1. Consumer Choice Indifference Curve Theory
Lecture 3
Consumer Choice
Indifference Curve Theory

2. Outline Indifference Curve Theory Deriving an indifference curve
The Marginal rate of substitution
The Indifference Map
What happens when things change
Changes in Income
Changes in price
Derivation of the consumer’s demand curve

3. Preferences (Recap) An individual
can compare any two options and decide which is best, or if equally attractive
Makes choices that are logically consistent
Rational preferences (1&2)
Prefers more of a good to less

4. An Indifference Curve Graphical Illustration of IC Point G (20M, 1C)
Assuming we give Kofi another concert. How many movies would we have to take away in order to leave him as satisfied as point G?
Point H (11M, 2C)
Kofi indifferent between point G and point H
Other points of indifference?

5. Indifference Curve Figure A.1 An Indifference Curve Number of Movies
per Month
Number of Concerts +1
If Kofi gets another concert… G 20 1 -9
he could give up 9 movies
and be just as satisfied H 11 2 J 6 3 K 4 4 L 3 5

6. Indifference Curve
An IC represents all combinations of two goods that make a consumer equally well off.
An indifference map is a set of ICs showing the _preferences of an individual
An Indifference Map is a set of Indifference Curves that describe Kofi’s preferences
Complete characterization of one’s preferences

7. PROPERTIES OF INDIFFERENCE MAPS
Completeness
Each basket lies on only one indifference curve
Monotonicity
Indifference curves have negative slope
Indifference curves are not “thick”

8. y
MONOTINICTY
Preferred to A • A
Less
preferred x

9. y
MONOTINICITY
Preferred to A • A
Less
preferred
IC1 x

10. y
Indifference Curves are NOT Thick B • • A
IC1 x

11. PROPERTIES OF INDIFFERENCE MAPS
3. Transitivity
Indifference curves do not cross
4. Averages preferred to extremes
Indifference curves are bowed toward the origin (convex to the origin).

12. • • • INDIFFERENCE CURVES CANNOT CROSS y
Suppose a consumer is indifferent between A and C
Suppose that B preferred to A.
IC1 • B • A C • x

13. • • • y INDIFFERENCE CURVES CANNOT CROSS
It cannot be the case that an IC contains both B and C
Why? because, by definition of IC the consumer is:
Indifferent between A & C
Indifferent between B & C
Hence he should be indifferent between A & B (by transitivity).
=> Contradiction.
IC2
IC1 • B • A C • x

14. The Marginal Rate of Substitution
Absolute value of IC Slope
Maximum number of movies that Kofi willing to trade for one additional concert
E.g. At G, greatest number of movies Kofi would sacrifice for an extra concert is 9
The MRS tells us the maximum amount of good y (movies) that a consumer would willingly trade for one more unit of good x (concerts)
When the quantity of good y is measured on the vertical axis and the quantity of good x is measured on the horizontal axis

15. The Marginal Rate of Substitution
If he was to give up10 movies for one concert, he would have been worse off and would not be willing to make that trade
The technical term for Kofi’s ‘willingness to trade’ is marginal rate of substitution of movies for concerts
The marginal rate of substitution of good y for good x (MRSy,x) along any segment of an indifference curve is the maximum rate at which a consumer would willingly trade of y for units of x
As we move down the IC, the MRS gets smaller
The number of movies Kofi is willing to give away for an additional concert gets smaller and smaller
- Illustrate with diagram

16. Starting from G(20m,1c) all the way to L(3m,5concerts)
Starting from G(20m,1c) all the way to L(3m,5concerts). Since Kofi ends up on the same IC, it implies he is willing to make that move
He is willing to give 17movies to get 4 more concerts so his MRS would be 17/4=4.5 . We could say Kofi is giving up 4.5 movies per concert.
The slope of the(imaginary) line joining points G and L which is also 4.5 is a graphical representation of the MRS of that segment of the IC
The value of the MRS depends on the size of the move
For a smaller move from G to J, Kofi is willing to give up 14 movies to get 2 more concerts. The MRS is now 14/2=7. The MRS here will be the slope between the line joining these two points.

