Transcript Consumer Surplus

Consumer Surplus
©1999, 2006,2010, 2011 by Peter
Berck
Money Measures
• How much would you be willing to pay
(WTP) for a new ski area?
• How much does it cost?
• Shouldn’t build unless total WTP is greater
than total cost.
• Need WTP in $. Need a money measure.
Overview
•
•
•
•
TWTP and CS
Relation of EV, CV and CS
EV and CV for a publicly provided good
Adding over consumers
– private good
– public good\
• WTA and WTP
Demand Curves
• Demand: Amount that will be purchased as
a function of price p.
• (Inverse) Demand: Price consumers will
pay for next unit as function of number of
units consumed, q.
• P(Q) is willingness to pay for next unit
– Marginal willingness to pay
Demand Slopes Down
• willing to pay a lot more for the first pint of
water (especially on a hot day in the desert)
than for the pint after you have 40 gallons.
• wtp decreases as quantity increases
Total Willingness to Pay
• Total Willingness to pay is area under
demand.
– demand price P(Q) is amount willing to pay for
next unit
– So total willing to pay for Q units is P(1) +
P(2) + ...+ P(Q)
• lower riemann sum and an approximation
• the area under the demand curve between 0 and Q
units, which is the integral of demand, is (total)
willingness to pay
Calculating Total Willingness
70
60
Price
50
40
AREA
Demand
30
20
10
0
1
2
3
4
Quantity
5
6
7
Consumer Surplus
• Consumer surplus is willingness to pay less
amount paid
• Amount paid is P Q
Consumer surplus is willingness
to pay less amount paid
• Willingness is blue + green. Surplus is
just the green
p
D
q
Willingness(Q)
The willingness to pay for q units is the
blue area while the willingness to pay
for q+n units is green and blue. Therefore
the willingness to pay for n extra units is
the green area
p
D
q
q+n
Money Measures-Theory
• Think of projects as lowering prices.
– A new bridge lowers the price of crossing the
bay by making one wait less time in toll plaza
lines
– A new ski area lowers price by making the
commute from LA to skiing be shorter
Lots of things
• can be thought of as price changes
– ipod mini brought price of carrying whole
music library around from essentially infinity to
$200.
– new dam reduces price of electricity (because
there is more of it and demand curves slope
down.)
• taxes, like environmental taxes, are price
increases.
Surplus and Price
Price increases from p to p’. CS was
green+yellow+ orange. After increase
it is only green. CS changes by the wedge
that is yellow plus orange.
p’
P
D
q’
q
CS is an Approximate Measure
and for markets goods a real
good approximation
at that.
When 1 unit bought demand
curve shifts in.
70
60
Price
50
40
AREA
Demand
30
20
10
0
1
2
3
4
Quantity
5
6
7
CS is easy
• All you got to do is calculate an area.
• All you need is a demand curve
• Trouble is that CS is an approximate money
measure
• Lets look at some exact money measures
and see how compare
Exact money measures
• Equivalent Variation
• Compensating Variation
– For a normal good, consumer surplus is in
between these two measures. (Willig’s
Theorem)
Equivalent Variation
• A consumer actually faces an increase in the
price of a good from p0 to p1.
• That will make his utility go down from one
indifference curve i to a lower indifference
curve ii.
Thought Experiment: $
Equivalent
• If prices were left the same and instead
money was taken away from the consumer
– How much money would you need to take
away to reduce the consumers utility from i to
ii?
– That amount of money is EV
EV Picture
Narrating the picture
• price doubled so now on new lower
indifference curve ii.
• budget constraint III has original prices
(parallel to budget constraint I) but is
tangent to lower indiff curve ii.
• read change in income between I and III on
the vertical axis (since the price of that good
is 1).
EV
• The equivalent variation to a price change
from p0 to p1 is the change in income that
makes the consumer just as well off as if
prices had changed from p0 to p1.
to remember EV..
• There are two equivalent ways to get the
consumer to the new utility level:
– change income
– change prices
CV
• The compensating variation to a price
change from p0 to p1 is the change in
income that leaves the consumer just as well
off at price p1 as he would have been with
his original income at p0.
CV Picture
narrate cv
• Start out on indifference curve i. The price
increases. Now you are on curve ii. How
much money needed to get back?
• Budget constraint III has the new prices and
enough income to get back to old
indifference curve.
CV
• The change in income compensates for the
change in price. The consumer is no better
or worse off than before.
Willig shows that CS isn’t such a
bad idea after all.
• for a price increase (for a normal good)
– cv > CS > ev
• For the example in the textbook all three of
these measures are within 63 cents and are
on the order of $107.
• CS is more than good enough as a measure
for a private good.
Does CS work for goods that are
not bought?
• Candy bars are bought. They are private
goods.
• The level of bio-diversity/wolves/air quality
are all things that you cannot change by
personally buying more. They are publicly
provided goods.
Publicly Provided Goods
• If the government provides a good and
– people have different preferences
– then some people won’t get the amount they
like
• People who can buy (or sell) a good all have
the price as their wtp for the next unit of the
good.
• Not true if government gives the good.
