Demand, Utility, and the Value of Time

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Demand, Utility, and the Value of Time

• Today An introduction to a route choice
  situation and utility

2
Route choice behavior

• Two routes
• Highway
• Bridge

3
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.

4
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

5
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 lt 20 minutes
• Travel the HW if bridge time gt 20 minutes
• The same decision rules above apply to each car
• Supply is determined by constraints on bridge

6
What happened?

minutes
S
D
20
of cars on bridge
11
N
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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 lt 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

8
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

9
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?

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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

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Bananas and utility

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

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Marginal utility

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

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Marginal utility of bananas
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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

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Diminishing marginal utility
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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

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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)

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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

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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

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The rational spending rule

• The rational spending rule helps us derive an
  individuals demand for a good
• Example Apples
• Suppose the price of apples goes up
• Without changing spending, this persons 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

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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

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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