chapter 5: choice

Question 1

The economic model of consumer choice

Answer 1

1. A consumer chooses the most preferred bundle in her budget set.
2. A consumer chooses a bundle that maximizes utility, subject to a budget
   constraint.

Question 2

necessary condition for optimality.

Answer 2

If we have an interior optimum with smooth indifference curves, the slope of the indifference curve and the slope of the budget line will be the same.

Under these two restrictions, the tangency condition is called a necessary condition for optimality.

Question 3

Is the tangency condition a sufficient condition for a bundle to be optimal?

Answer 3

• If we find a bundle where the indifference curve is tangent to the budget
  line, can we be sure we have an optimum?
• Not when there are multiple optima (Figure 4)

Question 4

When preferences are convex

Answer 4

any tangency point between the indifference
curve and the budget line must also be an optimum. the tangency condition is sufficient for an optimum, but there could still be multiple optima if indifference curves have flat spots.

Question 5

If the indifference curves are strictly convex

Answer 5

there will be only one optimal
choice on each budget line.

Question 6

At an interior optimum,

Answer 6

the marginal rate of substitution (MRS) must equal the slope of the budget line.

Question 7

consumer’s demanded bundle.

Answer 7

The optimal choice of goods 1 and 2 given prices and income

Question 8

The Marshallian demand function

Answer 8

is the quantity demanded of a particular
good as a function of its price, income, and the prices of other goods.

Question 9

If goods are perfect substitutes, what is the comsumer demand?

Answer 9

the consumer exclusively buys the cheaper one.

If both prices are the same, then the consumer doesn’t care which one he or
she purchases.

Question 10

If goods are Perfect complements, what is the comsumer demand?

Answer 10

A consumer will buy the same amount of good 1 and good 2, no matter what
prices. Let this amount be denoted by x.

Question 11

If goods are neutral or a bad, what is the comsumer demand?

Answer 11

If either good is a neutral or a bad, the consumer will spend all of her money
on the good she likes and none of it on the neutral or bad

Question 12

If goods are Discrete goods, what is the comsumer demand?

Answer 12

Suppose that good 1 is a discrete good that is available only in integer values,
while good 2 is money to be spent on everything else.

Question 13

A quantity tax

Answer 13

impacts the budget constraint by increasing the price of one good.

Question 14

A revenue-equivalent income tax

Answer 14

tax that generates the same amount of revenue which ensures that the optimal bundle under the quantity tax will still be available. Under the income tax the budget line will have the same slope as the original
budget line.

Question 15

why is An income tax is superior to a quantity tax?

Answer 15

because the consumer is better off
and you can raise the same amount of revenue from this consumer.

Question 16

limitations of Income tax versus a quantity tax result

Answer 16

1. This result applies to 1 consumer
   * The amount of the income tax will differ from person to person
   * A uniform income tax for all consumers is not necessarily better than a uniform quantity tax for all consumers.
2. An income tax changes incentives to work and could lead to a further decrease in income.
3. Supply will also respond to the tax.

Question 17

The indirect utility function

Answer 17

gives the consumer’s maximal
attainable utility when faced with prices (p1, p2) and an amount of income m.

Question 18

The dual problem of consumer theory

Answer 18

Instead of maximizing utility subject to a given income we can also minimize
expenditures subject to achieving a given level of utility ¯u.

Question 19

Properties of the expenditure function

Answer 19

1. Expenditure functions are homogeneous of degree 1 in prices
2. Expenditure functions are non-decreasing in prices ∂e / ∂pi ≥ 0 for every good i
3. Expenditure functions are concave in prices