1. Continuation of benefit estimation and non-renewable resources Econ 1661 Review Section February 25 th, 2011 Robyn Meeks (Based on slides from Avinash Kishore and Matt Ranson) 1

2. Lots to catch up on today Part 1: Benefit estimation – Complete review of remaining methods – This will be a quick review to make sure we get to practice problem, but if you have additional questions please come to office hours. Part 2: Non-renewable resources – Review two-period model – Go through practice problem 2

3. Part 1: Benefit estimation methods (List from Prof. Stavins’ course flow chart) Revealed preference – Recreation demand models – Hedonic pricing Property Wage – Averting behavior – Cost of illness – Non-methods Avoided cost Stated preference – CV – Others 3

4. Hedonic pricing models These models use attributes of market products, including environmental attributes to explain variation in product prices P = f (x, z, e) – P: price of market product (e.g., house) – x: vector of non-env. product attributes (e.g., lot size, bedrooms) – z: vector of non-env. local attributes (e.g., crime rate) – e: environmental attribute (e.g., local air pollution) Marginal implicit price of environmental attribute or marginal willingness to pay for environmental attribute: 4

5. Hedonic pricing model example Suppose we wanted to study the variation in housing prices due to proximity to an airport (which generates noise, a negative environmental externality) Price = β 0 + β 1 *Bedrooms + β 2 *Bathrooms + β 3 *Airport + β 4 *Crime + β 5 *Scores + β 6 *Sold2008 + error – Price: Sale price of house in dollars – Number of Bedrooms – Number of Bathrooms – Near Airport: Dummy variable equal to 1 if the house is near the airport and 0 otherwise (so coefficient is not a slope in this case) – Crime Rate: Annual number of incidents per 10,000 population – Test Scores: Average test scores at public high school (out of 100) – Sold in 2008: Dummy variable equal to 1 if the house sold this year Running this regression, we are interested in β 3 Other applications: estimate how much people value air quality, visibility 5

6. Issues with hedonic pricing models Simultaneity: Prices are determined by both supply and demand, but these models treat supply as exogenous (i.e., unaffected by environmental attributes). If supply is elastic, then could also see an increase in available land. Selection: Individuals differ in their tolerance of negative environmental attributes. Those most tolerant of pollution will be located in dirty areas. Information: Individuals’ perceptions of environmental attributes may differ from measurements. Omitted variable bias: Coefficients are too large or small if an explanatory variable associated with the dependent variable and correlated with other explanatory variables is left out Scope: Relatively narrow range of applications 6

7. Contingent valuation Use carefully designed surveys to elicit value individuals place on a change in environmental quality or service – This is hypothetical elicitation – Can be used when revealed preference methods aren’t possible and to elicit non-use value Issues/problems with CV – Information: Respondents may not know much about the environmental amenity or service or the change – Hypothetical bias: Respondents may not give accurate values because the payment or acceptance is hypothetical – Strategic response: Respondents may not give accurate values because they want to influence environmental policy – Anchoring: Responses may be sensitive to starting points – Warm glow: Respondents may give accurately high values to make themselves feel good about their environmentalism 7

8. Valuing Mortality Risk Reductions Calculate the benefits of public policies that reduce mortality – People male tradeoffs between mortality risk and money in their day-to-day lives – We can estimate the tradeoffs using several methodologies Hedonic wage method: job safety vs. Wage Averting behavior method: water filter vs. filter cost Stated preference method: risk of cancer vs. WTP for hypothetical vaccine – Studies give the $/incremental mortality risk reduction – Can use this to calculate VSL: 8

9. Valuing Mortality Risk Reductions Example – We observe that miners working in particularly dangerous mines are paid higher wages. – We conduct an hedonic wage study and find: MWTA of $6 per incremental.000001 increase in risk of death – We calculate VSL: VSL = $6 /.000001 = $6 million – We can now use benefits transfer to apply this VSL to estimate the benefits of an industrial safety regulation that prevents 100 deaths Benefits = 100 deaths * $6 million = $600 million 9

10. Part 2: Non-renewable resources outline Static versus dynamic efficiency Two-period model – Mathematical solution – Graphical Solution Resource prices and Hotelling Rule 10

