Transcript 7550_L8_CB1-2013

Benefit-Cost Analysis
FGS - Ch. 4
© Allen C. Goodman 2013
What is the Right Amount?
• Economists usually rely on market
solutions, but what if we don’t have
markets?
• What kind of mechanism can we
devise?
Some First Principles
What is the “right”
amount of a good to
provide for society?
Let’s look at consumers
surplus and
producers surplus.
More consumers
surplus makes
consumers happier!
Figure 4-1 Consumers’
Surplus
Demand
Price
Consumers’
Surplus
P1
P1
Additional
Consumer
Surplus
Expenditures
0
Q1
Quantity
Some First Principles
What is the “right”
amount of a good to
provide for society?
Let’s look at consumers
surplus and
producers surplus.
More producers surplus
makes producers
happier!
Figure 4-2 Producers’ Surplus
Supply
Price
Additional
Surplus
P1
P1
Producers’
Producer
Surplus
Cost to Sellers
0
Q1
Quantity
What’s the “right” quantity?
• We seek to maximize
sum of CS + PS.
• At Q < Q1, ↑ Q  ↑
both CS and PS.
• At Q > Q1, ↑ Q costs
more (S) than it is
worth (D).
Figure 4-3 Efficient
Quantity
Demand
Price
Supply
Consumers’
Surplus
P1
P1
Producers’
Producer
Surplus
Cost to
Sellers
0
Q1
Quantity
What’s the “right” quantity?
• We seek to
maximize sum
of CS + PS.
• At Q < Q1, ↑ Q
 ↑ both CS
and PS.
Figure 4-3 Efficient
Quantity
Demand
Price
Supply
Consumers’
Surplus
P1
Producers’
Producer
Surplus
+
P1
Cost to
Sellers
0
Q1
Quantity
What’s the “right” quantity?
• We seek to
maximize sum of
CS + PS.
• At Q > Q1, ↑ Q
costs more (S)
than it is worth
(D).
Figure 4-3 Efficient
Quantity
Demand
Price
Supply
Societal
Costs
Consumers’
Surplus
P1
P1
Producers’
Producer
Surplus
Cost to
Sellers
0
Q1
Quantity
What’s the “right” quantity?
• We seek to
maximize sum
of CS + PS.
• At Q > Q1, ↑ Q
costs more (S)
than it is worth
(D).
Figure 4-3 Efficient
Quantity
Demand
Price
Supply
Societal
Costs
Consumers’
Surplus
P1
-
Producers’
Producer
Surplus
Societal
Benefits
Cost to
Sellers
0
P1
Q1
Quantity
Key Point
• Efficiency is ALL ABOUT
Q!
• A monopolist is BAD
because Q* < Q1.
Figure 4-3 Efficient
Quantity
Demand
Price
Consumers’
Surplus
P1
• BUT, a perfectly
discriminating
monopolist appropriates
all of the CS.
• Eq’m quantity is
EFFICIENT!
Supply
P1
Producers’
Producer
Surplus
Cost to
Sellers
0
Q*
Q1
Quantity
MR
Benefit-Cost Analysis
• In a sense, everything economists do is
benefit-cost analysis.
• Competitive markets get us to the “right”
amount.
• Why don’t we just depend on markets?
Benefit-Cost
This is of particular concern with the public
health sector, in which you are considering
various types of public interventions.
Prime example, and a very successful one, is
fluoridation of water. It is something that
most (although not all) will agree has been
profoundly successful. Yet, it is unlikely to be
considered on a nonpublic basis. Moreover,
it may be subject to substantive economies of
scale.
It is also useful to consider the aspects of the
jargon, that often get confused.
Nelson and Swint, 1976
• Performed a prospective cost-benefit analysis
of fluoridating a segment of the water supply
for Houston, Texas,
• Explicitly introduced and evaluated the time
pattern of the costs and benefits. Showed that
neglect of the time structure of the costs and
benefits would significantly bias the results.
• A benefit-cost ratio of 1.51 and a net present
value (or “social profit”) of $1,102,970 were
found. The results are biased downwards and
should be considered a lower bound.
