1. Theory of Consumer Behavior Chapter 3

2. Discussion Topics The concept of consumer utility (satisfaction) Evaluation of alternative consumption bundles using indifference curves What is the role of your budget constraint in determining what you purchase? 2

3. The Utility Function A model of consumer behavior Utility: Level of satisfaction obtained from consuming a particular bundle of goods and/or services Utility function: an algebraic expression that allows one to rank consumption bundles with respect to satisfaction level A simple (unrealistic) example: Total utility = Q hamburgers x Q pizza Page 39-40 3

4. The Utility Function A more general representation of a utility function without specifying a specific functional form: Total Utility =f(Q hamburgers, Q pizza ) Interpretation: The amount of utility (i.e. satisfaction) is determined by the number of hamburgers and pizza consumed Page 40 General function operator 4

5. The Utility Function Given our use of the above functional notation  This approach assumes that one’s utility is cardinally measurable  Similar to a ruler used to measure distance  You can tell if one bundle of goods gives you twice as much satisfaction (i.e., utils is a satisfaction measure) Page 40 5

6. The Utility Function Ordinal vs. Cardinal ranking of purchase choices  Cardinally measurable: Can quantify how much utility is impacted by consumption choices  Commodity bundle X provides 3 times the utility than obtained from bundle Y  Ordinally measurable: You can only provide a relative ranking of choices  Commodity bundle X provides more utility than bundle Y  Don’t know how much more Page 40 6

7. Ranking Total Utility Bundle Quantity of Hamburgers Quantity of Pizza Total Utility A2.510.025 B3.07.021 C2.012.525 7

8. Ranking Total Utility Bundle Quantity of Hamburgers Quantity of Pizza Total Utility A2.510.025 B3.07.021 C2.012.525 Prefer A and C over B Indifferent (equal satisfaction) from consuming bundle A and C Prefer A and C over B Indifferent (equal satisfaction) from consuming bundle A and C 8

9. Marginal Utility Marginal utility (MU): The change in your utility (ΔUtility) as a result of a change in the level of consumption (ΔQ) of a particular good  MU i =  Utility ÷  Q i  Ceteris paribus concept MU will  ↓ as consumption ↑  Marginal benefit of last unit consumed ↓ as you ↑ consumption of a particular good  The opposite holds true  Total utility (satisfaction) could still be ↑ Page 40-41 9 ∆ means “change in” i identifies a good (i.e. the i th good) ∆ means “change in” i identifies a good (i.e. the i th good)

10. Q H /weekTotal UtilityMU 120---- 23010 3399 4478 5547 6606 7655 8694 9723 10742 11740 1270-4 Page 40-41 = (47-39) ÷ (4-3) 10 Marginal Utility Total Utility =f(Q H, Q P ) Q H = quantity of hamburgers Q P = quantity of pizza ∆Q H ∆U

11. Marginal utility goes to zero at the peak of the total utility curve (i.e., maximum utility) Marginal utility goes to zero at the peak of the total utility curve (i.e., maximum utility) Page 42 Note: MU is the slope of the utility function, ΔU÷ΔQ H Note: MU is the slope of the utility function, ΔU÷ΔQ H Total Utility Marginal Utility 11 Total Utility = f(Q H, |Q P ) Note: The other good, i.e. pizza, remains unchanged Example of ceteris paribus

12. Indifference Curves Cardinal measurement  Quantitative characterization of a particular entity  “I had 2 beers last night” Ordinal measurement  Ranking of a particular entity versus another  “I had more beers than you last night” Page 41-43 12

13. Indifference Curves Cardinal measurement of utility is both unreasonable and unnecessary  i.e., what is the correct functional form of the relationship between utility and goods consumed? Economists typically use an ordinal measurement of utility  All we need to know is that one consumption bundle is preferred over another Page 41-43 13

14. Indifference Curves Modern consumption theory is based upon the notion of isoutility curves  iso in Greek means equal  Isoutility curves are a collection of bundles of goods and services where the consumer’s utility is the same  Consumer is referred to as being indifferent between these alternative combinations of goods and services  For two goods connect these different isoutility bundles  Collection referred to as an isoutility or indifference curve Page 41-43 14

15. Page 43 Bundles N, P preferred to bundles M, Q and R Indifferent between bundles N and P Increasing utility Increasing utility The further from the origin the greater the utility (satisfaction) The further from the origin the greater the utility (satisfaction) 15 Assume you consume hamburgers and tacos Assume you consume hamburgers and tacos

16. Page 43 Note that the rankings don’t change if measured utility as 10 and 35 Note that the rankings don’t change if measured utility as 10 and 35 The two indifference curves here can be thought of as providing 200 and 700 utils of utility. 16

