Cost-Benefit Analysis CHAPTER 8 Cost-Benefit Analysis McGraw-Hill/Irwin Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Projecting Present Dollars into the Future RT = R0*(1+r)T one click per line
Projecting Future Dollars into the Present RT = R0*(1+r)T 5 lines visible 1st click – 6th line 7th click – “Present Value” 8th click – “discount rate” 9th click ‘ discount rate arrow disappears, bracket appears, “discount factor” Present Value R0 = RT/(1+r)T discount rate discount factor
Present Value of a Stream of Money
Inflation
Private Sector Project Evaluation Annual Net Return PV Year R&D Advertising R = $1,000 -$1,000 $150 $200 1 600 0.01 128 165 2 0.03 86 98 3 550 1,200 0.05 46 37 0.07 10 -21 Admissible Preferable Present Value Criteria
Internal Rate of Return Project Year 0 Year 1 ρ Profit PV X -$100 $110 10% $4 3.77 Y -$1,000 $1,080 8% $20 18.87
Benefit-cost ratio = B/C
Problems with the Benefit-Cost Ratio Method B C B/C I $250 $100 2.5 II $200 2.0 I: Subtract $40 mistake from B $210 2.1 I: Add $40 mistake to C $140 1.79
Discount Rate for Government Projects Returns in Private Sector Social Discount Rate Paternalism Market Inefficiency Discounting and the Economics of Climate Change Government Discounting in Practice
Valuing Public Benefits and Costs Market Prices Adjusted Market Prices Shadow price Monopoly Taxes Unemployment Consumer Surplus e Price per pound of avocados b d Sa $2.89 c g Sa’ 1st click – left-hand side text line-by-line 2nd click - axes and labels, D, S, A, d, and g 3rd click – S’, A1 $1.35 Da Pounds of avocados per year A0 A1
Inferences from Economic Behavior The Value of Time The Value of Life Lost earnings Probability of death
Valuing Intangibles Subverting cost-benefit exercises Reveal limits on intangibles Cost-effectiveness analysis
Games Cost-Benefit Analysts Play The Chain-Reaction Game The Labor Game The Double-Counting Game
Distributional Considerations Hicks-Kaldor Criterion – a project should be undertaken if it has positive net present value, regardless of distributional consequences Government costlessly corrects any undesirable distributional aspects Weighted benefits
Uncertainty Certainty Equivalent Project Benefit Probability EV X $1,000 1.00 Y 0.50 $2,000 Certainty Equivalent
Are Reductions in Class Size Worth It? Discount rate Costs Benefits The Bottom Line and Evaluation
Use (and Nonuse) by Government Using Cost-Benefit Analysis Not Using Cost-Benefit Analysis Clean Air Act Endangered Species Act Food, Drug, and Cosmetic Act
Calculating the Certainty Equivalent Value Utility U(E + y) U* U(E) Certainty Equivalent Expected income E C I* E + y Income per year