Transcript Lecture04 - UCSB Economics

Demand, Utility, and the Value
of Time
Today: An introduction to a route
choice situation and utility
Route choice behavior
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Two routes
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Highway
Bridge
highway
bridge
Travel times
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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.
Recall core principle:
Equilibrium
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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?
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Assume someone is rational if he/she has a
positive value of time
Equilibrium principle
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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
S
D
20
11
# of cars
N on bridge
Other issues
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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
Core principle: Efficiency
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Think of the economy as the amount of
goods and services available
The economy is efficient when
economic surplus is greatest
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Is equilibrium efficient here? This is a later
topic
And now, onto bananas
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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
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A fundamental concept in economics is
utility
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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
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Suppose our
volunteer from
Friday 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
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
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 usually
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 Wednesday
Also for Wednesday
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Re-read and try to understand the
Economic Naturalist examples on p.
136-138
Pay attention to consumer surplus, and
how it is calculated