Download Presentation
## Tastes / Preferences

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Tastes/Preferences**Indifference Curves**Rationality in Economics**• Rationality Behavioral Postulate: “Rational Economic Man”The decision-maker chooses the most preferred bundle from the set of available bundles. • We must model: Set of available bundles; and The decision-maker’s preferences.**PREFERENCES**X is the bundle (x1,x2) and Y is the bundle (y1,y2) Weakly preferred Bundle X is as least as good as bundle Y (X Y) ~Indifferent Bundle X is equivalent to bundle Y (X ~ Y) Strictly preferred Bundle X is preferred to bundle Y (X > Y)**PREFERENCES: Axioms**1. Completeness {A B or B A or A ~ B} Any two bundles can be compared. 2. Reflexive {A A } Any bundle is at least as good as itself. 3. Transitivity {If A B and B C then A C} Non-satiation assumption (I.e. goods, not bads)**f**f f ~ ~ ~ Axioms • Transitivity: Ifx is at least as preferred as y, andy is at least as preferred as z, thenx is at least as preferred as z; i.e.x y and y z x z.**PREFERENCES**Intransitivity? A>B B>C C>A Starting at C Willing to pay to get to B Willing to pay to get to A Willing to pay to get to C Willing to pay to get to B … “Money Pump” Argument (I.e. proof by contradiction)**INDIFFERENCE CURVES**The indifference curve through any particular consumption bundle consists of all bundles of products that leave the consumer indifferent to the given bundle. x2 x1 x2 x3 I(x’) x1~ x2~ x3 x1**INDIFFERENCE CURVES**x2 zxy p p x z y x1**INDIFFERENCE CURVES**I1 All bundles in I1 are strictly preferred to all in I2. x2 x z I2 All bundles in I2 are strictly preferred to all in I3. y I3 x1**INDIFFERENCE CURVES**x2 WP(x), the set of bundles weakly preferred to x. x I(x’) x1**INTERSECTING INDIFFERENCE CURVES?**From I1, x ~ y From I2, x ~ z Therefore y ~ z? I2 x2 I1 x y z x1**INTERSECTING INDIFFERENCE CURVES?**But from I1 and I2 we see y > z. There is a contradiction. I2 x2 I1 x y z x1**SLOPES OF INDIFFERENCE CURVES?**• When more of a product is always preferred, the product is a good. • If every product is a good then indifference curves are negatively sloped.**SLOPES OF INDIFFERENCE CURVES?**Good 2 Two “goods” therefore a negatively sloped indifference curve. Better Worse Good 1**SLOPES OF INDIFFERENCE CURVES?**• If less of a product is always preferred then the product is a “bad”.**SLOPES OF INDIFFERENCE CURVES?**One “good” and one“bad” therefore a positively sloped indifference curve. Good 2 Better Worse Bad 1**PERFECT SUBSITIUTES**• If a consumer always regards units of products 1 and 2 as equivalent, then the products are perfect substitutes and only the total amount of the two products matters.**PERFECT SUBSITIUTES**x2 Slopes are constant at - 1. Examples? • I2 I1 x1**PERFECT COMPLEMENTS**• If a consumer always consumes products 1 and 2 in fixed proportion (e.g. one-to-one), then the products are perfectcomplements and only the number of pairs of units of the two products matters.**PERFECT COMPLEMENTS**x2 45o Example: Each of (5,5), (5,9) and (9,5) is equally preferred 9 5 I1 x1 5 9**PERFECT COMPLEMENTS**x2 Each of (5,5),(5,9) and (9,5) is less preferred than the bundle (9,9). 45o 9 I2 5 I1 x1 5 9**WELL BEHAVED PREFERENCES**• A preference relation is “well-behaved” if it is monotonic and convex. • Monotonicity: More of any product is always preferred (i.e. every product is a good, no satiation). • Convexity: Mixtures of bundles are (at least weakly) preferred to the bundles themselves. For example, the 50-50 mixture of the bundles x and y is z = (0.5)x + (0.5)y. z is at least as preferred as x or y.**WELL BEHAVED PREFERENCES**Monotonicity • more of either product is better • indifference curves have negative slopes Convexity • averages are preferred to extremes • slopes get flatter as you move further to the right (not obvious yet)**WELL BEHAVED PREFERENCES Convexity**x x2 z is strictly preferred to both x and y x+y x2+y2 z = 2 2 y y2 x1+y1 x1 y1 2**WELL BEHAVED PREFERENCES Convexity**x x2 z =(tx1+(1-t)y1, tx2+(1-t)y2) is preferred to x and y for all 0 < t < 1. y y2 x1 y1**WELL BEHAVED PREFERENCES Convexity.**Preferences are strictly convex when all mixtures z are strictly preferred to their component bundles x and y. x x2 z y y2 x1 y1**WELL BEHAVED PREFERENCES Weak Convexity**Preferences are weakly convex if at least one mixture z is equally preferred to a component bundle, e.g. perfect substitutes. x’ z’ x z y y’**NON-CONVEX PREFERENCES**x2 Better The mixture zis less preferred than x or y. Examples? z y2 x1 y1**NON CONVEX PREFERENCES**x2 Better The mixture zis less preferred than x or y z y2 x1 y1**SLOPES OF INDIFFERENCE CURVES**• The slope of an indifference curve is referred to as the marginal rate-of-substitution (MRS). • How can a MRS be calculated?**MARGINAL RATE OF SUBSITITUTION (MRS)**x2 MRS at x* is the slope of theindifference curve at x* x* x1**MRS**x2 MRS at x* is lim {Dx2/Dx1}as Dx1 0 = dx2/dx1 at x* x* Dx2 Dx1 x1**MRS**MRS is the amount of product 2 an individual is willing to exchange for an extra unit of product 1 x2 x* dx2 dx1 x1**MRS**Two “goods”have a negatively sloped indifference curve Good 2 Better MRS < 0 Worse Good 1**MRS**Good 2 One “good” and one“bad” therefore a positively sloped indifference curve Better MRS > 0 Worse Bad 1**MRS**MRS decreases (in absolute terms) as x1 increases if and only if preferences are strictly convex. Intuition? Good 2 MRS = (-) 5 MRS = (-) 0.5 Good 1**MRS**x2 If MRS increases (in absolute terms) as x1 increases non-convex preferences MRS = (-) 0.5 MRS = (-) 5 x1**MRS**MRS is not always decreasing as x1 increases - non- convex preferences. x2 MRS = - 1 MRS= - 0.5 MRS = - 2 x1