10 Preferences and the Budget Constraint

Question 1

How do people choose?

Answer 1

“People choose, out of the combination of market products which they can afford, the combination which they most prefer.”

Question 2

What conditions are there for “well-behaved” preference relations? (4)

Answer 2

1. Completeness - any two bundles can be compared
2. Reflexivity - a bundle is weakly compared to itself
3. Transitivity - if X is weakly preferred to Y and Y is weakly preferred to Z, then X is weakly preferred to Z.
4. Continuity - the sets of bundles which are preferred to X, and the set of bundles to which X is preferred, are “closed” (contain their own boundaries)

Question 3

What is a utility function?

Answer 3

A utility function is a continuous function such that:

X is weakly preferred to Y iff u(X) ≥ u(Y)

It assigns a real number to every possible bundle: more-preferred bundles get higher values.

“Utility” is an arbitrary term - it means benefit, good, advantage etc.

Question 4

Production function vs utility function (3 aspects)

Question 5

Indifference curves and isoquants

Answer 5

When drawn graphically, the slope of the of the curves is the marginal rate of substitution (MRS). It represents the trade-off between the combinations.

Question 6

How do we show perfect substitutes diagrammatically?

Answer 6

Question 7

How do we show perfect complements diagrammatically?

Answer 7

Question 8

4 properties of indifference curves

Answer 8

1. Indifference curves are downwards sloping
2. Indifference curves are thin
3. Indifference curves do not cross
4. Indifference curves are (weakly) convex to the origin

Question 9

What is meant by the ordinality of utility functions?

Answer 9

Even if the utility function is changes (e.g. by adding 10) the numbers associated with utility are different, but the preferences have not changed.

Question 10

Order-preserving transformations examples (5)

Answer 10

Question 11

What do positive monotonic transformations do? (3)

Answer 11

• Change the numerical value which we put on the indifference curves
• Do not numerically re-order their labels
• Do not change the shapes of the indifference curve maps

Question 12

Why is there no “returns to scale” in consumer theory?

Answer 12

The ordinality of preference relations is why there is no meaningful version of “returns to scale” in consumer theory.

Question 13

Answer 13

Question 14

What is the budget set?

Answer 14

Question 15

Answer 15

Question 16

What does the slope of a budget line measure?

Answer 16

The slope measures the rate at which the market allows a consumer (exhausting their budget) to trade off one good for another. It measures the opportunity cost.

Question 17

Illustrate a budget line diagram with labels

Answer 17

Question 18

How do relative price changes alter the budget line if the changes are equal?

Answer 18

Proportional price changes are identical to a budget change (i.e. is the price of p₁ and p₂ change by the same degree, there is no difference in opportunity cost).

Question 19

How does the budget line change if the price of good 1 increases relative to good 2? + diagram

Answer 19

Changes in relative prices change the slope. E.g. if the price of good 1 increases relative to good 2, then:

The area of the budget set has also decreased - reduced consumer choice.

Question 20

How is the net effect of relative price and budget changes summarised?

Answer 20

In terms of the budget line as a combination of:

1. movements inwards/outwards due to changes in the budget, and
2. changes in slope due to relative price changes

Question 21

How does this endowment affect the constraint?

Answer 21

This does not alter anything. Expenditure ≤ income.

Question 22

What is the income with endowment?

Answer 22

Question 23

Derive the budget constraint with endowment

Answer 23

Question 24

Answer 24

Question 25

How would a relative increase in p₁ affect our budget line with endowment?

Answer 25

Question 26

Why does the budget constraint pivot around the endowment point when the relative price changes?

Answer 26

This is because this point must always remain on the budget line, as shown above. The effect on purchasing power depends on the location of endowment point.

Question 27

Construct a budget constraint

Answer 27

Question 28

What is the budget line? + diagram

Answer 28

Question 29

What is consumption and labour initially?

Answer 29

Question 30

The government then starts taxing labour income at rate t once a certain earnings threshold (Y*) is surpassed.

What is the budget constraint past threshold?

Answer 30

Question 31

Plot this constraint on a diagram

Answer 31

The min operator has the effect shown above - picking out the lowest constraint. Further tax thresholds have a similar effect.