Transcript Micro-economic Foundations for CBA

Social welfare economics
foundations for CBA
G. Mason
Updated 2013
D1
+
24
Q1
(a)
24
9
+
=
D1
36
Q2
(b)
Price ($/unit)
18
Price ($/unit)
Price ($/unit)
Generating the Market Demand Curve for a
Private Good
24
D = D1 + D2
9
=
60
Q = Q1 + Q2
(c)
– To construct the market demand curve for a
private good [panel (c)], we add the individual
demand curves [panels (a) and (b)]
horizontally.
LO3: The Optimal
Ch14 -2
© 2012 McGraw-Hill
Quantity of a Public
Ryerson Limited
FIGURE 14.2: Generating
the Demand Curve for a
Public Good
Price
($/unit)
18
9
D1
12
24
36
Q1
(a)
Price
($/unit)
•
To construct the demand
curve for a public good [panel
(c)], we add the individual
demand curves [panels (a)
and (b)] vertically.
24
16
D2
8
12
24
36
Q2
(b)
Price
($/unit)
42
25
D = D1 + D2
8
12
24
36
Q
(c)
LO3: The Optimal
Quantity of a Public
Ch14 -3
© 2012 McGraw-Hill
Ryerson Limited
The Optimal Quantity of Parkland
Marginal
cost
200
140
80
Demand
A0
A*
The optimal number of hectares of urban parkland is A*, the quantity at
which the public’s willingness to pay for additional parkland is equal to the
marginal cost of parkland.
LO3: The Optimal
Quantity of a Public
Ch14 -4
© 2012 McGraw-Hill
Ryerson Limited
The Loss in Surplus from a Pay-per-View Fee
Twice as many households would watch the program if
its price were zero instead of $10. The additional
economic surplus is the area of the blue triangle,
or $50
LO3: The Optimal
© 2012 McGraw-Hill
million.
Quantity
of a Public
Ryerson Limited
Under consumption of public good
• What examples exist of public goods you
care that others under consume?
• What examples of public goods make no
difference that others under-consume?
Direct and inverse demand
• Direct demand views quantity as the
“dependent” variable and price as the
“independent” variable or the driver.
– QA = A0 - A1PA
• Inverse demand, views price as a
marginal utility and measure of the
willingness to pay for a specific quantity.
– PA = A0 + A1QA
Social welfare rules
• Few actions by government make
everyone better off; usually there are
several winners and several losers.
• Who are the winners and losers in the
following scenarios
– Street repairs
– Subsidies to the arts and culture
– Mandatory vaccination of girls (under 12) for
HPV (see facts sheets)
Pareto Rules 1
• Program X improves the welfare of society if it
makes at least one person better off without
making anyone else worse off.
• Adler and Posner (reading cited in outline)
identify several factors that prevent this rule for
working.
– Un observability of states of welfare
– Un comparability of welfare among individuals
• Declining marginal utility of money suggests that
those who are well off, would be worsened, if
many others who are poor are made better off.
Pareto 2
• Assume a social preference function (aggregate demand
for a public good) given by:
U(X1,X2, …XN).
• Also assume H households in a community, and a single
road. Cyclists would like a bike path; council must
decide.
• If the bike path is built, the average household will
experience utility increase of ΔU.
• Council has an easy decision if:
– ΔUh > 0 for all households and ΔUh > 0 for at least one
household, or if
– ΔUh < 0 for at all one household and (ΔUh <0 for one household)
Pareto 3
• Most situations involve a mix of
households that experience increases,
neutral or negative utilities from a bike
path (Who loses from a bike path?)
• Naïve solution is add utilities
– Utot = ΔU1 + ΔU2 +…. ΔUh
• Utility is an ordinal measure, not cardinal
• That means we cannot compare utilities
directly
Willingness to Pay
Compensating Variation
• Beneficiaries of bike path
– What is the maximum amount you are willing to pay
to have the bike path constructed?
• Opponents of bike path
– What is the minimum amount you are willing to accept
of the bike path were constructed.
• This is a proxy for the change in utility from the
perspective of adopting the new.
• For household h, if compensating variation is
CVh >0, then ΔUh > 0; if CVh <0, then ΔUh < 0;
and if CVh =0, then ΔUh = 0.
Willingness to Pay
Equivalent Variation
• Beneficiaries of bike path
– What is the minimum amount you would accept to
forgo the bike path?
• Opponents of the bike path
– What is the maximum amount you would be willing to
pay to stop the bike path?
• This is the proxy for utility from the perspective
of preserving the old.
• For household h, if equivalent variation is EVh
>0, then ΔUh > 0; if EVh <0, then ΔUh < 0; and if
EVh =0, then ΔUh = 0.
