Consumer Choice Indifference Curve Theory Lecture 3 Consumer Choice Indifference Curve Theory

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

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

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?

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

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

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

y MONOTINICTY Preferred to A • A Less preferred x

y MONOTINICITY Preferred to A • A Less preferred IC1 x

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

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).

• • • 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

• • • 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

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

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

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.

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?

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

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.

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?

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

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…

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

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.

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

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.

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

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

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

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

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

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