17. Page 43 Theoretically there are an infinite (large) number of isoutility or indifference curves 17

18. Slope of the Indifference Curve Like any other curve one can evaluate the slope of each indifference curve  Indifference curve slope is given a special name: Marginal Rate of Substitution (MRS) Given the above graph the MRS of substitution of hamburgers for tacos as you move along an indifference curve is calculated as: MRS =  Q T ÷  Q H Page 43 Change in quantity of tacos (i.e., “rise”) Change in quantity of hamburgers (i.e., “run”) 18

19. Page 43 19

20. Slope of the Indifference Curve The MRS reflects (i)The number of tacos a consumer is willing to give up for an additional hamburger (ii)While keeping the overall utility level the same The MRS measures the curvature of indifference curve as you move along that curve Page 43 20

21. Slope of the Indifference Curve Lets assume we have two goods and an associated set of indifference curves  We can relate the MRS to the MU’s associated with consumption of these two goods Along an indifference curve we know that  ∆U = ∆Q T MU T + ∆Q H MU H = 0  → ∆Q T MU T = –∆Q H MU H  → MRS = ∆Q T ÷∆Q H = –MU H ÷MU T Page 43 Change in Utility 21 Due to being on the same indifference curve Due to being on the same indifference curve

22. Slope of the Indifference Curve Page 43 22

23. Page 43 The MRS of moving from point M and Q on I 2 equals: = (5 − 7) ÷ (2 − 1) = − 2.0 ÷ 1.0= − 2.0 23

24. Page 43 The MRS changes as one moves from on point to another  MRS M→Q ≠ MRS Q→R  What do you think happens to the MRS when going from M to Q? 24

25. Page 43 An MRS = − 2 means the consumer is willing to give up 2 tacos in exchange for 1 additional hamburger 25

26. Page 43 Which bundle would you prefer more…bundle M or bundle Q? 26

27. Page 43 The answer is that you would be indifferent as they give the same utility The ultimate choice will depend on the prices of these two products 27

28. Page 43 What about the choice between bundle M and P? 28

29. Page 43 You would prefer bundle P over bundle M because it generates more utility  Shown by being on a higher indifference curve Can you afford to buy 5 tacos and 5 hamburgers? 29

30. The Budget Constraint We can represent the weekly budget for fast food (BUD FF ) as: (P H x Q H ) + (P T x Q T )  BUD FF  P H and P T represent current price of burgers and tacos, respectively  Q H and Q T represent quantities of burgers and tacos you plan to consume during the week The budget constraint is what limits the amount that can be spent on these items Page 45 $ spent on ham. $ spent on tacos 30

31. The Budget Constraint The graph depicting this fixed amount of expenditure referred to as the budget constraint Page 45 QHQH 0 A B C Q T1 Q H1 Values on the boundary (BCA) can be represented as: BUD FF = (P H1 x Q H1 ) + (P T1 x Q T1 ) In the interior, (i.e., point D), amt. spent can be represented as: BUD FF > (P H1 x Q H1 ) + (P T1 x Q T1 ) → Not all of the budget is spent D Q H2 Q T2 QTQT 31

32. The Budget Constraint Points on the boundary of the budget constraint represent all commodity combinations whose total expenditure equals the available budget  Important Assumption: Prices do not change with the amount purchased Page 45 QHQH QTQT How can we transform the graph of the budget set shown on the left to a mathematical representation? How can we transform the graph of the budget set shown on the left to a mathematical representation? 32 $B

33. The Budget Constraint How can we determine the equation of the budget line (i.e., the boundary)?  Given the assumption of fixed prices, to determine the location of a budget in good space all we need is the Slope and Intercept on either the vertical or horizontal axis  Why do we only need the slope to identify where the $B budget curve is located in Good 1/Good 2 space? Page 45 33 Good 1 Good 2 $B budget line

34. The Budget Constraint How can we determine the equation of the budget line (i.e., the boundary)?  Remember from your calculus that the slope of a straight line is the ratio of the change in arguments of that straight line as you move along it Page 45 34 QPQP QTQT Slope at point A = ΔQ T ÷ ΔQ H as you move away from point A A

35. The Budget Constraint How can we determine the equation of the budget line (i.e., the boundary)?  Budget line represents the collection of pairs where total expenditures is $B  → movement along a budget line the change in amount spent is $0 (i.e., Δ$B = 0) ΔBUD ff = (P H x ΔQ H ) + (P T x ΔQ T ) = 0 → 0 = ( P H x ΔQ H ) + (P T x ΔQ T ) → – P H x ΔQ H = P T x ΔQ T → (–P H ÷ P T ) = (ΔQ T ÷ ΔQ H ) Page 45 Slope of budget constraint < 0, Why? QHQH QTQT Slope = ΔQ T ÷ ΔQ H 35

36. The Budget Constraint How can we determine the equation of the budget line (i.e., the boundary)?  What is the budget constraint’s slope?  Movement along a budget line means the change in amount spent is $0 ΔBUD ff = (P H x ΔQ H ) + (P T x ΔQ T ) → 0 = ( P H x ΔQ H ) + (P T x ΔQ T ) → – P H x ΔQ H = P T x ΔQ T → –(P H ÷ P T ) = (ΔQ T ÷ ΔQ H ) Page 45 Slope of budget constraint < 0 QHQH QTQT Slope = ΔQ T ÷ ΔQ H 36

