ratio). Alternatively, this can be written as M Uw M Uf =. pw pf 7.5. COMPARATIVE STATICS 98 7.5 Comparative statics 7.5.1 Demand - change of the price of the good Suppose that the initial price of water is 8 and that it falls to 6. Graphically, this does not affect the vertical intercept Y /py , but the budget line ‘rotates’ around this point outward. How does the quantity demanded change? There are two possible cases: 1. Picture on the left of Figure 7.6 depicts an ordinary situation where quantity demanded increases when price falls. This is known as the law of demand. 2. The picture on the right shows that the opposite may hold. A rational consumer with preferences satisfying all the standard assumptions may ex- hibit bizarre comparative statics where the quantity demanded increases as the price rises (while income, preferences and everything else remains un- changed). A good with such property is called a Giffen good. 7.5.2 Change of income - Engel curve Suppose that the initial income is 9 and that it falls to 6. Graphically, this change does not affect the slope of the budget line. Instead, the budget line shifts parallelly inward. The Engel curve is a relationship between income and quantity demanded. Two possible cases are depicted on Figure 7.7: normal goods and inferior goods. 7.5.3 Digression: Income and substitution effect We can distinguish between the income effect and substitution effect. Income effect: The change in quantity demanded caused by a change of income/wealth, while keeping prices constant. 7.5. COMPARATIVE STATICS 99 Food Law of demand Food Giffen paradox Y/py Y/py Y/8 Y/6 Water Y/8 Y/6 Water Price Price of of water water 8 8 6 6 Water Water Figure 7.6: Derivation of demand 7.5. COMPARATIVE STATICS 100 Food Water is normal Food Water is inferior 9/py 9/py 6/py 6/py 6/pw 9/pw Water 6/pw 9/pw Water Income Income Engel curve for Engel curve for 9 normal goods 9 inferior goods 6 6 Water Water Figure 7.7: Derivation of Engel curve 7.6. SUMMARY 101 Substitution effect: The change in quantity demanded caused by a change of price, while keeping real income/wealth constant. When income changes then the only effect is the income effect. But when the price changes, both income and substitution effects are present. Firstly, if the price decreases, the consumer becomes “richer,” similar to when the income increases. This is the income effect of the change in price. Secondly, the consumer shifts her purchases towards the cheaper product regardless of her income. This is the substitution effect of the change in price. The isolation of the income effect from the substitution effect when the price changes hinges on the fact how we define real wealth to be kept constant. 7.5.4 Change of a price of other goods Define complements and substitutes. Think about this yourself and read in the textbook 7.6 Summary We identified several factors that affect the quantity demanded: 1. Own price: Law of demand or Giffen paradox 2. Income: Normal goods or inferior goods 3. Price of other goods: Complements and substitutes 4. Preferences: we assume that preferences are stable and exogenous. However, one could contemplate preference formation. If preferences could change, then quantity demanded would change. 7.6. SUMMARY 102 5. Expectations or beliefs: Although not included in our simple model, in a model with some uncertainty, expectations might be affected by news, thereby influencing quantity demanded. This is more complicated to ana- lyse, and there are alternative plausible models for this scenario.