1. Benefit-Cost Analysis FGS - Ch. 4 © Allen C. Goodman 2013

2. 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?

3. 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! Additional Surplus

4. 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! Additional Surplus

5. What’s the “right” quantity? We seek to maximize sum of CS + PS. At Q < Q 1, ↑ Q  ↑ both CS and PS. At Q > Q 1, ↑ Q costs more (S) than it is worth (D).

6. What’s the “right” quantity? We seek to maximize sum of CS + PS. At Q < Q 1, ↑ Q  ↑ both CS and PS. +

7. What’s the “right” quantity? We seek to maximize sum of CS + PS. At Q > Q 1, ↑ Q costs more (S) than it is worth (D). Societal Costs

8. What’s the “right” quantity? We seek to maximize sum of CS + PS. At Q > Q 1, ↑ Q costs more (S) than it is worth (D). Societal Costs Societal Benefits -

9. Key Point Efficiency is ALL ABOUT Q! A monopolist is BAD because Q* < Q 1. BUT, a perfectly discriminating monopolist appropriates all of the CS. Eq’m quantity is EFFICIENT! Q* MR

10. 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?

11. 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.

12. 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

13. 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.

14. TB,TC Quantity 0 TC TB W = TB(Q) – TC(Q) dW/dQ = TB'(Q) - TC'(Q) = 0 MB = MC

15. TB,TC Quantity 0 TB B/C > 1 TC Efficient (MB=MC) Cost Efficient – everywhere on this curve W = TB(Q) – TC(Q) dW/dQ = TB'(Q) - TC'(Q) = 0 MB = MC

16. Exercise TC = a + bQ + cQ 2, (b, c >0) TB = d + eQ + fQ 2, (e>0, f<0) Calculate: Q*, Q | B/C  1

17. 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:

18. Flu (2) 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. U 1 = U 1 [x 1, H 1 (I)] + 1 (y 1 - x 1 - pi 1 ) U 2 =…… U n = U n [x 2, H n (I)] + n (y n - x n - pi n ) I = Σ j i j

19. Flu (3) Optimizing w.r.t. x j, i j, we get: U j 1 - j = 0 U j 2 H j ' - j p = 0, leading to: U j 2 H j '/U j 1 = p. This indicates the market level for Person j. BUT, is it optimal? Inoculations $ p U j 2 H j '/U j 1 ij*ij* External Benefits

20. 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?”

21. 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.

22. 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.

23. 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.

24. 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?

25. Ed and Harry 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 (E max - E 1 ) > (H max - H 1 ). Geometric presentation below

26. Ed and Harry 10 30 20 Ed Harry M

27. What do we find? Conventional production-possibility frontier. Equal outcomes @ 45 o line. Maximum production is tangent to a line w/ slope = -1.0. dR E =-dR H MPs are equal!

28. Harry and Ed What if we think that Harry and Ed should have the same QALYs? Draw 45 degree line. 10 30 20 Ed Harry What if we think that Harry and Ed should get the same inputs? 45 o Why? S H = S E  8 Slope = -1

29. Next Time Cost-Benefit readings from JHE Readings from Elgar –Reading 35 –Reading 37 –Reading 42 Applied CBA.

30. Supplemental Material Remainder of Slides

31. 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 30 20 Ed Harry Geometric Treatment

32. Harry and Ed What if we think that Harry and Ed should have the same QALYs? Draw 45 degree line. 10 30 20 Ed Harry What if we think that Harry and Ed should get the same inputs? 45 o Why? S H = S E  8

33. What’s the most cost-effective place? Thought experiment. Most cost effective place is where we get the highest mean score. Why? 10 30 20 Ed Harry 45 o We can draw a line with a slope of –1. This line gives us places with equal totals. Start with S = S E + S H = 10. S E +S H =10 S E +S H =20 S E +S H = max Mean = (0+10)/2 = 5 Mean = (8+8)/2 = 8 Mean = (20+0)/2 = 10 Highest mean!

34. What do we want? 10 30 20 Ed Harry 45 o S E +S H = max A B C D E Std. Dev. Mean. B' A' C' D' E'

35. What do we want? Std. Dev. Mean. B' A' Utility Functions –Leveler – Will only accept lower mean along with lower SD. –Why? Utility Functions –Elitist – Will accept lower mean with higher SD. –Why? C' E' D' L1L1 L2L2 L3L3

36. What do we want? Std. Dev. Mean. B' A' Utility Functions –Leveler – Will only accept lower mean along with lower SD. –Why? Utility Functions –Elitist – Will accept lower mean with higher SD. –Why? C' D' E3E3 E1E1 E2E2

37. What do we want? Std. Dev. Mean. B' A' 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. C' D' E3E3 E1E1 E2E2

38. Old Stuff

39. Fuchs on Cost 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. What are impacts of cost containment?

40. H = aQ - bQ 2. 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. Fuchs on Cost Containment and Cost-Benefit Q* = a/2b

41. 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 - bQ 2 - cQ. Here, we get: Q** = (a - c)/2b= Q* - (c/2b). Suppose a = 30, b = 1, c = 3 Q* = 13.5. Fuchs on Cost Containment and Cost-Benefit Suppose, instead, we’re at Q M, for the mean. compare to optimum w/o costs

42. Reducing costs Suppose that the mean for the population is Q M. So the mean health is: H M = aQ M - bQ M 2. Then if we reduce outputs by z: H M ' = a(Q M - z) - b(Q M - 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 = H M ' - H M = -2zb [Q * - (Q M - z/2)].

43. 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.

44. Distributions 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. Suppose we have Q M = 110, over 10 people. Quantity 120 2 100110 Social optimum is 100, or 10/person

45. 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)C_B_99

46. 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 Q M, and the variance  2. Starting with Q > Q opt, the larger the variance, the smaller can be Q M 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.