Chapter 7: Cost Benefit Analysis The best way to evaluate a government policy is through the social welfare function W=f(U 1, U 2…) BUT, this function is difficult to accurately calculate. A more practical way to evaluate public expenditure is through COST-BENEFIT ANALYSIS. 1
Chapter 7: Cost-Benefit Analysis Ø Present Value Calculations and Alternatives Ø Public Sector Discount Rate Ø Calculating Public Costs and Benefits Ø Cost-Benefit Analysis Errors Ø Distribution Ø Uncertainty
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 Year Calc. 1 Amount 100. 00 2 100*1. 02 102. 00 3 100*1. 022 104. 04 4 100*1. 023 106. 12 5 100*1. 024 108. 24
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
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
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
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)t is often referred to as the DISCOUNT FACTOR This PV formula changes if a stream of income occurs:
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.
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)
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:
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.
Theory - Present Value Criteria A firm will undertake projects based on the following: 1) A firm will only undertake projects whose PV is positive 2) If given a choice between many mutually exclusive projects, it will chose the one with the highest PV
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)
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
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 net PV could have a B/C value of only 1. 1
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 16
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. 17
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. 18
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 19
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: 1) Concern for future generations 2) Paternalism 3) Market Inefficiency 20
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 21 return
2) Paternalism Even if people are selfish, they may not be farsighted 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? 22
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) 23
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 24 argument exists for doing the project
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: 1) Market Prices (SMC) 2) Shadow/Adjusted Market Prices (SMC) 3) Consumer/Producer Surplus (SMB) 4) Inferences from Economic Behavior 25 5) Valuing Intangibles
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: 1) Market prices are simple and straightforward 2) Other measures are: a) Complicated and questionable 26 b) Time consuming and costly to calculate
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 27
2 a) 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) 28
2 b) 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) 29
2 c) 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, Wage. Private Sector = SHADOW PRICE ii) If the worker doesn’t leave another job, things are more complicated: -is the worker taking someone else’s job? Wage. Private Sector = SHADOW PRICE -would the worker have found a job? -what is the worker’s opportunity cost of 30 leisure?
2 c) 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 Wage. Private Sector = SHADOW PRICE 31
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 32 producer and consumer surplus
P Consumer Surplus S Consumer Surplus Equilibrium Or market Price P* D Q* Q Originally, consumer surplus is calculated as the area below demand above equilibrium price 33
P Consumer Surplus S’ S P* Consumer Surplus P’ D Q* Q’ Q If a government policy increases supply, consumer surplus also increases. 34
Producer Surplus P S Equilibrium Or market Price P* Producer Surplus D Q* Q Originally, producer surplus is calculated as the area above supply and below equilibrium price 35
P Producer Surplus S’ S P* P’ Producer Surplus D Q* Q’ Q If a government policy increases supply, producer surplus also changes (depending on who is producing the good). 36
Old Surplus P S’ S Consumer Surplus P* P’ Producer Surplus D Q* Q’ Q 37
New Surplus P S’ S P* P’ Consumer Surplus Producer Surplus D Q* Q’ Q 38
P Gained Surplus S’ S P* P’ D Q* Q’ Q Note that since producer surplus is lost, businesses are hurt, possibly having negative consequences (unemployment? ) 39
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 40
4 a) 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” 41
4 a) 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 42 AFTER-TAX WAGE RATE.
4 a) The Value Of Time BUT: 1) Some people can’t choose how many hours they work (ie: as involuntary unemployment) 2) 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 43
4 a) 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) 44
4 b) The Value Of 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? 45
4 b) 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? 46
4 b) 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 47
4 bi) 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 48 retired. This is unacceptable.
4 bii) 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 49 value can be used to calculate value of life.
4 bii) 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 50 treatment.
