Managerial economics guide 1

DEMAND ANALYSIS

Basic Concepts

Preference sets

The consumption set

X is the set of all conceivable consumption bundles. For simplicity, we will consider only bundles of 2

goods

Comparing different bundles ̂ ̃ ̂ ̃

 Strict preference relation: - the consumer prefers bundle over bundle

̂ ̃ ̂ ̃

 ∼

Indifference relation : - the consumer likes and equally well

̂ ̃

 ≿

Weak preference relation: - the consumer prefers or is indifferent between the two

bundles

Indifferent curve

An indifference curve is a set of consumption bundles (or, when there are two goods, points in a two-

dimensional graph) which the consumer thinks are all equally good; she is indifferent among them.

Preference assumptions

Assumption 1. Completeness.

̂ ̃ ̂ ̃

For all consumption bundles and , either , or

̃ ̂ ̂ ̃

∼

, or . That is, the consumer must like one better than the other, or like them

equally well.

Assumption 2. Transitivity.

You can establish preference between identical sets of good

This assumption has four parts:

• First, transitivity of preference:

̂ ̃ ̃ ̂

• Second, transitivity of indifference:

̂ ̃ ̃ ̂

∼ ∼ ∼

• Third,

̂ ̃ ̃ ̂

∼

• Fourth and finally,

̂ ̃ ̃ ̂

∼

Assumption 3. Monotonicity.

We normally assume that goods are desirable, which means the consumer prefers consuming more of a

̂ ̃ ̂

good to consuming less. That is, suppose and are two bundles of goods such that (1) has more of

̃ ̂ ̃ ̂ ̃

one good (or both) than does and (2) has at least as much of both goods as has. Then .

+ Weak monotonicity – you must make a big effort to increase consumer satisfaction. Must use

≫

the because you must give the consumer a lot more to make them happier.

+ Strong monotonicity – preference is very strong, so even if you give a little more, the ≽

preference is still strong – giving the consumer only a bit will make the consumer happier so use the

Assumption 4. Convexity for indifference curves.

This assumption means that averages of consumption bundles are preferred to extremes. Consider two

distinct points on one indifference curve. The (arithmetic) average of the two points would be found by

connecting them with a straight-line segment, and then taking the midpoint of that segment.

Convexity of preferences means that indifference curves are

convex, as in the figure, rather than concave.

Other characteristics

+ Preferences are monotonic → Indifference curves representing preferences over two desirable goods

cannot be thick or upward sloping. Nor can they be vertical or horizontal. The only graph compatible

with monotonic preferences is a downward sloping thin indifference curve. This way, the area below the

curve is less preferred (you get less of both goods) and the area

above is more preferred (you get more of both goods).

+ Preferences are monotonic and transitive → two distinct indifference curves cannot cross.

̂

Suppose the curves did cross at the point .

̂