W Nelson, J M Swint Cost-benefit analysis of fluoridation in Houston, Texas
Journal of public health dentistry. 01/02/1976; 36(2):88-95.
ISSN: 0022-4006
Terms
• Efficiency  Marginal Benefit = Marginal Cost. In principle, it
would pay to do all projects up to where marginal benefit =
marginal cost. This is our standard economic analysis.
• Benefit-Cost  A way of ranking alternative projects, that
typically aren't brought forward by the market. We want to
consider health care interventions, and I'll do some analytical
stuff in a moment. In a sense, it tries to provide some market
signals for goods for which markets do not exist.
• Cost-Effectiveness (Efficiency)  This is often confused,
particularly by non-economists. It does not require satisfying
any type of efficiency calculation. Basically, it assumes that a
chosen project that is beneficial. You then want to consider
the cheapest way to produce it. DOES NOT imply efficiency.
TC
TB
TB, TC
W = TB(Q) – TC(Q)
dW/dQ = TB'(Q) - TC'(Q) = 0
MB = MC
0
Quantity
MB 
B
Q
TC
MC 
C TB
Q
Cost Efficient – everywhere on this curve
TB, TC
Efficient (MB=MC)
W = TB(Q) – TC(Q)
dW/dQ = TB'(Q) - TC'(Q) = 0
MB = MC
B/C > 1
0
Quantity
Exercise
TC = a + bQ + cQ2, (b, c >0)
TB = d + eQ + fQ2, (e>0, f<0)
Calculate: Q*,
Q | B/C  1
Flu Vaccines
A good example with which to look at a health care
problem that requires some sorts of public
interventions is flu vaccinations. In this type of
situation, community health becomes a public stock.
If you are vaccinated, I am likely to be more healthy.
Consider a simple n person world. For each person,
well-being depends on the consumption of numeraire
good x and the production of health H, which comes
from input (inoculation) i.
So each is optimizing:
Flu (2)
I = Σj i j
Each person’s well-being depends on the
consumption of numeraire good x and the
production of health H, which comes from
input (inoculation) i. p is the price of an
inoculation.
U1 = U1 [x1, H1 (I)] + 1 (y1 - x1 - pi1)
U2 =
…
…
…
Un = Un [x2, Hn (I)] + n (yn - xn - pin)
Flu (3)
Uj2Hj'/Uj1
Optimizing w.r.t. xj, ij, we get:
Uj1 - j = 0
Uj2Hj' - jp = 0, leading to:
Uj2Hj'/Uj1 = p.
External Benefits
$
p
This indicates the market level
for Person j.
BUT, is it optimal?
ij*
Inoculations
Measuring Benefits
• A key feature of benefit-cost analysis is measurement
of the benefits.
• Key in the measurement of the benefits is the
estimation of the willingness-to-pay for them. This is
the inverse demand curve.
• In contrast to situation where we are saying “here is
the price; how much are you willing to buy?” we say
instead, “here is an amount; how much would you be
willing to pay?”
Willingness to pay
• One of the major problems is that since we do not
usually have market signals (which is why we are doing
benefit cost analysis), we have to guess what the
willingness to pay is. We could save thousands of lives
by lowering the speed limit to 15 M.P.H. Why don't we?
• We have moved to automobiles that are much much
cleaner than they were in the 1950s and 1960s. There
is an interesting question as to how we measure the
benefits of the cleaner cars, as opposed to the costs.
Many studies argue that we have cars that are
essentially cleaner than optimal, given the marginal
benefits.
QALYs
• Health community has resisted putting a $
value on health benefits. There are a lot of
equity considerations:
– Should the lives of poor people, elderly, be valued
differently than the lives of others?
– Lots of this moves from economics to ethics.
• Health community has embraced the idea of
Quality Adjusted Life Years, or QALYs. Idea is
to adjust incremental years by the quality of
life.
Example
• Someone faces an intervention (rather than dying)
that can increase the expected time of death from
age 70 to age 90.
