Econ 309 Cost-Benefit Analysis Lecture Notes

I. Review of tools

a. Opportunity cost: What do we give up to get something? Is it worth it?

b. Present discounted value of $X in n years at interest rate r = $X/(1+r)ⁿ

c. Present discounted value of $C per year forever at interest rate r = $C/r

d. From (a) and (b) you can derived PV formulas for just about anything you could need.

II. Cost-Benefit Analysis: What government policies are worth pursuing?

a. Does the present value of benefits exceed present value of costs?

b. Many fallacies are commonly invoked in such computations.

i. “Costs are dollar costs.” Social cost differs from cash-flow accounting, importance of opportunity costs, use of resources for other purposes. Pure transfers not a social cost!

ii. “This will create jobs!” Labor is a cost, not a benefit.

iii. “This new road will bring in business for local stores!” But if total demand is constant, it will draw business away from other stores (“crowd out other business).

iv. “This new road will increase land values!” But if total demand is the same, it will reduce land values elsewhere.

v. “It will increase housing values AND shorten commutes!” But this is double-counting in addition to ignoring negative side effects on housing prices elsewhere.

c. Difficulties in valuing things for which there are no market prices. Human lives? ANWR? Snail darters? Spotted owls? World temperatures? Clearly these values are greater than zero, but less than infinity. Difficulties of “contingent valuation.”

d. Importance of the choice of discount rate. (“You get me the project you want to do; I’ll find you the discount rate to make it work.”)

i. Suppose that a project, once built, would deliver $100 million of benefits per year forever, but that it would cost $200 million per year for four years to build it. Let the discount rate r = 10%.

ii. PV($100 million per year forever, starting in one year, at 10% discount rate) = $100 million/r = $1,000 million.

iii. PV($100 million per year forever, starting in five years, r= 10%) = (1/(1+r)⁴)*($100 million/r) = 0.68*$1,000 million = $683 million

iv. Suppose that the cost of building this project is $200 million per year for four years, starting next year.

v. PV($200 million per year for four years, starting next year, r=10%) = $200/r – ($200/r)*(1/(1+r)^4) = $634 million

vi. At r of 10%, PV of net benefit of project= $683 million - $634 million = $49 million

vii. At r of 11%, PV of net benefit of project= $599 million - $620 million = -$21 million

e. What discount rate to use? Long term government borrowing rate? Pre-tax corporate return? Effects of DWL of taxation.

f. What does government actually do? (Bazelon & Smetters, Journal of Economic Perspectives, 1999)

i. When discounting benefits or costs that are completely certain, we should use a “risk free” rate, generally taken to be the rate on US Treasury Bills (3 month government bonds, although these do have some small inflation and tax risk).

ii. When corporations evaluate projects, higher discount rates are generally used with riskier projects (the desire is for “comparable risk-rate of return” tradeoffs). With government this is rarely done.

iii. Office of Management and Budget (OMB): 7%, their estimate of the pre-tax rate of return on private-sector projects.

iv. However, on very long term projects the OMB uses 2%, their estimate of the consumption rate of time preference (intertemporal marginal rate of substitution over time), which should be equivalent to the after-tax rate of return.

v. In federal budgeting: Any new tax cut or spending program is considered for whether it will throw the budget out of balance over the next five years, effectively using a zero discount rate ($1 billion more spending now can be balanced off by $1 billion more in taxes five years from now.)

vi. In federal budgeting: Costs beyond five years out are discounted at infinity, that is, they are ignored. Gaining $1 billion now, but losing $100 billion in ten years would be judged a project that would bring a surplus to the government. D’oh!

g. Is this a good method? Many people hate it. Churchill’s joke about democracy.

III. What is a human life worth, statistically speaking?

a. This is a key factor in determining what sorts of social costs we undertake to prevent probable future deaths. And also, what costs we don’t undertake. Minnesota bridges anyone?

b. PV of future wages? (9/11) Value of leisure?

c. Wage premia for risky jobs? (Compensating differentials)

d. How much more do safer cars cost?

e. Government revealed preference: What is the cost per life saved of various government rules?

i. Vioxx was great for treating stomach problems, but it lead to an increase in heart attacks. Was removing it from use a good decision? What was the cost in terms of loss of its usefulness per life saved? Research continues:

ii. Childproof lighters: $100,000/life saved.

iii. Flame retardant child pajamas: $2,400,000

iv. Full belts in cars: $5,000,000

v. Asbestos ban: Somewhere between $6,000,000 to $85,000,000?

f. Kid down the well paradox: Do we make good decisions ex ante and ex post?