Chapter 7: Cost Benefit Analysis

1. Chapter 7: Cost Benefit Analysis The best way to evaluate a government policy is through the social welfare function W=f(U1, U2…) BUT, this function is difficult to accurately calculate. A more practical way to evaluate public expenditure is through COST-BENEFIT ANALYSIS.

2. Chapter 7: Cost-Benefit Analysis • Present Value Calculations and Alternatives • Public Sector Discount Rate • Calculating Public Costs and Benefits • Cost-Benefit Analysis Errors • Distribution • Uncertainty

3. Math- Compound Interest Investment: $100 Interest rate: 2% Derived Formula: S = P (1+r)t S = value after t years P = principle amount r = interest rate t = years

4. Compound Interest Example The City loans $2 million to a local sports team, to be paid back in 10 years at 3% interest. How much will the City get? S = P (1+r)t S = $2 million (1+0.03)10 S = $2.69 million

5. Math - Present Value How much do I have to invest now to have a given sum of money in the future? How much is a future amount worth now? PV = S/[(1+r)t] PV = present value (money invested now) S = sum needed in future r = real, compound interest rate t = years

6. Present Value Example If the City wins their bid for the Video Games Olympics (VGO) in 5 years, they will gain $10 billion in economic activity. What is the present value of that gain if interest rates are 4%? PV = S/[(1+r)t] PV = $10 billion/[(1+0.04)5] PV = $8.22 billion

7. Theory – Discount Rate Since the future value is “discounted” according to the interest rate r, r is often referred to as the DISCOUNT RATE. Similarly, (1+r)tis often referred to as the DISCOUNT FACTOR This PV formula changes if a stream of income occurs:

8. Math - Present Value of a stream If an investment today yields future returns of Rt, where t is the year of the return, then the present value becomes: Note that failing to use present values to discount future benefits can overestimate the value of a project.

9. Theory - Inflation Typically, all prices in an economy change (typically increase) with inflation. A $100 DVD player today with 3% inflation will cost $103 next year. A $50,000 salary tied to inflation will be $50,150 next year. NOMINAL VARIABLES are the “sticker price” variables, the variables/prices actually faced in that year. (ie: $103 DVD player) REAL VARIABLES are variables after inflation has been factored out (ie: $100 DVD player)

10. Inflation Rule When doing financial calculations, the general rule is that ALL VARIABLES MUST BE IN NOMINAL TERMS OR ALL VARIABLES MUST BE IN REAL TERMS. -Therefore if future revenues/costs are in nominal terms, simply use the going interest rate r -If future revenues/costs are in REAL terms, the nominal interest rate must be converted into the real interest rate through:

11. Math - Private Firm Evaluation -In order to evaluate public projects, it is best to begin with private projects -If a firm is considering project X with costs and benefits Ctx and Btx in year t, present value is calculated: Where r is the firm’s rate of return; or its opportunity cost of funds.

12. Theory - Present Value Criteria • A firm will undertake projects based on the following: • A firm will only undertake projects whose PV is positive • If given a choice between many mutually exclusive projects, it will chose the one with the highest PV

13. Private Firm Evaluation Note that r should represent a firm’s accurate opportunity cost of funds -a high r favors projects with a quick return (therefore an incorrectly high r discriminates against long projects) -a low r allows for project with a longer return (therefore an incorrectly low r discriminates against short projects)

14. Math - Benefit-Cost Ratio -One limited way to evaluate projects is using a cost benefit ratio -Given a present value of costs and benefits: -The BEFEFIT-COST ratio is B/C

15. Benefit-Cost Ratio -A project can be undertaken if B/C>1 -This implies that B-C>0, similar to the present value calculation considered earlier -The benefit-cost ratio is poor for comparing between projects, as it doesn’t consider the amount of PV: -$3 net PV could have a B/C value of 1.7 while $2,000,000 net PV could have a B/C value of only 1.1

16. Theory - Public Sector Discount Rate In the private sector, the discount rate, r, is the opportunity cost of funds -ie: the highest return on another investment or through the bank For public projects, the public sector discount rate is harder to calculate -Is the project funding through reducing: 1) Private investment or 2) Private consumption

17. 1) Private Investment Funding Assume that funding a public project decreases private investment. Ie: A new road costs $10,000, but the private sector would have used that $10,000 to make $2,000 – 20% return. In this case the public sector discount rate is the private sector’s before-tax return.

