Transcript of the last dollar spent

Demand, Utility, and the Value
of Time
Today: A route-choice activity,
and an introduction to utility
Second: An activity
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Form groups of three or four people
Each group represents a carpool
If you are not in a group of three or
four people, please raise your hand and
Rosemarie or I will find a group for you
Your carpool will represent one of N
cars on the road
4 rounds of choosing routes
Your task
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Choose between a highway and a
bridge in each of the 4 rounds
highway
bridge
More information on your task
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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.
Remember: This is extra
credit
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Your extra credit
grade will have 3
components
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Attendance here
today
Total travel time
A set of questions on
the first page
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You may talk with
other people in your
carpool about which
choice you want to
make
You are not allowed
to talk to anyone
outside of your
carpool
What happened?
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Assume someone is rational if he/she has a
positive value of time
A rational person would likely decide to travel
the bridge if bridge time < 20 minutes
Travel the HW if bridge time > 20 minutes
Notice that the same decision rules above
apply to each car
Supply is determined by constraints on bridge
What happened?
minutes
S
D
20
11
# of cars
N on bridge
Other issues with this traffic
network
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In real commuting situations, some people
have higher values of time than others
Suppose we charge a toll on the bridge
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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
And now, onto bananas
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Where is our banana eater from Wed.?
How many did you eat?
Your bananas were “free,” right?
Why did you not eat more than you
did?
Bananas and utility
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A fundamental concept in economics is
utility
Think of utility as a level of satisfaction
(similar to total benefit)
The higher your utility, the more
satisfied you are
Bananas and utility
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Suppose our
volunteer from
Wednesday has
the following
utility relationship
for bananas
Banana quantity Total utility
(bananas/hour) (utils/hour)
0
0
1
70
2
120
3
150
4
160
5
150
Marginal utility
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Marginal utility (MU) tells us how much
additional utility gained when we
consume one more unit of the good
Marginal utility of bananas
Banana quantity
(bananas/hour)
Total utility
(utils/hour)
0
0
Marginal utility
(utils/banana)
70
1
70
50
2
120
30
3
150
10
4
160
-10
5
150
If P = $0, maximize utility
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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
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Notice that marginal utility is decreasing
as the number of bananas increases
Economists typically assume diminishing
marginal utility, since this is consistent
with actual behavior
Diminishing marginal utility
and the rational spending rule
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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
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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
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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
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The rational spending rule helps us derive an
individual’s demand for a good
Example: Apples
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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
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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 Monday