1. AGEC 608 Lecture 08, p. 1 AGEC 608: Lecture 8 Objective: Examine the “theoretically correct” measure of willingness to pay when individuals face uncertainty Readings: –Boardman, Chapter 8 Homework #2: Chapter 3, problem 1 Chapter 3, problem 2 Chapter 4, problem 3 due: today Homework #3: Chapter 4, problem 2 Chapter 5, problem 1 Chapter 6, problem 4 due: March 27

2. AGEC 608 Lecture 08, p. 2 Three issues to consider 1. Ex Ante Willingness to Pay (Option Price) how much would people pay (in advance) for a project with uncertain contingencies? 2. Bias in Expected Surplus what is the sign of an “option value”? 3. Expected surplus as a practical measure if risks are individual, rather than collective, then expected surplus might be “good enough”

3. AGEC 608 Lecture 08, p. 3 1. Option Price Goal: determine how much people would pay (in advance) for a project with outcome that arise under uncertain circumstances. Uncertainties relate to the individual – e.g. uncertainty regarding disease infection, side effects, etc. How to value gov’t projects that increase or reduce risks to individuals?

4. AGEC 608 Lecture 08, p. 4 Example 1: dam Policy RiskDamNo Dampipi Wet1101000.50 Dry100500.50 Expected Value10575 Surplus1050 Expected surplus = ½ (10) + ½ (50) = 30 This is the “typical” measure of benefits used in CBA (ignores option price)

5. AGEC 608 Lecture 08, p. 5 Example 1: dam Policy RiskDamNo Dampipi Wet1101000.50 Dry100500.50 Expected Value10575 Variance25625 Note that the dam reduces income risk: income variance is 25 with dam but 625 without dam.

6. AGEC 608 Lecture 08, p. 6 Option price = the maximum the farmer would be willing to pay for the dam = the dollar payment that provides the same expected utility with the dam as without the dam (and without the payment) To find the option price we need to know the farmer’s utility function. Normally we don’t know this.

7. AGEC 608 Lecture 08, p. 7 Option price See Figure 8.1 – utility function: U=ln(x) Without the dam, the farmer gets $50 if it is dry and $100 if it is wet: U(50) = 3.91, U(100) = 4.60 Wet and dry are equally likely, so expected utility is: EU=0.5U(50) + 0.5U(100) = 4.26 With the dam, the farmer gets $100 if it is dry and $110 if it is wet: U(100) = 4.60, U(110) = 4.70 How much would the farmer be willing to pay to get the dam? He must have the same utility with dam (and payment) as without dam: EU=0.5U(110-OP) + 0.5U(100-OP) EU = 4.26 so solve: 4.26=0.5U(110-OP) + 0.5U(100-OP) for U=ln(x) OP = $ 34

8. AGEC 608 Lecture 08, p. 8 Option Price In this example, building the dam increases the individual’s expected utility. Expected surplus = 30 (positive) Option price = 34 (positive) Option price is greater than expected surplus. So the dam should be built: it has a positive expected surplus and increases welfare.

9. AGEC 608 Lecture 08, p. 9 Example 2: bridge Policy RiskBridgeNonepipi No quake2001000.80 Quake100800.20 Expected Value18096 Surplus10020 Expected surplus =.8 (100) +.2 (20) = 84 This is the “typical” measure of benefits used in CBA (ignores option price)

10. AGEC 608 Lecture 08, p. 10 Example 2: bridge Policy RiskBridgeNonepipi no quake2001000.80 quake100800.20 Expected Value18096 Variance160064 Note that the bridge increases income but also increases risk: income variance is higher with bridge than without.

11. AGEC 608 Lecture 08, p. 11 Option price assume utility function: U=ln(x) Without the bridge: U(100) = 4.60, U(80) = 4.38 Pr(quake)=0.20, Pr(no quake) =0.80, so expected utility is: EU=0.2U(80) + 0.8U(100) = 4.56 With the bridge: U(200) = 5.30, U(100) = 4.60 How much would the person be willing to pay to get the bridge? She must have the same utility with bridge (and payment) as without: EU=0.8U(200-OP) + 0.2U(100-OP) EU = 4.56 so solve: 4.56=0.8U(200-OP) + 0.2U(100-OP) for U=ln(x) OP = $ 71

12. AGEC 608 Lecture 08, p. 12 Option Price In this case, building the bridge would reduce the individual’s expected utility. Expected surplus = 84 (positive) Option price = 71 (positive) Option price is less than expected surplus. E(S) > 0, but the bridge should not be built because it reduces the individual’s welfare.

13. AGEC 608 Lecture 08, p. 13 Key insight In general, if individuals are risk averse, then expected surplus can either underestimate or overestimate the option price, depending on the source of risk.

14. AGEC 608 Lecture 08, p. 14 2. Option Value If an individual does not currently use a resource, might he or she nevertheless value it? Option Value refers to the value someone assigns to a resource because he or she values the opportunity of future use. Standard definition: OV = OP – E(S) For the dam, OV = $34 – $30 = $4.

15. AGEC 608 Lecture 08, p. 15 Key insight Option value may be positive or negative. In addition, it is typically very difficult to assign a sign or magnitude (theoretically) to OV. It is very difficult to measure in practice. Bequest value is an additional value: the value someone assigns to a resource because he or she values the use by others in the future. Existence value: non anthropocentric value

16. AGEC 608 Lecture 08, p. 16 Catalog of values: Net benefits Expected surplus Quasi-option value Option value Option price Bequest value Existence value

17. AGEC 608 Lecture 08, p. 17 Practical considerations: 1. Society should be risk neutral 2. Individual risks are typically pooled 3. It is difficult to measure OV, OP, etc. Expected Surplus is the practical measure for most CBAs.