Theory of Consumer Behavior Chapter 3
Discussion Topics üUtility theory üIndifference curves üThe budget constraint 2
The Utility Function ü Utility: Level of satisfaction obtained from consuming a particular bundle of goods and services ü Utility function: 3 an algebraic expression that allows one to rank consumption bundles with respect to satisfaction level • A simple example: Page 39 -40 Total utility = Q x. Q
The Utility Function üA more general representation of a utility function without specifying a specific functional form: Total Utility =f(Qhamburgers, Qpizza) General function operator Page 40 4
The Utility Function ü Given our use of the above functional notation ØThis approach assumes that ones utility is cardinally measurable § In the same sense that a ruler measures distance ØYou can tell if one bundle of goods gives you twice as much satisfaction (i. e. , utils) Page 40 5
The Utility Function ü Ordinal versus cardinal ranking of choices Ø Cardinally measurable: Can quantify how much utility is impacted by consumption choices Ø i. e. , Commodity bundle X provides 3 times the utility than bundle Y Ø Ordinally measurable: Can only provide a relative ranking of choices § i. e. , Commodity bundle X provides more utility than bundle Y Page 40 6
Ranking Total Utility Bundle A Quantity of Hamburgers Pizza Total Utility 2. 5 10. 0 25 B 3. 0 7. 0 21 C 2. 0 12. 5 25 Ranking of consumption bundles 7
Ranking Total Utility Bundle A Quantity of Hamburgers Pizza Total Utility 2. 5 10. 0 25 B 3. 0 7. 0 21 C 2. 0 12. 5 25 Prefer A and C over B Indifferent between A and C 8
Marginal Utility ü 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 ØMUH = utility ÷ QH ü MU will Ø↓ as consumption ↑ § Marginal benefit of last unit consumed ↓ Ø↑ as consumption ↓ ØMarginal benefit of last unit consumed ↑ Page 40 -41 9
Marginal Utility QH/week MU 1 20 ---- 2 30 10 3 39 9 4 47 8 5 54 7 6 60 6 7 65 5 8 69 4 9 72 3 10 74 2 11 74 0 12 10 Total Utility 70 -4 = (47 -39) ÷ (4 -3) Page 40 -41
Total Utility Marginal Utility Note: MU is the slope of the utility function, ΔU÷ΔQH Marginal utility goes to zero at the peak of the total utility curve Note: The other good, i. e. pizza, remains unchanged 11 Page 42
Indifference Curves üCardinal measurement of utility is both unreasonable and unnecessary Ø i. e. , what is the correct functional form of the relationship between utility and goods consumed? üWe can instead use an ordinal measurement of utility Ø All we need to know is that one consumption bundle is preferred over another Page 41 -43 12
Indifference Curves üModern consumption theory is based upon the notion of isoutility curves Øiso is the Greek meaning equal ØA collection of those bundles of goods and services where the consumer’s utility is the same § The consumer is referred to being as 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 13 Page 41 -43
The further from the origin the greater the utility ü Bundles N, P preferred to bundles M, Q and R ü Indifferent between bundles N and P Increasing utility Page 43 14
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 15 Page 43
Theoretically there an infinite (large) number of isoutility or indifference curves 16 Page 43
Slope of the Indifference Curve ü Like any other curve one can evaluate the slope of each indifference curve ü Given a special name Ø Marginal Rate of Substitution (MRS) ü Given the above graph the MRS of substitution of hamburgers for tacos is calculated as: MRS = QT ÷ QH Change in quantity of tacos 17 Change in quantity of hamburgers Page 43
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Slope of the Indifference Curve ü The MRS reflects Ø The number of tacos a consumer is willing to give up for an additional hamburger Ø While keeping the overall utility level the same § → movement along an indifference curve Page 43 19
Slope of the Indifference Curve ü Lets assume we have two goods and an associated set of indifference curves Ø We can relate the MRS to the MU’s associated with consumption of these two goods ü Along an indifference curve Change Ø ∆U = ∆QTMUT + ∆QHMUH = 0 in Utility 20 Ø → ∆QTMUT = –∆QHMUH Ø → MRS=∆QT÷∆QH = –MUH ÷MUT Page 43
Slope of the Indifference Curve 21 Page 43
The MRS between points M and Q on I 2 is equal to: = (5 -7)-(2 -1) = -2. 0 ÷ 1. 0= -2. 0 22 Page 43
An MRS = -2 means the consumer is willing to give up 2 tacos in exchange for one additional hamburger 23 Page 43
Which bundle would you prefer more…bundle M or bundle Q? Page 43 24
ü The answer is that you would be indifferent as they give the same utility ü The ultimate choice will depend on the prices of these two products Page 43 25
What about the choice between bundle M and P? Page 43 26
ü You would prefer bundle P ü over bundle M because it gives us more utility Ø Shown by being on a higher indifference curve Can you afford to buy 5 tacos and 5 hamburgers? Page 43 27