• For the first 10 years, life will be fine. For the next
10, not so good.
• Each of the first 10 year increment is equivalent to 1
QALY. Each of the next 10 is equivalent to 0.5
QALY.
• So, the effectiveness of the intervention is:
– 10 years * (1 QALY/year) + 10 years* (0.5 QALY/year) = 15
QALYs.
• This is your denominator.
• Then, calculate cost/QALY.
Several Non-Trivial Issues
• What about children? How do we
evaluate their QALYs?
• Who evaluates their QALYs?
• Do you add adult + children's QALYS?
• How are QALYs developed?
Ed and Harry
Geometric
presentation below
• Start at point M. Assume that Ed can gain health at a
lower incremental cost than Harry. Hence, a given
level of expenditures will give more incremental
QALYs for Ed than for Harry.
• That’s why (Emax - E1) > (Hmax - H1).
Ed and Harry
30
Ed
10
M
10
20
Harry
What do we find?
• Conventional production-possibility frontier.
• Equal outcomes @ 45o line.
• Maximum production is tangent to a line w/ slope = -1.0.
  QE ( RE )  QH ( RH )   ( R  RE  RH )
 QE

  0
RE RE
 QH

  0
RH RH
dRE=-dRH
MPs are equal!
QE QH

RE RH
QE
QH

RE
RE
QE
 1
QH
Harry and Ed
30
• What if we think that
Harry and Ed should
have the same QALYs?
Draw 45 degree line.
45o
Ed
Slope = -1
SH = SE  8
• What if we think
that Harry and Ed
should get the
same inputs?
• Why?
10
10
20
Harry
Next Time
• Cost-Benefit readings from JHE
• Readings from Elgar
– Reading 35
– Reading 37
– Reading 42
• Applied CBA.
Supplemental Material
• Remainder of Slides
Geometric Treatment
Ed and Harry
• At age 10, Harry and Ed
30
both have certain levels of
health, 10 each.
• Assume that Ed (easy)
can gain health at a lower Ed
incremental cost than
Harry (hard). Hence, a
given level of
expenditures will give Ed
20 incremental points but
would give Harry only 10.
• Suppose half of the
10
people are like Ed and
half are like Harry.
10
20
Harry
Harry and Ed
30
45o
• What if we think that
Harry and Ed should Ed
have the same
QALYs? Draw 45
degree line.
• What if we think that
Harry and Ed should
get the same inputs?
SH = SE  8
10
• Why?
10
20
Harry
What’s the most cost-effective
place?
30
Highest mean!
Mean = (20+0)/2 = 10
• Thought experiment.
Most cost effective
place is where we get
the highest mean
score. Why?
• We can draw a line
with a slope of –1.
This line gives us
places with equal
totals. Start with S = SE
+ SH = 10.
45o
SE+SH= max
Ed
SE+SH=20
Mean = (8+8)/2 = 8
SE+SH=10
10
Mean = (0+10)/2 = 5
10
20
Harry
What do we want?
E
Mean.
30
D
45o
SE+SH= max
D'
Ed
E'
C'
C
B
B'
A'
A
10
10
20
Harry
Std. Dev.
L3
L2
What do we
want?
Mean.
• Utility Functions
– Leveler – Will only
accept lower mean
along with lower SD.
– Why?
L1
D'
E'
C'
B'
A'
• Utility Functions
– Elitist – Will accept
lower mean with higher
SD.
– Why?
Std. Dev.
What do we
want?
Mean.
• Utility Functions
– Leveler – Will only
accept lower mean
along with lower SD.
– Why?
E3
D'
C'
E2
B'
A'
• Utility Functions
E1
– Elitist – Will accept
lower mean with higher
SD.
– Why?
Std. Dev.
What do we want?
• So, it’s not altogether
clear that we always
want to raise the
mean.
• The levelers here,
want to push up the
lower end, and this
lowers the SD.
• Means fewer special
programs.
Mean.
E3
D'
C'
E2
B'
A'
E1
Std. Dev.
Old Stuff
Fuchs on Cost
What are impacts of
cost containment?