18. 2) Private Consumption Funding Assume that funding a public project decreases private consumption. Ie: If the private sector consumes $10,000, that could have made 20% return, or $2,000. If tax is 50%, they are effectively giving up $1,000 or 10% return. In this case the public sector discount rate is the private sector’s after-tax return.

19. Public Sector Discount Rate Difficulty Typically, government funding decreases both private consumption and private investment. Ie: If $10,000 funding decreased consumption and investment by $5,000 each, r = (20%)/2+(10%)/2=15% -But it is hard to calculate impact on consumption and investment, and this impact changes with each tax

20. Theory - Social Discount Rate Some argue that a SOCIAL RATE OF DISCOUNT is more appropriate, representing the value SOCIETY places on decreased consumption. SOCIAL DISCOUNT RATE is less than market rate of return for 3 reasons: • Concern for future generations • Paternalism • Market Inefficiency

21. 1) Concern for Future Generations One may argue that the private sector has a high discount rate, heavily discounting benefits to future generations -Therefore the social discount rate should be lower to take the future into account BUT -The government is not fully omniscient and benevolent towards future generations -Plus projects with long-term benefits should have long-term profits, expressed in the rate of return

22. 2) Paternalism Even if people are selfish, they may not be far-sighted enough to take the future into account (“I’ll never get sick – I don’t need to save”) -The government would use the discount rate people would use if they knew better -the government is paternalistic – forcing decreased consumption now in order to save for the future BUT Should public preference be forced upon people?

23. 3) Market Inefficiency Often private investment results in positive externalities. -These positive externalities are UNDERPROVIDED -A lower social discount rate can correct this inefficiency BUT -How big is this externality? -Would a subsidy make more sense (chapter 5)

24. Public Discount Rate Conclusion -The arguments for a social discount rate instead of a market discount rate still fail to provide for a specific discount rate -Typical discount rates fall between the before-tax and after-tax private sector rates of return -The Treasury Board Secretariat (1976) “recommended the use of a social discount rate of 10 per cent, and of 5 and 15 percent for sensitivity analysis” -If PV is positive with all these rates, a good argument exists for doing the project

25. Theory - Valuing Public Benefits and Costs Private benefits and costs are easy to calculate – revenue and expenditures. Public benefits and costs are harder to calculate since SOCIAL costs and benefits may not be reflected in market prices. Some approaches and considerations are: • Market Prices (SMC) • Shadow/Adjusted Market Prices (SMC) • Consumer/Producer Surplus (SMB) • Inferences from Economic Behavior • Valuing Intangibles

26. 1) Market Prices If the First Fundamental Theorem of Welfare Economics holds, then -P=SMC; we have Pareto Efficiency -In this case market prices can be used for project valuation Even if the Theorem fails, market prices are often used because: • Market prices are simple and straightforward • Other measures are: • Complicated and questionable • Time consuming and costly to calculate

27. 2) Adjusted Market Prices The SHADOW PRICE of a commodity is its underlying social marginal cost in an imperfect market SHADOW PRICE relates to MARKET PRICE depending on how the market reacts to government intervention. Ie: a) Monopoly b) Taxes c) Unemployment

28. 2a) Monopoly and Shadow Price In a monopoly, P>MC i) If use of a monopoly input increases its production by the full amount, MC = SHADOW PRICE ii) If the project consumes inputs that are taken directly from the private consumer, PMonopoly = SHADOW PRICE iii) If production is increased somewhat, PMonopoly < SHADOW PRICE < MC (weighted average)

29. 2b) Tax and Shadow Price Taxes force Pconsumer>Pproducer i) If production of the fully expands, Pproducer = SHADOW PRICE ii) If the project consumes inputs that are taken directly from the private consumer, Pconsumer = SHADOW PRICE iii) If production increases somewhat, Pproducer < SHADOW PRICE < Pconsumer (weighted average)

30. 2c) Unemployment and Shadow Price Employment in government projects can come from other jobs or the unemployed i) If a worker is hired away from another job, WagePrivate Sector = SHADOW PRICE ii) If the worker doesn’t leave another job, things are more complicated: -is the worker taking someone else’s job? WagePrivate Sector = SHADOW PRICE -would the worker have found a job? -what is the worker’s opportunity cost of leisure?

