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Theory of Consumer Behavior

Theory of Consumer Behavior. Chapter 3. 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. The Utility Function.

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Theory of Consumer Behavior

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  1. Theory ofConsumerBehavior 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 = Qhamburgers x Qpizza 3 Page 39-40

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

  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) 5 Page 40

  6. The Utility Function • Ordinalvs. Cardinalranking 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 • Ordinallymeasurable: You can only provide a relative ranking of choices • Commodity bundle X provides more utility than bundle Y • Don’t know how much more 6 Page 40

  7. Ranking Total Utility 7

  8. Ranking Total Utility 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 • MUi= Utility ÷ Qi • 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 ↑ • ∆ means “change in” • iidentifies a good • (i.e. the ith good) 9 Page 40-41

  10. Marginal Utility Total Utility =f(QH, QP)QH = quantity of hamburgersQP = quantity of pizza ∆QH ∆U = (47-39) ÷ (4-3) 10 Page 40-41

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

  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” 12 Page 41-43

  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 13 Page 41-43

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

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

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

  17. Theoretically there are an infinite (large) number of isoutility or indifference curves Page 43 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 = QT÷ QH Change in quantity of hamburgers (i.e., “run”) Change in quantity of tacos (i.e., “rise”) 18 Page 43

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

  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 = ∆QTMUT + ∆QHMUH = 0 • → ∆QTMUT = –∆QHMUH • → MRS = ∆QT÷∆QH = –MUH ÷MUT Due to being on the same indifference curve Change in Utility 21 Page 43

  22. Slope of the Indifference Curve Page 43 22

  23. The MRS of moving from point M and Q on I2equals: = (5 − 7) ÷ (2 − 1) = − 2.0 ÷ 1.0= − 2.0 Page 43 23

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

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

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

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

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

  29. 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 Page 43

  30. The Budget Constraint • We can represent the weekly budget for fast food (BUDFF) as: (PH x QH) + (PT x QT)  BUDFF • PH and PT represent current price of burgers and tacos, respectively • QH and QTrepresent 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 $ spent on ham. $ spent on tacos 30 Page 45

  31. The Budget Constraint • The graph depicting this fixed amount of expenditure referred to as the budget constraint QT Values on the boundary (BCA) can be represented as: BUDFF= (PH1 x QH1) + (PT1 x QT1) In the interior, (i.e., point D) , amt. spent can be represented as: BUDFF> (PH1 x QH1) + (PT1 x QT1) → Not all of the budget is spent B C QT1 D QT2 QH 0 QH1 QH2 A 31 Page 45

  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 QT How can we transform the graph of the budget set shown on the left to a mathematical representation? $B QH Page 45 32

  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? Good 2 $B budget line Page 45 33 Good 1

  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 QT Slope at point A =ΔQT÷ΔQH as you move away from point A A • QP Page 45 34

  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 alonga budget line the change in amount spent is $0 (i.e., Δ$B = 0) • ΔBUDff = (PH x ΔQH) + (PT x ΔQT) = 0 • → 0 = (PH x ΔQH)+ (PT x ΔQT) • → –PH x ΔQH = PT x ΔQT • → (–PH÷ PT) = (ΔQT÷ΔQH) QT Slope = ΔQT÷ ΔQH Slope of budget constraint < 0, Why? QH Page 45 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 • ΔBUDff = (PH x ΔQH) + (PT x ΔQT) • → 0 = (PH x ΔQH)+ (PT x ΔQT) • → –PH x ΔQH = PT x ΔQT • → –(PH÷ PT) = (ΔQT÷ΔQH) QT Slope = ΔQT÷ ΔQH Slope of budget constraint < 0 QH Page 45 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: • BUDFF = (PH x QH) + (PT x QT) • → (PT x QT) = BUDff – (PH x QH) • → QT = (BUDFF ÷ PT ) – ((PH x QH) ÷ PT ) • → QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH) This equation shows the combinations of tacos and hamburgers that equal budget BUDFF given fixed prices Page 45 37

  38. The Budget Constraint • Given the above we can represent the budget constraint in quantity (QT, QH) space via: How many hamburgers are represented by A? QT (BUDFF ÷ PT) 0BCA are combinations of burgers and tacos that can be purchased with $BUDFF Slope of BCA = – PH ÷ PT B • QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH) C QT1 Line BCA are all combo’s of burgers and tacos where total expenditures = $BUDFF QH 0 QH1 A Page 45 38

  39. Example of a Budget Constraint Combinations representing points on budget line BCA shown below 39 Page 46

  40. The Budget Constraint • Given a budget of $5, PH = $1.25, PT = $0.50: • You can afford either 10 tacos, or 4 hamburgers or a combination of both as defined by the budget constraint QT 20 15 • QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH) • = ($5 ÷ $0.50) – (($1.25 ÷ $0.50) x QH) • →QT = 10 – 2.5 x QH • →QH = 4 – 0.4 x QT B 10 C At B, QH = 0 At A, QT = 0 5 A QH 0 6 2 8 4 Page 45 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: QT = 5 – 1.25 x QH QH = 4 – 0.8 x QT • Note that the budget line pivots around point A given that the hamburger price does not change! QT 20 15 B 10 F 5 A QH 0 6 2 8 4 41 Page 45

  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: QT = 20 – 5 x QH QH = 4 – 0.2 x QT QT E 20 15 B 10 F 5 A QH 0 6 2 8 4 42 Page 45

  43. The Budget Constraint • Changes in the price of burgers: • Similar to what we showed with respect to taco price • If you ↑ PH (i.e., double it), the budget constraint shifts inward with 10 tacos still being able to be purchased (BG • If you ↓ PH, (i.e., cut in half) the budget constraint shifts outward with 10 tacos still being able to be purchased QT 20 15 B 10 5 A QH 0 Page 45 G 6 2 8 4 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 ↓ QT 20 15 B 10 Budget ↑ Budget ↓ 5 A QH 0 Page 45 G 6 2 8 4 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: Q2 = (BUD ÷ P2 ) – ((P1÷ P2) x Q1) QT 20 15 B 10 5 A QH 0 Page 45 G 6 2 8 4 45

  46. The Budget Constraint • BUDreduced by 50%: • Original budget line (BA) shifts in parallel manner (same slope) to FG • Same if both prices doubled • Real income ↓ • BUDdoubled: • BA shifts in parallel manner (same slope) out to ED • Same if both prices cut by 50% • Real income ↑ QT E 20 15 B 10 F 5 A D G QH 0 Page 46 G 6 2 8 4 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 whichwe represent by the amount of purchases of the available commodities actually made 48

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