Microeconomic Theory- Preferences (Chapter 3 notes)

What is a preference of a commodity?

This is the commodity you want more- not the one you need more or wish for because it is picked out of feasible options

What is the notation for a strict preference?

≻ (not greater than symbol- strict preference)

x ≻ y (x is strictly preferred to y)

What is the notation for indifference?

~ (i.e. x ~ y ) (x is exactly as preferred as y)

What is the notation for weak preference?

≿ (i. e. x ≿ y)(x is at least as preferred as y)

What is the completeness assumption about preference relations?

For any two bundles x and y it is always possible to make the statement that either x ≻ y or x ≿ y

What is the reflexivity assumption about preference relations?

Any Bundle is exactly as good as itself x~x

What is the transitivity assumption about preference relations?

If x ≿ y and y ≿ z, then x ≿ z

What is an indifference curve?

Collections of bundles which are equally preferred

What is another assumption about indifference curves in terms of the amount of commodities

Regardless of preferences, we always assume that more is better when it comes to indifference curves.

Why can’t indifference curves intersect?

This would violate the transitivity assumption, if the curves intersect then this would mean that the intersecting point is no longer preferred to the points on either line. Indifference curves must maintain their ratios and once the ratio is thrown off, that bundle no longer has an indifferent preference relationship.

Indifference curves with two goods are — sloped

negatively sloped, because when you have less of one good, you’ll want more of the other good. Meaning that they have a negative relationship, while one is increasing the other is decreasing.

Indifference curves with one good and one bad are —- sloped

positively sloped because you’ll always want more of the good if you happen to have more of the bad. the Trade off being that you are willing to have a certain amount of bad if you receive a certain amount of good in return. You’ll feel indifferent if you have 5 pizzas but 10 trash bags in your living room- theoritically.

What does a graph showing perfect substitutes of two goods appear as?

When commodities 1 and 2 are equivalent then they are considered perfect substitutes. The graph is linear because the MRS is constant, it doesn’t change because the substitutes are perfect- meaning that the same ratio of the substitutes would satisfy you.

What does a graph showing perfect complements of two goods appear as?

If consumer always consumes commodities in a fixed proportion then the commodities are perfect complements, the indifference curve is only expressing the rank of each bundle in order of preference. They appear as right angles because you’ll never actually feel satiation until you have both compliments. You can have a lot of either commodity, but you won’t feel that bliss point without both.

What is the satiation point on an indifference curve?

This is the best possible bundle for the consumer because the proportion exactly matches their preference.

What are discrete commodities?

A commodity is discrete if it comes in unit lumps of 1,2,3 and so on (i.e. aircrafts, ships, you can’t have a gallon of ships, you either have 1 or many ships)

What is an infinitely divisible commodity?

A commodity is infinitely divisible if it can be acquired in any quantity. i.e. water or cheese (1 gallon, 1 drop, 1 bottle of water 1)

What is the well-behaved preference of a monotonic indifference curve?

Monotonicity refers to an indifference curve in which more of any commodity is always preferred and there is no satiation or bliss point.

What is the well-behaved preference of a convex indifference curve?

Convex indifference curves that contain mixtures of bundles that are always (at least weakly) preferred to the bundles themselves. A 50-50 mixture of the bundles x and y is (0.5)x + (0.5)y= Z

(i.e. 1,5 and 3,1 have a 50-50 mixture worth 2,3)

1(0.5) + 3(0.5) = 2, 5(0.5) +1(0.5)= 3

What is a “strictly convex” indifference curve?

An indifference curve that is strictly convex when all mixtures, z, are strictly preferred to their component bundles, x and y. This is because you are better off with bundle z as opposed to being indifferent to bundles x and y

What is a “weakly convex” indifference curve?

Preferences are weakly convex if at least one mixture, z, is equally preferred to a component bundle- x or y

What does an indifference curve with non-convex preferences look like?

An indifference curve with non-convex preferences will appear concave, in which mixture z is less preferred than x or y, as mixture z is now under the indifference curve.

What is the Marginal Rate of Substitution?

The slope of an indifference curve is referred to as the marginal rate of substitution, which is the ratio of goods you prefer to buy. There is a diminishing marginal rate of substitution for most indifference curves. Since it is the slope of the curve, it can also be taken as the derivative of the curve at different points.

MRS will always — commodity 1 as increases if and only if preferences are strictly convex.

increase, this is bc the MRS starts off negative and becomes less negative as the curve becomes flatter- b/c the curve will start to get near a slope of 0.

MRS —- as commodity 1 increases, if and only if preferences are nonconvex

decreases, the MRS will become more steep and more negative as commodity 1 increases if preferences are nonconvex.

What happens if MRS increases, but isn’t always increasing with commodity one?

If MRS isn’t always increasing with commodity one, then the preferences are nonconvex.