Chapter 3- Preferences

Question 1

Assumptions about preferences: Completeness

Answer 1

Any two bundles can be compared

X1, X2) > (Y1,Y2

Question 2

Reflexivity

Answer 2

Any bundle is at least as good as itself

X1,X2) >~(X1, X2

Question 3

Transitivity

Answer 3

If (X1, X2) >~ (Y1, Y2) and (Y1, Y2) >~ (Z1, Z2) then (X1, X2) >~ (Z1, Z2)

Question 4

Perfect substitutes

Answer 4

Two goods are perfect substitutes if the consumer is willing to substitutes one good for the other at a constant rate.

Linear indifference curves

Ex. Slope =-2, (must be given 2 units of good 2 in order to give up one unit of good 1

Question 5

Perfect compliments

Answer 5

Goods that are always consumed together in fixed proportions

L-shaped indifference curves because adding one extra unit of one good does not increase utility. With the vertex of the L occurring where the number of good 1 and 2 are equal (in a 1 to 1 proportion I.e left and right shoes)

Weakly monotonic ( moving up and to the right does not mean we are strictly better off)

Question 6

Bads

Answer 6

A bad is a commodity that the consumer doesn’t like. For example if the pepperoni and anchovies, there may be some amount of pepperoni that makes up for having to consume anchovies. And in order to make this compromise the increase in pepperoni must be greater than the increase in anchovies.

This upward sloping indifference curves />/ utility increase down and to the right because that symbolizes decreasing anchovies and increasing pepperoni

Question 7

Neutrals

Answer 7

Neutrals are goods the consumer doesn’t care about.

Indifference curves are vertical lines. A consumer who is neutral about anchovies doesn’t care whether they decrease or increase they only care about the pepperoni, utility increase to the right (I > I > I)

Question 8

Satiation

Answer 8

Where there is some overall best bundle for the consumer, and the “closer” he is to that best bundle the better off he is in terms of his own preferences.

Bliss point.

Question 9

Discrete good

Answer 9

A good that is only available in integer amounts

Indifference curve looks like a set of discrete points . The set of bundles at least as good as a given bundle will be a set of line segments

Question 10

Monotonicity

Answer 10

“More is better”

If bundle x is a bundle with at least as much of both goods in bundle y, and more of one then bundle x is strictly preferred to y

Monotony city implies that the slope of indifference curves will be negative because you have to move down and to the left or up and to the right to remain indifferent ( change in goods moves in the opposite direction)

Question 11

Averages are preferred to extremes

Answer 11

The average bundle will be at least as good or strictly prefers to the two extreme bundles

For any weight τ between 0 and 1 we assume:
(τX1 + (1-τ)Y1, τX2 +(1-τ)Y2) >~ (X1, X2)

Question 12

Marginal rate of substitution:

Answer 12

Rate at which the consumer is just willing to trade substitute one good for another and remain equally happy.

The slope of the indifference curve

MUx/ MUy

MRS=2/1 ( I would have to revive 2 units of good y in order to give up 1 unit of good x… Or I would give up 2 units of y to get 1 unit of x)

Question 13

Concave indifference curves

Answer 13

With concave indifference curves you typically want to consume at the extremes because if you take the middle point you will be worse off so to the concavity

Question 14

Convex indifference curves

Answer 14

A convex set has the property that if you take any two pins in the set and draw a line connecting the two points the line segment lies entirely in the set. (Averages preferred to extremes)

Question 15

Strictly convex indifference curves

Answer 15

The weighted a average of the two indifferent bundles is strictly preferred to the two extreme bundles.

Must have indifference curves that are rounded

Question 16

Weakly convex

Answer 16

Preferences may have flat spots

Question 17

Behavior if MRS in:

• perfect Substitutes
• perfect Compliments
• Neutrals

Answer 17

Perfect substitutes: MRS is constant at -1 (

perfect compliments: MRS is either zero or infinity, and nothing in between

neutrals: MRS is infinity everywhere ( because since you don’t care about the good you will give up infinite amounts of it)

Question 18

Diminishing marginal rate of substitution

Answer 18

The slope of convex indifference curves decreases (absolute value) as we increase the amount of X1.

The amount of good 1 that a person is willing to give up for good 2 increases the the higher amount of good 1 you have.

Can also be thought of as the more x you have the less y you need to be compensated for giving up some x

If you have a million apples and 2 bananas you’re willing to give up a lot more apples in order to get another banana than if you had less apples.

Or if you have a million apples and a little bananas, it only takes a small quantity of bananas to convince you to give up some apples.

Question 19

Consumption bundle

Answer 19

Are lists of goods and service that the consumer makes a choice about how much to consume.

Example: consumes 2 apples and 5 bananas:
(Xa, Xb) is (2,5)