Beneficiaries Opponents
Compensating
Variation
Move to
New
Payment to get
project
Payment to
accept project
Equivalent
Variation
Maintain
the Old
Payment
Payment to
received to forgo prevent bike path
project
Several methods exist to measure willingness to pay, including revealed
preference (demand studies) and direct surveys. These will be reviewed
in more detail, later in the course
First compensation rule
• It may be tempting to conduct a survey and then add
CVh across all households. If CVh > 0 this is the first
compensation test in public policy
• Issues
– To ensure Pareto optimality, those whose welfare declines with
the change must actually be compensated. (This raises
mechanical issues of getting winners to pay losers). It also
causes strategic biases if survey respondents raise “price” to get
more money (ie., overstate their need for compensation)
– Marginal utility of income means that one can compare CV and
EV only for those at the same income.
Key assumption of CBA – Government uses tax and transfer policies to
ensure an optimal distribution of income, such that the marginal utility of
income is equivalent for all.
Second compensation rule
• If EVh > 0 this is the second compensation
test in public policy (subject to equal marginal
utilities of income).
• This is the preservation scenario. If EV>0, then
the minimum amount needed by cyclists to forgo
the path, exceeds the maximum amount
opponents would be willing to pay to preserve
the status quo. This means the project proceeds
• If EV<0, then the opponents can buy off the
beneficiaries and the project does not proceed.
Combining the rules
1.CV> 0, EV > 0 (proceed)
– Both compensation rules are satisfied. Winners can compensate losers if the project were
build, and losers could not compensate winners if the project were not built. If path does not
exist, build it; the path exists retain it.
2.EV<0, CV<0 (do nor proceed)
– Those who gain fro the status quo can compensate those who want the project; if the project
exists, those that want to cancel it, can compensate those that want to maintain it. If the
path does not exist, do not build it; if it exists, destroy it.
3.CV>0, EV<0
– If there no path, winners can compensate losers. If there is a path, losers can compensate
winners. If there is no path, build it; if a path exists, get rid of it!
4.EV>0, CV<0
– EV>0 implies that if there is a path, then destroying it would cause a welfare loss; if CV<0,
then if there is no path, constructing it would cause a welfare loss.
The third and fourth situations are the essence of what is called the Scitovsky
paradox or Scitovsky reversal If EV and CV are negative reject the project; If EV
and CV are positive, adopt the project. Combinations 3 and 4 offer no guidance, and
the status quo should be maintained, pending more data.
Consumer surplus
At P1, consumers are
willing to buy X1. At
smaller quantities, they
are prepared to pay
more, but not have to. “a”
is the consumer surplus
at P1
When prices drop,
consumer surplus
rises to a+b+c
a
P1
b
c
P2
D
d
e
X1
X2
Consumer surplus and CV,EV
• Normal goods – EV>ΔCS>CV
• Inferior goods – EV<ΔCS<CV
• EV= ΔCS=CV when income elasticity is
zero.
• In general, measures of consumer surplus
perform reasonably well in measuring
changes in social welfare
Changes due to price of substitutes
and complements
• Assume that X, Y and Z are three
commodities
• Y is substitute for X and Z is a
complement of X.
• A price decrease in X, reduces demand for
Y, and increases the demand for Z
Price of X increases, reduces
the demand for Y
Price of X increases,
increase the demand for z
P
Dzy1
Py
f
g
y1
Dy2
Dz2
h
y2
i
z1
Dz1
z2
Overall income has not changed: Therefore
b+d+f+g+h = d+e+f+h+j
Refer to previous figure
as well for b, c d, and e
Rearranging
b=e–g+j
And therefore b+c = (c + e) – g +j
Recall that b+c was the increase
in consumer surplus from a price
reduction in x
Change in undistorted markets
Undistorted means
that P = MC
Px
a
P1
b
c
P2
MC
d
Dx
e
Price of X drops, but
demand for the
substitute Y falls and
increases for the
complement
ΔB=c+e-g+j
ΔW = ΔB - ΔC
X1
X2
Py
Pz
MC
Pz
Py
Dy1
f
MC
Dz2
h
g
j
Dz1
Dy2
y2
z1
y1
ΔW = [c+e-g+j] – [e-g+j], or market by
market
ΔW = [c+e-e] +[-g+g] + [j-j],
x
y
z
z2
Distorted markets
Pj
The economy has
three goods – J, K,
L. L is a composite
good representing
all other goods
except J and K
P2
k
P1
MCj
Dj
m
J2
J1
J, K, and L are assumed to be
substitutes – when the price of J drops
the demand for K and l increases.
The price of J rises
from P1 to P2. The
demand drops for J,
but rises for K and
L.
The price of K is
distorted because it
is less than its
marginal cost.
Pk
PL
MCk
MCk
q
Pk
MCL
PL
DK2
n
DL2
r
DL1
DK1
K1
K2
L1
In market J, consumers lose k + m
In markets K and L, they receive n + r.
ΔB = n + r – (k + m)
The resource cost declines for J = m, increases for K
(q + n) and L (r)
ΔW = ΔB - ΔW = q + n + r - m
L2