Benefit-Cost Analysis

FGS - Ch. 4

© Allen C. Goodman 2014

Some First Principles

What is the “right” amount of a good to provide for society?

Let’s look at consumers surplus and producers surplus.

0 Q 1

C o n s u m e r s ’ S u r p lu s

P r ic e

Q u a n ti ty

P 1

D e m a n d

C o n s u m e r E x p e n d i tu r e s

F ig u r e 4 - 1 C o n s u m e rs ’ S u rp lu s

P 1

More consumers surplus makes consumers happier!

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!

Producer

P ri ce

Q u a n tit y

P 1

F ig u re 4 -2 P ro d u c ers ’ S u rp lu s

Q 1 0

Producers’ Surplus

Cos t to Selle rs

S u p p ly

P 1

What’s the “right” quantity?

• We pick Q 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).

D em a n d

C o n s u m e r s ’ S u r p lu s

P r o d u c e r C o s t t o S e l l e r s

P r ic e

Q u an tity

P 1

S u p p ly

Q 1

F igu re 4-3 E ff ic ien t Q u an tity

0

P r o d u c e r s ’ S u r p lu s

P 1

D em a n d

C o n s u m e r s ’ S u r p lu s

P r o d u c e r C o s t t o S e l l e r s

P r ic e

Q u an tity

P 1

S u p p ly

Q 1

F igu re 4-3 E ff ic ien t Q u an tity

0

P r o d u c e r s ’ S u r p lu s

P 1

What’s the “right” quantity?

• We seek to maximize sum of CS + PS.

• At Q < Q1, ↑ Q ↑ both CS and PS.

+

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).

D em a n d

C o n s u m e r s ’ S u r p lu s

P r o d u c e r C o s t t o S e l l e r s

P r ic e

Q u an tity

P 1

S u p p ly

Q 1

F igu re 4-3 E ff ic ien t Q u an tity

0

P r o d u c e r s ’ S u r p lu s

P 1

SocietalCosts

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).

D em a n d

C o n s u m e r s ’ S u r p lu s

P r o d u c e r C o s t t o S e l l e r s

P r ic e

Q u an tity

P 1

S u p p ly

Q 1

F igu re 4-3 E ff ic ien t Q u an tity

0

P r o d u c e r s ’ S u r p lu s

P 1

SocietalCosts

SocietalBenefits

-

Key Point

• Efficiency is ALL ABOUT Q!

• A monopolist is BAD because Q* < Q1.

D em a n d

C o n s u m e r s ’ S u r p lu s

P r o d u c e r C o s t t o S e l l e r s

P r ic e

Q u an tity

P 1

S u p p ly

Q 1

F igu re 4-3 E ff ic ien t Q u an tity

0

P r o d u c e r s ’ S u r p lu s

P 1

• BUT, a perfectly discriminating monopolist appropriates all of the CS.

• Eq’m quantity is EFFICIENT!

Q*

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, TexasJournal of public health dentistry. 01/02/1976; 36(2):88-95.

ISSN: 0022-4006

But … (June 17, 2014)• Fluoride stays in city water• BY BRIAN McGILLIVARYbmcgillivary@record-eagle.com

• TRAVERSE CITY —An hour of public comment by more than 25 people didn’t sway a single commissioner from their previous position. Water fluoridation in Traverse City will continue, following a 5 to 1 vote on Monday. Commissioner Jim Carruthers cast the lone no vote.

• “It’s nothing unusual,” said Carruthers, who has forced a roll-call vote on the issue for six years. “Maybe one day I’ll win, but I don’t expect to.”

• Dental and health professionals outnumbered fluoride foes more than 2 to 1. They stressed the benefits of fluoride to prevent tooth decay in both children and adults. They cited studies and their own anecdotal experiences, telling commissioners they see greater tooth decay among patients who don’t have fluoride in their water.

• Opponents expressed concerns about impurities in the fluoride solutions and possible negative health consequences from the additive.

http://www.record-eagle.com/local/x1927803388/Fluoride-stays-in-city-water

From Dr. Strangelove

• http://www.youtube.com/watch?v=rKR32ImWYzw

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 may 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 project that is chosen is beneficial. You then want to consider the cheapest way to produce it. DOES NOT imply efficiency.

TB, TC

Quantity0

TC

TB

W = TB(Q) – TC(Q)ΔW/ΔQ = TB'(Q) - TC'(Q) = 0MB = MC

TB, TC

Quantity0

TB

B/C > 1

TC

Efficient (MB=MC)

Cost Efficient – everywhere on this curve

W = TB(Q) – TC(Q)ΔW/ΔQ = TB'(Q) - TC'(Q) = 0MB = MC

BMB

Q

CMC

Q

Measuring Benefits

• 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, or rich people, 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.