11. Static vs. dynamic efficiency Static efficiency – Economically efficient allocation maximizes net benefits (TB-TC) – At this point MB=MC – Key: incremental benefits associated with the last unit preserved are exactly equal to the incremental opportunity cost of preserving the last unit Dynamic efficiency – Economically efficient allocation maximizes the present value of net benefits – At this allocation, PV (Marginal Net Benefits) are equal across time periods Discounting: present value = future value / (1+r) t – Trading off the consumption in different time periods, subject to budget constraint (total stock of resource) – Dynamically efficient allocation: requires that present value of the marginal net benefit from the last unit in Period 1 equals the present value of the marginal net benefit in Period 2 (for 2 period model) 11

12. Non-renewable resources: dynamic efficiency Dynamically efficient allocation: PDV [MNB 1 (q 1 )] = PDV [MNB 2 (q 2 )] This allocation maximizes the present value of net benefits 12

13. Price = MUC + MEC Marginal extraction cost (MEC) Marginal user cost (MUC): “scarcity rent” is the opportunity cost of forgone future consumption is the additional marginal value of a resource due to its scarcity If MUC = 0 and P = MEC, then the resource is not economically scarce Non-renewable resources: dynamic efficiency 13

14. Two-period non-renewable resource model Basic setup: – There are two periods. – There is a total stock of 20 units of oil in the ground. – Consumer demand for oil is: q 1 (p 1 ) = 20 – 2.5p 1 in period 1  p 1 (q 1 ) = 8 -.4q 1 q 2 (p 2 ) = 20 – 2.5p 2 in period 2  p 2 (q 2 ) = 8 -.4q 2 – The marginal cost of extracting the resource is: MEC 1 = 2 in period 1 MEC 2 = 1 in period 2 (because of improved technology) – The interest rate is r =.1 14

15. Question: What are the socially optimal quantities of resource extraction in the two periods? Answer: Socially optimal implies that we want to choose q 1 and q 2 to maximize the present discounted value of the net benefits of oil extraction in the two periods. So, we want to maximize: PDV[NB 1 (q 1 )]+PDV[NB 2 (q 2 )]...while taking into account the stock constraint: q 1 +q 2 = 20. Two-period non-renewable resource model 15

16. Mathematical solution Two equations define the optimal extraction in the two periods: – Condition #1 (Maximization): PDV [MNB 1 (q 1 )] = PDV [MNB 2 (q 2 )] This equation says that when the PDV of net benefits is maximized, the PDV of the marginal net benefits in period 1 must equal the PDV of the marginal net benefits in period 2. If this weren't true, then we could increase the discounted net benefits by switching a unit of extraction from period 1 to 2 (or vice versa), and so we wouldn't be at a maximum. – Condition #2 (Constraint): q 1 +q 2 = 20 This is just the constraint that we can't extract more oil than we have. 16

17. The steps to find the optimal q* 1 and q* 2 : – Step 1: Write down marginal extraction costs in each period. MEC 1 = 2 in period 1 MEC 2 = 1 in period 2 – Step 2: Write down marginal benefits in each period. Remember that marginal benefits are given by the inverse demand function. MB 1 (q 1 ) = p 1 (q 1 ) = 8 -.4q 1 MB 2 (q 2 ) = p 2 (q 2 ) = 8 -.4q 2 – Step 3: Calculate marginal net benefits in each period. Marginal net benefits are just equal to marginal benefits minus marginal extraction costs. MNB 1 (q 1 ) = MB 1 (q 1 ) - MEC 1 (q 1 ) = 8 - 4q 1 - 2 = 6 -.4q 1 MNB 2 (q 2 ) = MB 2 (q 2 ) - MEC 2 (q 2 ) = 8 - 4q 2 - 1 = 7 -.4q 2 Mathematical solution 17

18. – Step 4: Write down the present discounted value of marginal net benefits in each period. Remember that the PDV of x dollars t years from now at interest rate r is PDV = x / (1+r ) t PDV [MNB 1 (q 1 )] = (1+.1) 0 * (6 -.4q 1 ) = 6 -.4q 1 PDV [MNB 2 (q 2 )] = (1+.1) -1 * (7 -.4q 2 ) = 6.363 -.363q 2 – Step 5: Write down conditions #1 and #2. Condition #1: Maximization PDV[MNB 1 (q 1 )] = PDV[MNB 2 (q 2 )], which we can rewrite as: 6 -.4q 1 = 6.363 -.363q 2 Condition #2: Constraint – q 1 +q 2 = 20 Mathematical solution 18

