chapter 4: utility

Question 1

a utility function, u(x)

Answer 1

A utility function assigns a number to every possible consumption bundle such that more-preferred bundles get assigned larger numbers than less preferred bundles.

Question 2

ordinal utility

Answer 2

The only important feature of the numbers a utility function assigns to bundles is that it preserves the ranks. Because of this emphasis on ordering bundles of goods, this kind of utility is referred to as ordinal utility

Question 3

monotonic transformation, f(u)

Answer 3

Any transformation of a set of numbers that preserves the order of the numbers is called a monotonic transformation.

transformation is monotonic if it has a positive slope: df (u)/du > 0

Question 4

In a cardinal theory of utility

Answer 4

the size of the utility difference between two bundles of goods is supposed to have some sort of significance.

• It tells us how much more a consumer prefers bundle A over bundle B.
• Cardinal utility isn’t needed to describe choice behavior.

Question 5

Well-behaved preferences

Answer 5

satisfying the assumptions of completeness,
transitivity, monotonicity, convexity.
->can be represented by a utility function.

Question 6

An indifference curve

Answer 6

is a chart showing various combinations of two goods or commodities that leave the consumer equally well off or equally satisfied—hence indifferent—when it comes to having any combination between the two items that is shown along the curve.

Question 7

What are the requirements for a well behaved indifference curve?

-> give the four properties of indifferece curves

Answer 7

(1) indifference curves can never cross
(2) the farther out an indifference curve lies, the higher the utility it indicates
(3) indifference curves always slope downwards
(4) indifference curves are convex.

Question 8

Quasilinear preferences

Answer 8

In this case, the utility is linear in good 2 but possibly nonlinear in good 1.
- All indifference curves are vertically shifted versions of one indifference curve

Question 9

marginal utility, MU

Answer 9

The rate of change of the utility function as we add a little more of good 1 is called the marginal utility with respect to good 1. This shows how utility changes when the quantity of good 1 is changed, for a given quantity of good 2.

Question 10

the magnitude of the marginal utility

Answer 10

depends on the magnitude of utility:
* Taking monotonic transformations of the utility function will change the magnitude of the marginal utility.
* Marginal utility itself has no behavioral content, but we care only about the ordering of bundles implied by any utility function.

Question 11

The MRS

Answer 11

(marginal rate of substitution) measures the slope of the indifference curve at a given bundle of goods. It can be interpreted as the rate at which a consumer is just willing to
substitute a small amount of good 2 for good 1. The MRS is negative, because to stay on the same indifference curve, an increase in one good implies a decrease in the other.

Question 12

Utility for commuting

Answer 12

Utility functions are a way of describing choice behavior. In the field of transportation economics, economists have estimated utility functions to study consumers’ commuting behavior:

Question 13

Estimated utility functions

Answer 13

can be very valuable for determining whether or not it is worthwhile to make some investments in the public transportation system. We can also answer questions like, what happens to commuting decisions when
the price of gasoline goes up, or when the price of transit passes goes up?