1. Consumer preferences and utility Modelling consumer preferences

2. Consumer preferences and utility How can we possibly model the decision of consumers ? What will they consume? How much of each good? Actually, a very simple framework is enough ! This framework can explain a lot of the behaviour of people on markets.

3. Consumer preferences and utility Last week’s “general rule”: A rational consumer will always choose the best basket of goods amongst all the ones it can afford But we need to clarify : What we mean by rational What we mean by best What we mean by afford Today Next week

4. Consumer preferences and utility The utility function as a measure of satisfaction Indifference curves as a representation of preferences The marginal rate of substitution

5. The Utility function Historically, utility as a measure of satisfaction is grounded in utilitarianism Jeremy Bentham (1748-1831): “It is the property of an object to produce pleasure, well-being or happiness” Stanley Jevons (1835-1882): The father of the “marginalist revolution”, who generalised this concept to consumer behaviour

6. The Utility function Cardinal utility assigns a value to the level of satisfaction associated with the consumption of a basket of goods. Total utility is the sum of the satisfactions derived from the consumption of several goods. Marginal utility is the increase in utility following the consumption of an extra unit of a good. Beers consumed Total Utility Marginal Utility 000 110 2155 3183 4191

7. The Utility function The marginal utility of a good (mU ) measures the increase (or decrease) in total utility (∂U) following a small variation in the quantity consumed (∂x) Remember last week’s lecture: Marginal utility is the first derivative of the utility function. It gives the slope of the utility function

8. The Utility function mU = 10 mU = 5 mU = 3 mU = 1

9. The Utility function The marginal utility of the good (beers) gets smaller as the quantity consumed increases. This phenomenon is called the law of diminishing marginal utility

10. The Utility function The initial, historical approach to consumer behaviour used this concept of cardinal utility However, this is a problematic concept: Is it possible to quantify the satisfaction derived from consuming a good ? Is it possible for the quantities of utility derived from 2 different goods to be compared ? More importantly, do consumers actually think that way when they choose goods ??? This problem was solved by the introduction of ordinal utility More general, more realistic and more powerful

11. The Utility function Ordinal utility is a representation of preferences What is important is not the ability to quantify « how much » utility is provided by a bundle, but the ability to rank bundles in order of increasing utility This is much closer to the “real” behaviour of agents

12. The Utility function Some types of preferences cannot be represented by an ordinal utility function Some simplifying assumptions have to be made Preferences are complete :  Agents can always rank bundles (i.e. preferences exist for all possible bundles) Preferences are transitive :

13. The Utility function An example of non-transitive preferences Your favourite childhood game: Rock Paper Scissors

14. The Utility function You are exploring the desert, you get lost, and you run out of fuel and supplies. Luckily, another truck finds you and offers some help, but you have to choose amongst some options. None is 100% satisfactory because they also have to keep some resources to be able to get back. How do you rank those options ? FuelSuppliesMap Option 1Full tankVery littleYes Option 2Full tankPlentifulNo Option 3NonePlentifulYes

15. The Utility function Such preferences cannot be represented by an ordinal utility function !! This is a first example of how consumer theory simplifies a complex reality Consumer theory (and economic theory in general) often “breaks down” in extreme situations People’s behaviour becomes governed by different priorities

16. Consumer preferences and utility The utility function as a measure of satisfaction Indifference curves as a representation of preferences The marginal rate of substitution

17. Indifference curves Indifference curves represent preferences in “consumption space” They are built from the ordinal utility function As seen above, an ordinal utility function can represent preferences (under some conditions) The ranking of bundles in order of preference corresponds to the ranking in order of increasing (or decreasing utility) Good 1 Good 2

18. Indifference curves

19. Utility function for a single good

20. Indifference curves But how would you draw a utility function for the consumption of 2 goods ?

21. Indifference curves Seen from above, the 3-D diagram looks like this... Lines of constant utility

22. Indifference curves This is the same “trick” as for this kind of diagram...

23. Indifference curves Indifference curves are a graphical (2-D) representation of a 3-D utility function Just like the contour lines of a 2-D road map represent the 3 rd dimension (altitude) A given indifference curve represents all the baskets of goods that provide the same utility to a consumer The consumer is therefore indifferent to all these baskets

24. Indifference curves Indifference curves further from the origin correspond to higher levels of utility Good 1 Good 2 x1x1 x2x2  X U(x 1,x 2 ) < U(y 1,y 2 ) y1y1 y2y2 Y 

25. Indifference curves Because they are derived from a utility function, indifference curves are a representation of preferences However, at this point, indifference curves can still take a wide range of shapes Some examples are in the exercise for next week For a general theory of choice, economists like “well-behaved” indifference curves 2 more simplifying assumptions need to be made

26. Indifference curves Monotonicity (non-satiation) In other words, “more is always preferred to less” Extra units of a good always increase utility, so consumers always prefer to have more of a good The implication is that regardless of which indifference curve you are on, there always exists a higher one right next to it.

27. Indifference curves Convexity (preference for variety) Good 1 Good 2 y1y1 y2y2 Y x1x1 x2x2 X A combination z of extreme bundles x and y is preferred to x and y Z

28. Indifference curves Example of concave preferences Good 1 Good 2 y1y1 y2y2 Y x1x1 x2x2 X The extreme bundles x and y are preferred to a combination z of x and y Z What can we say about marginal utility?

29. Indifference curves “Well-behaved” indifference curves don’t cross Good 1 Good 2 Y X Let’s assume they can Z This violates monotonicity (more is preferred to less)

30. Consumer preferences and utility The utility function as a measure of satisfaction Indifference curves as a representation of preferences The marginal rate of substitution

31. What is a rate of substitution ? You currently have a bundle composed of 10 tubs of ice-cream and 3 DVDs. You want to keep your satisfaction the same How many tubs of ice-cream are you prepared to give up to get some extra DVDs? The rate at which you are prepared to exchange is known as the “rate of substitution”

32. The marginal rate of substitution Ice-cream DVD y1y1 y2y2  Y x1x1 x2x2  X  DVD (+)  IC (-)

33. The marginal rate of substitution What is a marginal rate of substitution ? Exactly the same idea, but this time we are talking about a tiny change in your bundle (∂x) instead of a large change (∆x) You have 10 tubs of ice-cream and 3 DVDs. How many tubs of ice-cream are you prepared to give up to get ONE extra DVD ? This means that the marginal rate of substitution is the slope of the indifference curve

34. The marginal rate of substitution Ice-cream DVD y1y1 y2y2  Y x1x1 x2x2  X ∂IC ∂DVD ∂IC ∂DVD The MRS is decreasing along the indifference curve

35. The marginal rate of substitution So the marginal rate of substitution is the slope of the indifference curve The amount of ice-cream you are willing to give up for an extra DVD is lower the less ice-cream you have This suggests a link with the idea of decreasing marginal utility Is there a way of clarifying this link ?

36. The marginal rate of substitution Ice-cream DVD x1x1 x2x2  X Let’s “zoom in” on the indifference curve until it looks flat Giving up ∂IC ice- cream causes a loss of utility Receiving ∂DVD DVDs causes a gain of utility Because we are still on the same indifference curve, loss=gain

37. The marginal rate of substitution The loss of utility from giving up one good equals the gain from receiving the other good Or equivalently: Rearranging (dividing both sides by mU IC and ∂DVD): The MRS is equal to the ratio of marginal utilities!

38. The marginal rate of substitution In general, with two goods x and y, we have : Note: Economists typically “forget” about the minus sign and give the MRS as a positive number This is result may seem a bit pointless, but it will become clear when we examine consumer choice next week