The Budget Constraint üWe can represent the weekly budget for fast food (BUDFF) as: (PH x QH) + (PT x QT) BUDFF $ spent on ham. $ spent on tacos Ø PH and PT represent current price of hamburgers and tacos, respectively Ø QH and QT represent quantities you plan to consume during the week üThe budget constraint is what limits the amount that can be spent on these items Page 45 28
The Budget Constraint ü The graph depicting this constraint is referred to as the budget constraint QT Values on the boundary (BCA) can be represented as: BUDFF = (PH 1 x QH 1) + (PT 1 x QT 1) B QT 1 C QT 2 0 29 D QH 1 QH 2 In the interior, point D, values can be represented as: BUDFF > (PH 1 x QH 1) + (PT 1 x QT 1) →Not all of the budget is spent QH A Page 45
The Budget Constraint ü In other words, points on the boundary represent all commodity combinations whose total expenditure equals the available budget QT ØImportant Assumption: All prices do not change How can we transform the graph of the budget shown on the left to a mathematical representation? 30 QH Page 45
The Budget Constraint üHow can we determine the equation of the budget line (i. e. , the boundary)? Ø What is the budget constraint’s slope? Ø 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) Q Slope = ΔQT÷ ΔQH → –PH x ΔQH = PT x ΔQT → –(PH ÷ PT) = (ΔQT÷ ΔQH) T Slope of budget constraint < 0 31 QH Page 45
The Budget Constraint üHow can we determine the equation of the budget line (i. e. , the boundary)? Ø 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) Equation that shows the combinations of tacos and hamburgers that equal budget BUDFF given fixed prices 32 Page 45
The Budget Constraint üGiven the above we can represent the budget constraint in quantity (QT, QH) space via: QT 0 BCA are combinations of hamburgers and tacos that can be B purchased with $BUDFF QT 1 (BUDFF ÷ PT) How many hamburgers are represented by A? Slope of BCA = – PH ÷ PT C QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH) BCA are all combo’s of hamburgers and tacos where total expenditures = $BUDFF 0 33 QH 1 A QH Page 45
Example of a Budget Constraint Point on Budget Line B C Tacos (PT = $0. 50) 10 5 A 0 Hamburgers Total (PH = Expenditure $1. 25) (BUDFF) 0 $5. 00 2 $5. 00 4 Combinations representing points on budget line BCA shown below 34 $5. 00 Page 46
The Budget Constraint ü Given a budget of $5, PH = $1. 25, QT 20 PT=$0. 50: ØYou can afford either 10 tacos, or 4 hamburgers or a combination of both as defined by the budget constraint equation 15 B 10 C 5 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 At B, QH=0 At A, QT=0 A 0 35 2 4 6 8 QH Page 45
The Budget Constraint ü Doubling the price of tacos to $1. 00: ØYou can afford either 5 tacos, or 4 hamburgers or a combination of both as shown by new budget constraint, FA: QT 20 QT = 5 – 1. 25 x QH QH = 4 – 0. 8 x QT 15 ØNote that the budget line pivots around point A given that the hamburger price does not change! B 10 F 5 A 0 36 2 4 6 8 QH Page 45
The Budget Constraint ü Lets cut the original price of tacos in half to $0. 25: QT ØYou can afford either 20 tacos, or 4 hamburgers or a combination of both as shown by new budget constraint, EA: E 20 15 QT = 20 – 5 x QH QH = 4 – 0. 2 x QT B 10 F 5 A 0 37 2 4 6 8 QH Page 45
The Budget Constraint ü Changes in the price of hamburgers: ØSimilar to what we showed with respect to taco price ØIf you ↑ PH (i. e. , double it), the budget constraint shifts inward with 10 tacos still being able to be purchased (BG ØIf you ↓ PH, (i. e. , cut in half) the budget constraint shifts inward with 10 tacos still being able to be purchased QT 20 15 B 10 5 A 0 38 G 2 4 6 8 QH Page 45
The Budget Constraint ü What is the impact of a change in your budget (i. e. , income)? QT ØUnder this scenario both prices do not change 20 § →the budget constraint slope does not change 15 Ø→A parallel shifit of budget constraint depending on whether income ↑ or ↓ B 10 Budget ↑ Budget ↓ 5 A 0 39 G 2 4 6 8 QH Page 45
The Budget Constraint ü With prices fixed, why does a budget change result in a parralell budget constraint shift? QT 20 ØDue to the equation that defines the budget constraint: 15 Q 2 = (BUD ÷ P 2 ) – ((P 1÷ P 2) x Q 1) B 10 5 A 0 40 G 2 4 6 8 QH Page 45
The Budget Constraint ü BUD reduced by 50%: ØOriginal budget line (BA) shifts in parallel manner (same slope) to FG ØSame if both prices doubled ØReal income ↓ ü BUD doubled: ØBA shifts in parallel manner (same slope) out to ED ØSame if both prices cut by 50% ØReal income ↑ QT E 20 15 B 10 F 5 0 41 A G G 2 4 D 6 8 QH Page 46
In Summary üConsumers rank preferences based upon utility or the satisfaction derived from consumption üA budget constraint limits the amount we can buy in a particular period • 42 Given a fixed budget, the amount of commodities that could be purchased are determined by their prices
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 43
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