Budget & Preferences

Question 1

What is the budget constraint, set, and equation for a consumer with income m buying x and y at prices p and q respectively?

Answer 1

Constraint: px + qy ≤ m
Set: all affordable bundles (denoted with set notation B(p, q, m) = {(x, y) | x, y > 0, constraint)
Equation (or line): px + qy = m

Question 2

How is a budget usually represented graphically?

Answer 2

Downward sloping line in the space of the two goods (or one good against all other goods)

Question 3

What can modify the usual representation of a budget?

Answer 3

The consumer facing different prices or a different income depending on circumstances (e.g. shops with entrance fees but different prices) or a tax/subsidy could be imposed above a certain level of consumption (changes price ratio so slope at some point) which would both put a kink in the budget line

Question 4

What is a consumption bundle?

Answer 4

A potential choice the agent can make

Question 5

What are the intercepts and slope of the budget line for income m, goods x and y, and prices p and q?

Answer 5

The y intercept is m/q, the x intercept is m/p, the slope is -p/q

Question 6

How would an increase in income be represented?

Answer 6

Budget line shifts out with same slope

Question 7

How would an increase in the price of good x be represented?

Answer 7

The x intercept would move closer to the origin (rotation around y intercept)

Question 8

What is a numeraire price or good and why is it possible?

Answer 8

Since only ratios between prices and income determine the budget set, one price can always be set to 1 by scaling everything accordingly, this price is the numeraire price and the matching good is the numeraire good

Question 9

What is the equation for a budget line involving a composite good?

Answer 9

If interested in x at price p against everything else, with income m, line is px + y = m where y is the money spent on everything else

Question 10

What assumptions are required to study preferences?

Answer 10

Completeness: A consumer is able to rank any two consumption bundles (weakly prefers x to y or weakly prefers y to x or both)
Transitivity: if x preferred to y and y preferred to z then x preferred to z
Consistency: can’t have x strictly preferred to y and y strictly preferred to x (in same time period)

Question 11

What is the notation for strict preference, weak preference, and indifference between bundles (a, b) and (c, d)?

Answer 11

(a, b) ≻ (c, d)
(a, b) ≽ (c, d)
(a, b) ~ (c, d)

Question 12

How are preferences represented graphically?

Answer 12

In the space of two goods, an indifference curve plots all bundles which the consumer is indifferent between
More preferred bundles are indicated with an arrow pointing towards the more preferred indifference curve

Question 13

What are perfect substitutes and perfect complements and what shape are their ICs?

Answer 13

Perfect substitutes have a constant rate of substitution (the consumer is always willing to substitute a units of x for b units of y and vice versa) and the ICs are downward sloping straight lines
Perfect complements are always consumed together in fixed proportions and have L shaped ICs

Question 14

When can we say that bundle A is directly revealed preferred to bundle B?

Answer 14

If a consumer chooses some bundle A on the budget line over another bundle B, A is directly revealed preferred to B, as well as to all other choices on the budget set and so must be the unique most preferred bundle in the budget set

Question 15

If A is directly revealed preferred to B, when is A indirectly revealed preferred to C?

Answer 15

When B is directly revealed preferred to C (under a new budget constraint)

Question 16

How can revealed preferences be used to analyse welfare?

Answer 16

If a consumer chooses A over B in one budget set and then chooses B when the budget set changes to no longer include A, the consumer is worse off
More generally, revealed preferences can easily show that a consumer is worse off or at least as well off by a change in budget set

Question 17

What are monotonic preferences?

Answer 17

When the consumer strictly prefers more to less
Formally, monotonic preferences have (a, b) ≻ (c, d) whenever a ≥ c and b ≥ d and at least one of these is strict
Correspond to downward sloping indifference curves with everything closer to the origin being less preferred

Question 18

How would you draw preferences involving satiation?

Answer 18

There would be some satiation/bliss point in the middle of some circles which are less preferred moving out
These are an example preferences which are not monotonic

Question 19

What are convex preferences?

Answer 19

Preferences are convex if for two bundles (a, b) ~ (c, d) and any weight t between 0 and 1
(ta + (1 - t)c, tb + (1 - t)d) ≽ (a, b)
i.e. weighted average of two equivalent bundles (line connecting them) at no point crosses their indifference curve to the less preferred side
Intuitively this means averages are preferred to extremes
Strict convexity replaces weak with strict preference (perfectly complements are convex but not strictly convex)

Question 20

Why is strict convexity of preferences often assumed?

Answer 20

Strictly convex preferences imply that there is a unique best bundle in a given budget set

Question 21

What are the assumptions for well behaved preferences?

Answer 21

Complete, transitive, continuous, monotone, strictly convex
==> there is a unique most preferred bundle in the budget set

Question 22

How is the unique most preferred bundle in budget set B(p, m) denoted?

Answer 22

x*(p, m) (definitely lies on budget line)