What is the idea?

• Can you have 0 QALY?

• Can you have negative QALY?

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.

• Then, calculate cost/QALY.

Example – Breast Cancer Treatment

Cost per QALY• Paclitaxel generates 0.5111 QALYs and

docetaxel (Taxotere®) 0.6016 QALYs - a difference of 0.0905 QALYs, equivalent to an additional 33 days of perfect health (0.0905 x 365).

• The additional costs of docetaxel amount to £220 per patient, which means that it costs £2,431 (£220/0.0905) to generate an additional QALY by using docetaxel.

Hutton J, Brown R, Borowitz M et al. A new decision modelfor cost-utility comparisons of chemotherapy in recurrentmetastatic breast cancer. PharmacoEconomics 1996; 9 (Suppl 2):8-22.

Link

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• At age 10, Harry and

Ed both have certain levels of health, 10 each.

• Assume that Ed (easy) can gain health at a lower 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 people are like Ed and half are like Harry.

10

10

30

20

Ed

Harry

Geometric Treatment

Harry and Ed

• What if we think that Harry and Ed should have the same QALYs? Draw 45 degree line.

10

10

30

20

Ed

Harry

• What if we think that Harry and Ed should get the same inputs?

45o

• Why?

SH = SE 8

What’s the most cost-effective place?

• Thought experiment. Most cost effective place is where we get the highest mean score. Why?

10

10

30

20

Ed

Harry

45o

• We can draw a line with a slope of –1. This line gives us places with equal totals. Start with S = SE + SH = 10.

SE+SH=10

SE+SH=20

SE+SH= max

Mean = (0+10)/2 = 5

Mean = (8+8)/2 = 8

Mean = (20+0)/2 = 10

Highest mean!SE+SH ≈ 22

Good example

Manns, Meltzer, Taub, Donaldson, Health Economics 12, 949-958, 2003, “Illustrating the impact of including future costs in economic evaluations: an application to end-stage renal disease.”

(1) How does high cost of ongoing dialysis affect cost/QALY?

(2) What impacts do “future costs” have?(3) Do QALYs represent adequate measures of

benefits for ESRD (end-stage renal disease)?

Future Costs for ESRD

Ongoing dialysis 3 times per week and/or transplantation.

Unrelated medical and non-medical expenditures.

Both could end up being big!

They looked at a comparison between synthetic (new) hemodialysers and cellulose (older) hemodialysers.

Discounted QALYs at 5% per year.

Various Analyses

(1) inclusion of the cost of the dialyser only, excluding the cost of related medical care;

(2) inclusion of the cost of the dialyser and of related medical costs, such as dialysis and transplantation, assuming that all patients are treated with in-center hemodialysis;

(3) inclusion of the cost of the dialyser and both related and unrelated medical costs; and

(4) inclusion of the cost of the dialyser and all related and unrelated medical costs and nonmedical expenditures.

Items 3 and 4

(3) The cost of unrelated health care (including the annual cost of non-kidney failure-related medications and the annual mean cost of non-kidney failure related hospitalisation) for hemodialysis patients using synthetic dialysers was estimated from a local study (Table 1).

(4) Non-medical expenditures were estimated by calculating lifetime total net resource use for patients by adding age-specific estimates of average consumption [28,29] net of earnings [6,30]. Average consumption by age was estimated with data from the Canadian Survey of Household Spending and included the annual consumption of non-medical and medical goods.

ITEM: In baseline analyses, the estimates considered for each of the above variables were for 60-year-old men.

Major findings

Over a 19 year horizon, synthetic dialysers an extra 0.38 QALYs/patient compared to cellulose. They were also more expensive.

Looking ONLY at intervention (dialyser only), cost/Q gained = $5,036.

When Related Costs included (costs of dialysis and transplantation*), cost/QALY gained = $83,501

*Includes nursing salary, physician charges,overhead, cost of kidney failure-related admissions, and cost of erythropoietin.

When all future costs included, cost/QALY gained = $121,124!

Magnitude of increases was largely related to high costs of future dialysis and possible transplantation.

These are HIGH!!!• “Critical value” is often taken as $50 000/Q.• Why do we provide hemodialysis if costs are so high?

– Cost estimates for future care are critical. How good are they?

– Are some QALYs different than others?

• W/O dialysis, patients with ESRD WILL DIE! Possibly a QALY that prevents certain death is more valuable than one resulting from an improvement in the probability of survival or of experiencing a higher quality of life.

• AG: Also, if you’re going to add future costs to the formula, you’ll have to increase the “critical value.”