17. How MRS is Changing along the IC
Notice that as we move downward and rightward, the IC gets flatter ie the absolute value of the slope decreases.
Ie. As we move down an IC, the MRS(the number of movies Kofi is willing to trade for another concert)gets smaller and smaller.
Why?

18. Diminishing Marginal Rate of Substitution
MRSm,c (slope of IC) relatively large at G
At G, Kofi has many movies and value them lowly
Willing to give movies away for additional concerts
MRSm,c (slope of IC) relatively small at L
At this point, Kofi has fewer movies and values them more highly.
Therefore, less willing to give movies away for additional concerts

19. An Indifference Map Figure A.2 An Indifference Map Number of Movies
per Month
Number of Concerts G 20 J 6 1 3 2 H 11 R S
1.Max prefers any point on
this indifference curve…
3.And any point on this curve
is preferred to any point on
the other two.
2.to any point
on this one.

20. The Indifference Map
Any point on a higher IC is preferred to any point below it- How do we know?
Consider points H and S
H has more movies but fewer concerts
S has more concerts but fewer movies
Why, then, is S preferred to H?

21. Consumer Decision-Making
At optimal point,
slope of IC= slope of budget line
Slope of IC
Rate at which Kofi would willingly trade movies for concerts
Slope of BL
Rate at which Kofi is actually able to trade movies for concerts
Graphical Illustration

22. Consumer Decision Making
Figure A.3 Consumer Decision Making with Indifference Curves 15 12 9 6 3 1 2 4 5
Number of
Movies
per Month
Number of Concerts D
2. but point D (also affordable) is preferred because it is on a higher indifference curve. B E
1. Points B and E
are affordable…

23. Consumer Decision-Making
At D,
Slope of IC = slope of BL = 3
Rate at which Kofi is willing to trade movies for an additional concert is equal to rate at which he is able to trade movies for an additional concert

24. Changes in Income Income rises
Normal good - quantity demanded increases
Inferior good - quantity demanded decreases
Depends on the individual’s preferences, as represented by his indifference map.

25. What happens when things change? Changes in Income
If Kofi’s income increases to Ghc 300
BL shifts outwards
Kofi will shift downwards along his BL until he is tangent with highest IC

26. Changes in Income Figure A.4 An Increase in Income 3
Number of Concerts
per Month 15 6 5
Number of
Movies 30 D
1. When Kofi’s income rises to $300,
his budget line shifts outward. 10
H’’ H’
3.But different preferences
could lead him to other
points like H’ or H’’ 12 6 H
2.If his preferences are shown by
these two indifference curves,
he'll choose point H.

27. Income-Consumption Line
For each level of income, there is an equilibrium position where IC is tangent to BL
Joining up these points of equilibrium, we derive an individual’s income-consumption line
Shows how consumption bundle changes as income changes, holding prices constant
Graphical illustration

28. What happens when things change? Changes in Price
If Price of concerts decreases from Ghc30 to Ghc10
BL rotates

29. Derive the demand curve
Additional decreases in the price of concerts leads to continuous rotation of the budget line
(Graphical Illustration)

30. Appendix: Deriving the Demand Curve
Figure A.5 Deriving the Demand Curve
1.When the price of concerts is $30, MRSm,c=Pc/Pm
at point D. 15 6 3 5 30 10 8 7
Number of Movies per Month
2. But when the price falls to $10, this condition is satisfied at point J. K D J D
Price per Concert
$30 10 5 3 7
Number of Concerts per Month
3. The demand curve shows the quantity Max chooses at each price. J K

31. Price-Consumption line
Change in price of a good changes the slope of the budget line, holding price of other good constant
There is an equilibrium consumption bundle for each price of the goods
Joining up these equilibriums gives the price-consumption line
Line showing how a consumer’s purchases reacts to changes in price of one good, holding other price and income constant

32. Next Class Income and substitution effects
Individual and market demand
Wrap up