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Demand, Utility, and the Value of Time
Today: An introduction to a route choice situation and
utility
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
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