37. The Budget Constraint How can we determine the equation of the budget line (i.e., the boundary)?  The equation for the budget line can be obtained via the following: BUD FF = (P H x Q H ) + (P T x Q T ) → (P T x Q T ) = BUD ff – (P H x Q H ) → Q T = (BUD FF ÷ P T ) – ((P H x Q H ) ÷ P T ) → Q T = (BUD FF ÷ P T ) – ((P H ÷ P T ) x Q H ) Page 45 This equation shows the combinations of tacos and hamburgers that equal budget BUD FF given fixed prices 37

38. The Budget Constraint Given the above we can represent the budget constraint in quantity (Q T, Q H ) space via: Page 45 QTQT QHQH Q T = (BUD FF ÷ P T ) – ((P H ÷ P T ) x Q H ) (BUD FF ÷ P T ) 0 A B 0BCA are combinations of burgers and tacos that can be purchased with $BUD FF C Line BCA are all combo’s of burgers and tacos where total expenditures = $BUD FF Q T1 Q H1 Slope of BCA = – P H ÷ P T How many hamburgers are represented by A? 38

39. Example of a Budget Constraint Point on Budget Line Tacos (P T = $0.50) Hamburgers (P H = $1.25) Total Expenditure (BUD FF ) B100$5.00 C52 A04 Page 46 Combinations representing points on budget line BCA shown below Combinations representing points on budget line BCA shown below 39

40. The Budget Constraint Given a budget of $5, P H = $1.25, P T = $0.50:  You can afford either 10 tacos, or 4 hamburgers or a combination of both as defined by the budget constraint Page 45 QTQT QHQH 0 5 10 15 20 2 4 6 8 B C A Q T = (BUD FF ÷ P T ) – ((P H ÷ P T ) x Q H ) = ($5 ÷ $0.50) – (($1.25 ÷ $0.50) x Q H ) →Q T = 10 – 2.5 x Q H →Q H = 4 – 0.4 x Q T At B, Q H = 0 At A, Q T = 0 40

41. The Budget Constraint Doubling the price of tacos to $1.00:  You can now afford either 5 tacos or 4 burgers or a combination of both as shown by new budget constraint, FA: Q T = 5 – 1.25 x Q H Q H = 4 – 0.8 x Q T  Note that the budget line pivots around point A given that the hamburger price does not change! Page 45 QTQT QHQH 0 5 10 15 20 2 4 6 8 B A F 41

42. The Budget Constraint Lets cut the original price of tacos in half to $0.25:  You can afford either 20 tacos, or 4 hamburgers or a combination of both as shown by new budget constraint, EA: Q T = 20 – 5 x Q H Q H = 4 – 0.2 x Q T Page 45 QTQT QHQH 0 5 10 15 20 2 4 6 8 B A F E 42

43. The Budget Constraint Changes in the price of burgers:  Similar to what we showed with respect to taco price  If you ↑ P H (i.e., double it), the budget constraint shifts inward with 10 tacos still being able to be purchased (BG  If you ↓ P H, (i.e., cut in half) the budget constraint shifts outward with 10 tacos still being able to be purchased Page 45 QTQT QHQH 0 5 10 15 20 2 4 6 8 B A G 43

44. The Budget Constraint What is the impact of a change in your budget (i.e., income), ceteris paribus?  Under this scenario both prices do not change  →the budget constraint slope does not change  →A parallel shifit of budget constraint depending on whether income ↑ or ↓ Page 45 QTQT QHQH 0 5 10 15 20 2 4 6 8 B A G Budget ↑ Budget ↓ 44

45. The Budget Constraint With prices fixed, why does a budget change result in a parralell budget constraint shift?  Due to the equation that defines the budget constraint: Q 2 = (BUD ÷ P 2 ) – ((P 1 ÷ P 2 ) x Q 1 ) Page 45 QTQT QHQH 0 5 10 15 20 2 4 6 8 B A G 45

46. The Budget Constraint Page 46 QTQT QHQH 0 5 10 15 20 2 4 6 8 B A G BUD reduced by 50%:  Original budget line (BA) shifts in parallel manner (same slope) to FG  Same if both prices doubled  Real income ↓ BUD doubled:  BA shifts in parallel manner (same slope) out to ED  Same if both prices cut by 50%  Real income ↑ F G E D 46

47. In Summary Consumers rank preferences based upon utility or the satisfaction derived from consumption A budget constraint limits the amount we can buy in a particular period Given a fixed budget, the amount of commodities that could be purchased are determined by their prices 47

48. Chapter 4 unites the concepts of indifference curves with the budget constraint to determine consumer equilibrium which we represent by the amount of purchases of the available commodities actually made 48