Containment
and Cost-
Benefit
You can ultimately contain costs in one of three ways:
1. Increase production efficiency. Old systems don't
necessarily reward inefficient production. Most agree
that there was more to do with what was delivered
rather than how it was delivered.
2. Reduce input prices. In the short run, you can try to
squeeze some of the inputs, like nurses' wages,
physicians’ fees, or drug industry profits. In the long
run they can go elsewhere.
3. Deliver fewer services.
Fuchs on Cost Containment and Cost-Benefit
Health and Marginal Benefits
250
200
Health Benefits
H = aQ - bQ2.
If we want to maximize
health, irrespective of costs,
we maximize this, and we
get:
dH/dQ = a - 2bQ = 0,
or Q* = a/2b.
Suppose a = 30, b = 1.
Q* = 15.
150
H
Q* = a/2b
100
MB
50
0
0
5
10
15
-50
Health Care
20
25
Fuchs on Cost Containment and Cost-Benefit
Marginal Benefits
30
Marginal Benefits, Marginal Costs
We recognize that this differs from
the optimum if we recognize the
(constant) costs c, so that we are
optimizing:
L = Benefits - Costs
L = aQ - bQ2 - cQ.
Here, we get:
Q** = (a - c)/2b= Q* - (c/2b).
Suppose a = 30, b = 1, c = 3
Q* = 13.5.
25
20
15
MB
10
MC
5
0
-5
0
5
10
15
-10
Health Care
Suppose, instead, we’re at QM,
for the mean.
20
compare to
optimum
25
w/o
costs
Reducing costs
Marginal Benefits
30
Marginal Benefits, Marginal Costs
Suppose that the mean for the
population is QM. So the mean
health is:
HM = aQM - bQM2. Then if we
reduce outputs by z:
HM' = a(QM - z) - b(QM - z)2.
We may wish to discover whether mean
health improves or decreases with z.
Remember that Q* = a/2b.
When we expand this expression, we
get:
H = HM' - HM = -2zb [Q* - (QM - z/2)].
25
20
15
MB
10
MC
5
0
-5
0
5
10
15
-10
Health Care
20
25
Distributions
If you think of this as a population distribution, all that
you're doing is shifting the distribution. If you're moving
toward social optimum, you have a similar situation.
You're either moving more people toward the optimum
(making society better off) or more people away (making
society worse off).
What about if you mandate equal percentage decrease,
rather than equal amount decrease. The algebra is trickier,
and it is worthwhile to go to the marginal product marginal cost diagram. Equal percentage decreases imply
unequal absolute decreases, because those with larger
amounts have larger decreases.
Distributions
Social optimum is
100, or 10/person
Suppose that a = 12, b = 0.05,
and c = 2.
Then Q* = a/2b = 120.
Q** = (a - c)/2b= Q* - (c/2b) =
120 - 20 = 100.
2
Suppose we have QM = 110, over
10 people.
100
Quantity
110
120
Distributions
Suppose you have Q = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} 
mean = 11
Several different mandates (in reducing Q by 10 overall)
• Reduce everyone by 1. First 5 are worse off; next 5 are
better off. We now have {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
• Reduce everyone by 1/11.
We now have {1.8, 3.6, 5.5, 7.3, 9.1, 10.8, 12.7, 14.5, 16.3,
18.2}
EXCEL Slide (C_B_99)
Distribution
• If social welfare is related to mean (+) and to variance (-), then with
option 1, we’re going to be better off, although some will be far
worse off.
• With option 2, effects on health and on social welfare depend on the
size of z, the mean of the distribution QM, and the variance 2.
Starting with Q > Qopt, the larger the variance, the smaller can be QM
consistent with a favorable effect on health or social welfare.
• Why? You're pulling those who are using the most services much
closer, and, at worse, those who are using less (and possibly less than
optimal) services less farther away. One could conceivably improve
mean health, or mean welfare, even if you started below mean health
or mean welfare. One might even do better, by reducing those at the
right hand tail by even more, and those on the left hand tail by
somewhat less.