Theory of Consumer Behavior Chapter 3

Discussion Topics Utility theory Indifference curves The budget constraint 2

The Utility Function Utility: Level of satisfaction obtained from consuming a particular bundle of goods and services Utility function: an algebraic expression that allows one to rank consumption bundles with respect to satisfaction level A simple example: Total utility = Qhamburgers x Qpizza Page 39-40 3

The Utility Function A 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 Given our use of the above functional notation This approach assumes that ones utility is cardinally measurable In the same sense that a ruler measures distance You can tell if one bundle of goods gives you twice as much satisfaction (i.e., utils) Page 40 5

The Utility Function Ordinal versus cardinal ranking of choices Cardinally measurable: Can quantify how much utility is impacted by consumption choices i.e., Commodity bundle X provides 3 times the utility than bundle Y Ordinally measurable: Can only provide a relative ranking of choices i.e., Commodity bundle X provides more utility than bundle Y Page 40 6

Quantity of Hamburgers Ranking Total Utility Bundle Quantity of Hamburgers Quantity of Pizza Total Utility A 2.5 10.0 25 B 3.0 7.0 21 C 2.0 12.5 Ranking of consumption bundles 7

Quantity of Hamburgers Ranking Total Utility Bundle Quantity of Hamburgers Quantity of Pizza Total Utility A 2.5 10.0 25 B 3.0 7.0 21 C 2.0 12.5 Prefer A and C over B Indifferent between A and C 8

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 MUH = utility ÷ QH MU will ↓ as consumption ↑ Marginal benefit of last unit consumed ↓ ↑ as consumption ↓ Marginal benefit of last unit consumed ↑ Page 40-41 9

Marginal Utility = (47-39) ÷ (4-3) Page 40-41 QH/week Total Utility MU 20 ---- 2 30 10 3 39 9 4 47 8 5 54 7 6 60 65 69 72 74 11 12 70 -4 = (47-39) ÷ (4-3) 10 Page 40-41

the total utility curve 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 Marginal Utility Note: The other good, i.e. pizza, remains unchanged 11 Page 42

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? We can instead use an ordinal measurement of utility All we need to know is that one consumption bundle is preferred over another Page 41-43 12

Indifference Curves Modern consumption theory is based upon the notion of isoutility curves iso is the Greek meaning equal A 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 Page 41-43 13

Page 43 Bundles N, P preferred to bundles M, Q and R The further from the origin the greater the utility Bundles N, P preferred to bundles M, Q and R Indifferent between bundles N and P Increasing utility Page 43 14

thought of as providing 200 and 700 utils of utility. 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 15

Theoretically there are an infinite (large) number of isoutility or indifference curves Page 43 16

Slope of the Indifference Curve Like any other curve one can evaluate the slope of each indifference curve Given a special name Marginal Rate of Substitution (MRS) Given the above graph the MRS of substitution of hamburgers for tacos is calculated as: MRS = QT ÷ QH Change in quantity of tacos Change in quantity of hamburgers 17 Page 43

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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 → movement along an indifference curve Page 43 19

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 ∆U = ∆QTMUT + ∆QHMUH = 0 → ∆QTMUT = –∆QHMUH → MRS=∆QT÷∆QH = –MUH ÷MUT Change in Utility Page 43 20

Slope of the Indifference Curve Page 43 21

The MRS between points M and Q on I2 is equal to: = (5-7)-(2-1) = -2.0 ÷ 1.0= -2.0 Page 43 22

An MRS = -2 means the consumer is willing to give up 2 tacos in exchange for one additional hamburger Page 43 23

Which bundle would you prefer more…bundle M or bundle Q? Page 43 24

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 Page 43 25

What about the choice between bundle M and P? Page 43 26

You would prefer bundle P over bundle M because it gives us more utility Shown by being on a higher indifference curve Can you afford to buy 5 tacos and 5 hamburgers? Page 43 27

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 hamburgers and tacos, respectively QH and QT represent quantities 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 Page 45 28

The Budget Constraint The graph depicting this constraint is 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, point D,values can be represented as: BUDFF > (PH1 x QH1) + (PT1 x QT1) →Not all of the budget is spent B C QT1 D QT2 QH QH1 QH2 A Page 45 29

The Budget Constraint In other words, points on the boundary represent all commodity combinations whose total expenditure equals the available budget Important Assumption: All prices do not change QT How can we transform the graph of the budget set shown on the left to a mathematical representation? Page 45 QH 30

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 31

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) Equation that shows the combinations of tacos and hamburgers that equal budget BUDFF given fixed prices Page 45 32

QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH) 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 hamburgers and tacos that can be purchased with $BUDFF Slope of BCA = – PH ÷ PT B QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH) C QT1 BCA are all combo’s of hamburgers and tacos where total expenditures = $BUDFF QH QH1 A Page 45 33

Example of a Budget Constraint Point on Budget Line Tacos (PT = $0.50) Hamburgers (PH = $1.25) Total Expenditure (BUDFF) B 10 $5.00 C 5 2 A 4 Combinations representing points on budget line BCA shown below Page 46 34

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 equation 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 Page 45 2 4 6 8 35

The Budget Constraint Doubling the price of tacos to $1.00: You can afford either 5 tacos, or 4 hamburgers 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 Page 45 2 4 6 8 36

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 Page 45 2 4 6 8 37

The Budget Constraint Changes in the price of hamburgers: 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 inward with 10 tacos still being able to be purchased QT 20 15 B 10 5 A QH Page 45 G 2 4 6 8 38

The Budget Constraint What is the impact of a change in your budget (i.e., income)? 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 Page 45 G 2 4 6 8 39

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 Page 45 G 2 4 6 8 40

The Budget Constraint 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 ↑ QT E 20 15 B 10 F 5 G A D QH Page 46 G 2 4 6 8 41

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 42

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