5) Valuing Intangibles Some costs and benefits seem impossible to value (ie: pride at winning Olympics) 3 issues arise from intangibles: a) Intangibles can subvert the entire cost-benefit exercise. b) Cost-benefit analysis can force planners to put a limit on the value of intangibles c) Even if intangibles can’t be measured, alternative measures be examined to find the cheapest possible 51
5 a) Intangibles can ruin everything -if you complain or believe that an intangible cost or benefit is big enough, you can approve or deny many projects ie: “Losing the Oilers would be unbearable, we should build them a new arena!” “The piece of mind is worth it, buy the warrantee!” “PS 3 - $300. Giving your boyfriend the best 52 birthday gift ever – priceless. ”
5 b) Intangible Value Limit Decisions can reveal the value of an intangible: If, for the Oiler’s Arena, (Cost-Benefits)=$50 million, and the city DOES build the arena, the Oiler’s are worth at least $50 million Ie: If the cost of a laptop is $1000, with a $200 warrantee, and the laptop failure rate is 5%, (Cost-Benefits)=$200 -$50=$150, and someone DOESN’T buy the warrantee, laptop peace of mind is worth less than $150 53
5 c) Cheapest Method to achieve Intangibles Cost-effectiveness analysis can be used to chose an option to achieve a benefit that can’t be measured. ie: If you can’t put a value on health, you don’t need a gym membership ($600/year), when you can walk or run outside or at a mall ($0/year). 54
Theory - Cost-Benefit Analysis Errors We’ve already discussed a variety of issues with cost-benefit analysis. Tresch (2002) noted the following common errors in cost-benefit analysis: 1) The Chain-Reaction Game 2) The Labour Game 3) The Double-Counting Game 55
1) The Chain-Reaction Game Often proposals consider SECONDARY profits arising from their benefits. ie: A downtown arena produces $1 million profit itself and increases local business profit by $4 million BUT, if you consider secondary benefits, one must also consider secondary COSTS ie: Moving the arena from the Northeast would hurt Northeastern businesses by $X million. Often secondary benefits are simply transfers 56 across individuals.
2) The Labour Game Often a project calls “creating employment” a benefit. BUT wage rates are a COST. As mentioned earlier, for the truly involuntary unemployed, social cost is less than wage. 57
3) The Double-Counting Game One can’t count the benefit of two mutually exclusive uses of a commodity (ie: selling and farming on farmland) ie: If the government provides housing for low income families, the benefit is either: 1) Housing low income families Or 2) Selling the house on the market Not both. 58
Theory - The Problem of Distribution In PRIVATE projects, distribution is irrelevant -if the present value is positive, it is assumed that the winners COULD compensate the losers -The POTENTIAL PARETO IMPROVEMENT CRITERION -The HICKS-KALDOR CRITERION -Public projects can be based on this POTENTIAL gain in social welfare -Some can endure cost as long as others 59 gain more benefits
The Added Problem of Distribution ON TOP of the cost-benefit calculation, one could also be concerned about DISTRIBUTION. We can AVOID this problem by assuming that: 1) The government can costlessly transfer between winners and losers 2) This transfer is nondistortionary Ø This assumption is difficult to justify 60
The Added Problem of Distribution We can ADDRESS this problem by assuming that certain members of society are especially deserving -A dollar benefit to these members is greater than a dollar benefit to others BUT: 1) Who is more deserving (poor, disabled, hard workers, women, men)? 2) How much more than a dollar ($1. 10, $2)? POLITICS now complicates the issue. 61
Theory – The Problem of Uncertainty Often the costs and benefits of a project are UNCERTAIN. (ie: Vaccines MAY prevent the swine flu, or they may go to people who were at no risk. ) Costs and Benefits must therefore be converted to CERTAINTY EQUIVALENTS – the amount of certain cost or benefit that a person would trade for an uncertain cost or benefit scheme. 62
Uncertainty Example 1 Many game shows give an opportunity for the winner to keep their winning or RISK IT ALL (ie: pick what’s in case #2). Assume a suitcase can hold $0 with a probability of 0. 5 and $20, 000 with a probability of 0. 5 E($)=$0(0. 5)+$20, 000(0. 5)=$10, 000 If a contestant would take the chance UNTIL his winnings increased to $4, 000, that would be his CERTAINTY EQUIVALENT. 63
Uncertainty Example 2 Jonah wants a laptop. He can buy a Whale laptop worth $1000 or a Ninva laptop worth $600 with a 4 -year warrantee. (Same price) From Gartner (2006) we can infer a 25% failure rate on laptops over 4 years. Ninva: Benefit=$600 Whale: Benefit=$1000(0. 75)+0(0. 25)=$750 If Jonah is indifferent between laptops, he has a 64 CERTAINTY EQUIVALENT of $600
Chapter 7 Summary Ø Since costs and benefits occur over time, their PRESENT VALUE must be calculated Ø Typically, the public sector discount rate (r) is: before tax return>r>after-tax return Ø Alternatively, social discount rates argue for less than public sector discount rates Ø Costs and benefits can be measured at market prices or shadow prices Ø Labour costs are calculated considering unemployment and chance to remain 65 unemployed
Chapter 7 Summary Ø Consumer and Producer surplus can be effective ways of measuring costs and benefits Ø The prices of some nonmarket commodities (time, life) have to be inferred from observing behavior Ø Some intangible benefits cannot be measured Ø In cost benefit analysis, never: count secondary benefits without secondary costs, view wages as a benefit, or double-count Ø Distributional issues and uncertainty further 66 confuse cost-benefit analysis
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