19. Step #6: We finally have two equations (Conditions #1 and #2) and two unknown variables (q 1 and q 2 ). We can now use algebra to solve for the socially optimal q* 1 and q* 2 : 6 -.4(20 - q 2 ) = 6.363 -.363q 2  q* 2 = 10.952 q 1 + 10.952 = 20  q* 1 = 9.048 So, in this example, the socially optimal quantity of extraction is higher in period 2. Even though net benefits in period 2 are discounted, the marginal cost of extraction is lower in period 2. Thus, it makes sense to extract more in the second period, when extraction is cheaper. Mathematical solution 19

20. First 4 steps are the same as in the mathematical solution: – Step 1: Write down marginal extraction costs in each period. MEC 1 = 2 in period 1 MEC 2 = 1 in period 2 – Step 2: Write down marginal benefits in each period. Remember that marginal benefits are given by the inverse demand function. MB 1 (q 1 ) = p 1 (q 1 ) = 8 -.4q 1 MB 2 (q 2 ) = p 2 (q 2 ) = 8 -.4q 2 – Step 3: Calculate marginal net benefits in each period. Marginal net benefits are just equal to marginal benefits minus marginal extraction costs. MNB 1 (q 1 ) = MB 1 (q 1 ) - MEC 1 (q 1 ) = 8 - 4q 1 - 2 = 6 -.4q 1 MNB 2 (q 2 ) = MB2(q 2 ) - MEC 2 (q 2 ) = 8 - 4q 2 - 1 = 7 -.4q 2 – Step 4: Write down the present discounted value of marginal net benefits in each period. PDV [MNB 1 (q 1 )] = (1+.1) 0 * (6 -.4q 1 ) = 6 -.4q 1 PDV [MNB 2 (q 2 )] = (1+.1) -1 * (7 -.4q 2 ) = 6.363 -.363q 2 Graphical solution 20

21. Step 5: Draw the PDV of marginal net benefits in each period on the same graph (see following slides). – This graph is a little complicated, so be careful. – We'll put prices (p 1 and p 2 ) on the vertical axes. – We'll put extraction quantities (q 1 and q 2 ) on the horizontal axis, running in opposite directions. Since the total stock of the resource is 20, each of the axes will end at 20. By drawing the quantities in opposite directions on the same axis, we are building in the resource constraint (Condition #2). – We'll then draw the PDV of MNB in period 1 on the p 1 and q 1 axes (on the left side), and the PDV of MNB in period 2 on the p 2 and q 2 axes (on the right side). Graphical solution 21

22. Step 6: Find the optimal extraction quantities where the two lines intersect (see following slides). – This is just a graphical version of Condition #1 (maximization). – If we picked some other point, then we could increase the sum of discounted net benefits in the two periods by switching a unit of extraction from period 1 to 2 (or vice versa). Thus, we wouldn't be at a maximum. Graphical solution 22

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29. Resource prices To calculate the optimal price in the two periods, we can just plug the optimal quantities into the inverse demand functions:  p 1 (q 1 ) = 8 -.4q 1 = 8 -.4 * 9.048 = 4.38  p 2 (q 2 ) = 8 -.4q 2 = 8 -.4 * 10.952 = 3.62 – NOTE: should be optimal real (current ) prices. Why aren't these prices equal to the marginal extraction costs? The answer is because the prices also include a marginal user cost (also known as scarcity rent) that accounts for the fact that once we extract a unit of oil, it is gone forever. To calculate marginal user cost, we just subtract the marginal extraction cost from the optimal price in each period:  MUC 1 = p 1 - MEC 1 = 4.38 - 2 = 2.38  MUC 2 = p 2 - MEC 2 = 3.62 - 1 = 2.62 29

30. Hotelling Rule At the dynamically efficient allocation of a non-renewable resource with constant MEC, the MUC rises over time at the rate of interest (the opportunity cost of capital) Assumes a model of constant MEC, private competitive owners of non- renewable resource We check the Hotelling Rule with the two-period example on slide 13, in which MEC was constant, discount rate was r =.1, MUC 1 = 1.905, and MUC 2 = 2.095 MUC 1 * 1.10 = MUC 2 1.905 * 1.10 = 2.095 So Hotelling Rule does hold in this example. 30

31. Additional information I will have office hours immediately following this section (2:30-3:30) in Taubman, carrel 3. If you didn’t get your graded problem set #1 on Wednesday, please collect it now. 31