• Wolves in the yellowstone ecosystem
–
–
–
–
some like em
some don’t
some like em more than others
everyone “gets” the same number—they are
just out there—get over it.
Diagram on next slide
• Has indifference curves. They are very
sharply curved to create an extreme
example.
– You could draw some indifference curves not
quite so sharply curved and see if the general
point still works
Exact money measure for wolves
• The “reality” is to get more wolves
– Previous example was a higher price
– Here it is a change in quantity
• More wolves increase utility
• EV is the amount of added $ that increases
utility the same as the added wolves
• CV is the amount of money removed to
return to original level of utility
EV and CV for Publicly Provided
Good
35
30
i
ii
25
20
B
$
A
15
10
C
5
0
0
5
10
15
20
Wolves
25
30
35
EV and CV for Wolves
• Starting from point A, we calculate CV for 5 more wolves
as follows. By adding 5 wolves, the consumer would be
on indifference curve ii at point B. To return to
indifference curve i, the consumer would need to give up
$10 in income, so the CV is $10. For EV, the question is,
how can we get the consumer back to indifference curve ii
without providing wolves? The consumer can get from
point A on i to point B on ii by adding 5 wolves, but even
an infinite amount of income will not get her to ii, holding
wolves constant; it will instead move her vertically along i.
Hence EV is infinite.
Publicly provided conclusion
• If the indifference curves have are close to
square shaped
• and the optimal amount (corners in this
case) are not provided
• then ev and cv are very different.
Loose Ends
• So area under one person’s demand is twtp
for that person.
• How do we find twtp for a private good for
a market demand curve
– Market demand = sum of individual demands
• Same question for many people and a public
good.
Private good
• Market demand
• For each price, add up the quantities each
consumer will buy. Horizontal addition of
individual demand curves.
QTotal ( P) 

i  consumers
Qi ( P)
TWTP private sum: horizontally
add demand and find area under
P
Q
Public Good
• P(Q) is marginal wtp (marginal means for
the next unit) for one person.
• There are N people
• N P(Q) is the what they are collectively
willing to pay. (why?)
• Add vertically!
WTP for Public Good: vertically
add and find area under
40
35
30
Total Demand
$
25
20
15
Person 2's
Demand
Person 1's
Demand
10
5
0
0
10
20
30
Wolves
The marginal willingness to pay for a public good is the vertical sum of the individuals’ marginal willingness to pay values.
CS, EV, CV , WTP blind
• To the distribution of income.
• We just find the twtp for each individual
and add them up. (Or take area under
market demand for private good).
• Means each individuals $ count the same
• Will these measures help you explain why
Egypt subsidizes bread?
Valuation Questions
• How do CV and EV relate to questions you
could ask people?
– Willingness to pay
– Willingness to accept
Remember!
Utility Change is what
determines whether it is EV or
CV
change only happens with EV!
WTP can lead to EV or CV
• What is the most
money you would be
willing to pay to have
wolves in yellowstone
– No util change so CV
• Most money willing to
pay so that ranchers
won’t kill wolves?
– Util goes down.
– You pay or wolves die
– EV
WTA can lead to EV or CV
• Least money willing
to accept instead of
having increase in
wolf numbers.
– You get wolves or cash
– Uitl changes
– EV
• Least money willing
to accept to allow
ranchers to kill
wolves.
–
–
–
–
Wolves die,
But you get paid
Uitl constant
CV
Using WTP to explain a two or
more part tariff for Electricity
Price Discrimination
• Charging different
consumers different
prices.
• Could be the car
salesman who tries to
get all the twtp
– Each consumer buys
one car
• Simplified electricity
tariff
– 10c/kwh for first
100kwh
– Then 20c for all others
– (inverted block)
• Diff prices for diff
usage==diff prices for
different people
Simplified Problem:
• Once $10b has been
paid to construct a
distribution system
• Electricity costs
10c/kwh to generate
and distribute
• How to price?
If we charge 10c
• Then marginal
willingness to pay will
equal cost of
producing next unit of
power.
• Making more or less
power won’t make any
one better off without
making someone else
worse off
• Supply is horizontal
and equals demand
where we produce.
• But it won’t recover
the 10b
Where Should produce
suppose at 20c we cover the 10c
cost of power and the $10b
20c
S
10c
D
q-high price=100b kwh
Can we do better with a two part
tariff?
20c
S
10c
D
q-high price
q-10c price
Charge $20 per mo. + 10c Kwh
• Make up the fixed costs by charging a flat
fee per month plus the cost of the electric.
• Works
Politics (right wing
interpretation)
• Voters want to make someone else pay.
• Politicians call it concern for the poor.
• Want to set electric rates to
– Load fixed costs on a small minority
– Pay off powerful interests
Increasing Block Pricing
• First $115/MWH up to baseline
• Then Higher price till 130 percent of
baseline usage
• Then $410/MWH
• The fixed costs get covered by the people
who buy the most, who are also the richest
with the biggest pools.
Public Utilities Commission
•
•
•
•
Covers costs
Overcharges minority of pool owners
Undercharges majority of renters
And the kicker….
– Has special rates for industry that are even
lower than $115. Some ag rates where as low
as $50.