Demand, Utility, and the Value of Time

Today: An introduction to a route choice situation and

utility

Route choice behavior

Two routes Highway Bridge

highway

bridge

Travel times Travel time on the highway is 20

minutes, no matter how many other cars travel on this route

The bridge is narrow, and so travel time is dependent on the number of other cars on the bridge

If 1 car is on the bridge, travel time is 10 minutes; 2 cars, 11 minutes; 3 cars, 12 minutes; etc.

Recall core principle: Equilibrium

If you know the route choice of all other people, you can figure out which route is best for you

When there are no possible gains by switching routes equilibrium

What happened? Assume someone is rational if he/she has

a positive value of time Equilibrium principle

A rational person would likely decide to travel the bridge if bridge time < 20 minutes

Travel the HW if bridge time > 20 minutes The same decision rules above apply to each

car Supply is determined by constraints on

bridge

What happened?

minutes

# of cars on bridge

D20

S

11 N

Other issues In real commuting situations, some people

have higher values of time than others Suppose we charge a toll on the bridge

New equilibrium: Bridge time < 20 min. Why? Think both time and money as costs Who travels on bridge now? People with high

values of time, since they look at the toll as a relative bargain

Is “no toll” or “toll” best? This is a later topic

Core principle: Efficiency

Think of the economy as the amount of goods and services available

The economy is efficient when economic surplus is greatest Is equilibrium efficient here? This is a

later topic

And now, onto bananas

Where is our banana eater from Friday?

How many did you eat? Your bananas were “free,” right? Why did you not eat more than you

did?

Bananas and utility

A fundamental concept in economics is utility Hypothetical unit of utility: util

Think of utility as a level of satisfaction (similar to total benefit)

The higher your utility, the more satisfied you are

Bananas and utility

Suppose our volunteer from Friday has the following utility relationship for bananas

Banana quantity

(bananas/hour)

Total utility

(utils/hour)

0 0

1 70

2 120

3 150

4 160

5 150

Marginal utility

Marginal utility (MU) tells us how much additional utility gained when we consume one more unit of the good

Marginal utility of bananasBanana quantity (bananas/hour)

Total utility (utils/hour)

Marginal utility (utils/banana)

0 0

70

1 70

50

2 120

30

3 150

10

4 160

-10

5 150

If P = $0, maximize utility

Utility is maximized when 4 bananas are eaten

When P ≠ $0, we need a way to maximize utility given a budget

We can easily maximize utility if we have diminishing marginal utility

Diminishing marginal utility

Banana quantity (bananas/hour)

Total utility (utils/hour)

Marginal utility (utils/banana)

0 0

70

1 70

50

2 120

30

3 150

10

4 160

-10

5 150

Diminishing marginal utility

Notice that marginal utility is decreasing as the number of bananas increases

Economists typically assume diminishing marginal utility, since this is usually consistent with actual behavior

Diminishing marginal utility and the rational spending rule

If diminishing marginal utility is true, we can derive a rational spending rule

The rational spending rule: The marginal utility of the last dollar spent for each good is equal

Exceptions exist when goods are indivisible (we will ignore this for now)

The rational spending rule

Why is the rational spending rule true with diminishing marginal utility?

Suppose that the rational spending rule is not true

We will show that utility can be increased when the rational spending rule does not hold true

The rational spending rule Suppose the MU per dollar spent was higher

for good A than for good B I can spend one more dollar on good A and

one less dollar on good B Since MU per dollar spent is higher for good

A than for good B, total utility must increase

Thus, with diminishing MU, any total purchases that are not consistent with the rational spending rule cannot maximize utility

The rational spending rule The rational spending rule helps us

derive an individual’s demand for a good Example: Apples

Suppose the price of apples goes up Without changing spending, this person’s MU

per dollar spent for apples goes down To re-optimize, the number of apples

purchased must go down Thus, as price goes up, quantity demanded

decreases

Individual demand

Now that we have derived that individual demand is downward sloping, how do we get market demand?

Keep reading Chapter 5 and you can find out…

…or you can wait until Wednesday

Also for Wednesday

Re-read and try to understand the Economic Naturalist examples on p. 136-138

Pay attention to consumer surplus, and how it is calculated