1. Theory of Consumer Behavior
Chapter 3

2. Discussion Topics Utility theory Indifference curves
The budget constraint 2

3. 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

4. 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

5. 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

6. 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

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
Ranking of consumption bundles 7

8. 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

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
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

10. Marginal Utility = (47-39) ÷ (4-3) Page 40-41 QH/week Total Utility MU20
---- 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

11. 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

12. 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

13. 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

14. 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

15. 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

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

17. 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

18. Page 43 18

19. 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

20. 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

21. Slope of the Indifference Curve
Page 43 21

22. 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

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

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

25. 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

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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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