31. 2c) Unemployment and Shadow Price -Forcasting future employment is difficult -Fully understanding unemployment is difficult (in 2011 Alberta had both high vacancies and higher unemployment due to imperfect job matches) -Without a major recession, it is assumed that WagePrivate Sector = SHADOW PRICE

32. 3) Consumer/Producer Surplus Typically, private firms have little effect on the price of a commodity in the market The government, however, can have a huge impact on the price of a commodity in a market -How should the project be valued? -Pre-project prices? -Post-project prices? -Somewhere in between? -A good alternative is to calculate change in producer and consumer surplus

33. Consumer Surplus Consumer Surplus Equilibrium Or market Price P S P* D Q Q* Originally, consumer surplus is calculated as the area below demand and above equilibrium price

34. Consumer Surplus Consumer Surplus P S’ S P* P’ D Q Q* Q’ If a government policy increases supply, consumer surplus also increases.

35. Producer Surplus Producer Surplus Equilibrium Or market Price P S P* D Q Q* Originally, producer surplus is calculated as the area above supply and below equilibrium price

36. Producer Surplus Producer Surplus P S’ S P* P’ D Q Q* Q’ If a government policy increases supply, producer surplus also changes (depending on who is producing the good).

37. Old Surplus Producer Surplus Consumer Surplus P S’ S P* P’ D Q Q* Q’

38. New Surplus Producer Surplus Consumer Surplus P S’ S P* P’ D Q Q* Q’

39. Gained Surplus P S’ S P* P’ D Q Q* Q’ Note that since producer surplus is lost, businesses are hurt, possibly having negative consequences (unemployment?)

40. 4) Inferences from Economic Behavior If no market exists for a commodity, other strategies must be used to estimate costs or benefits such as: a) The value of time b) The value of life i) Lost earnings ii) Probability of Death

41. 4a) The Value Of Time Often public projects save time, or (temporarily or permanently) cost time: ie: Edmonton LRT saves time compared to the bus ie: Edmonton bridge construction slows traffic until its done; closing of Keillor Road increases travel time And “time is money”

42. 4a) The Value Of Time The theory of leisure-income choice states that people will work up until the point where their wage is equal to their value of one extra hour of leisure. If AFTER-TAX WAGE > Leisure value, the person will work If AFTER-TAX WAGE < Leisure value, the person will relax Therefore one could value time saved as the AFTER-TAX WAGE RATE.

43. 4a) The Value Of Time BUT: • Some people can’t choose how many hours they work (ie: as involuntary unemployment) • Not all time away from a job is equal -ie: someone who likes the bus may have a lower opportunity cost of time -ie: someone who hates the morning commute may have a higher opportunity cost of time

44. 4a) The Value Of Time Alternately, one could compare the cost of slow and fast travel ie: (Cost of a taxi)-(Cost of the bus) = value of time saved by using a taxi BUT Other things affect choice of travel (fear of taxis, income, environmental concerns) Typically, travelling time cost is estimated at about 50% of before-tax wage rate (Small, 1992)

45. 4b) The Value Of Life Life is priceless But Resources ($) are limited Therefore Life has a dollar value attached A community hospital has $1 million in funding. Does it spend it on an MRI to catch obscure diseases and save 4 young adult lives, or on flu clinics to save 10 elderly lives?

46. 4b) The Value Of Life Question Approximately 200 people die of the flesh-eating disease (Necrotizing Fasciitis) each year. Assume that if all the resources spent on the internet were redirected to this disease (internet would shut down), these deaths would be prevented. Is it worth it? What if only youtube shut down? Itunes?

47. 4b) The Value Of Life Unfortunately, as an aggregate society we need to quantify the value of life. Two methods of assigning finite value to human life are: i) Lost Earnings ii) Probability of Death

48. 4bi) Lost Earnings Law courts often consider the present value of a person’s lifelong earnings when assigning compensation to relatives of fatal accidents. This is one way to estimate the value of life BUT It assigns a value (benefit) of ZERO to the old and retired. Since everyone in society carries a cost, cost benefit analysis would execute the old and retired. This is unacceptable.

49. 4bii) Probability of Death A better value of life is determined through varying the probability of death. (As most projects affect the probability of death; they don’t guarantee avoiding death forever). People often accept a probability of death to save time or make money in their everyday lives (driving without snow tires, driving a small car, taking a dangerous job). The change in probability of death and money value can be used to calculate value of life.

50. 4bii) Probability of Death Studies have used this device to put the value of a life between $4 million US and $10 million US (Viscusi, 2006) -This is a great range, but still allows reasonable projects (ie: safety rails) and argues against “unreasonable” projects (ie: Asbestos removal: $100 million per life saved) -This approach is still controversal. A new cancer treatment reducing probability of death by 0.01% takes on new meaning if you need the treatment.