Problem Set 3 Environmental Valuation 1. Arturo derives utility from a composite good X and indoor air quality, Q such that. Indoor air quality depends on pollution levels outside, P, and defensive expenditures, D, such that. Arturo s income is Y and the price of the composite good is equal to 1. 1.1 Write Arturo s objective along with any constraint(s) that he faces. 1.2 Suppose Y=10 and P=1. What are the optimal amounts of X and Q for Arturo? Show your work by writing the Lagrangian equation along with the relevant first order conditions. 1.3 What happens to X and Q if P increases to 2? What happens to X and Q if Y increases to 20 (assuming P is back to 1)? 1.4 It is observed that low income individuals are exposed to more pollution. Is your answer to part (c) consistent with this observation? 1.1 1.2 Lagrange is FOCs max,.. 1 0 2 0 0 Using the first two FOCs we have the equilibrium, /2. Substitute the value of into the last FOC. We derive, 0. So,. If Y=10, X* is 6.67. Substitute the expression for X* into the equilibrium condition /2 and solve for Q*. We find,.. If Y=10 and P=1 we have Q* is 1.826. 1.3 If P increases to 2, we find X* still equal to 6.67. But now, Q* is equal to 1.29. If Y increases to 20, we find X* still equal to 13.33. But now, Q* is equal to 2.58. 1.4 Yes because their demand for Q* is lower which means the exposed level of pollution is higher. 2. A housing developer is deciding to purchase a large piece of land currently used as a park in order to convert the park into subdivisions. You are tasked by the government to see if the benefits of selling the land outweigh the benefits from its current use as a park. At the moment,
there is no admission fee charged and 4075 people visit the park daily. You have interviewed visitors and delineated 6 geographical zones where the visitors originate. The following table summarizes the travel cost of visitors to the park: 2.1 Using the travel cost method calculate, calculate the demand schedule illustrating the total number of visitors at different admission fee levels for fees from $1 to $5. Show your solution for at least one fee level. (Hint: try to find the equation relating travel cost to visitors per population). Answer: Need to find visitor equation: V/pop = 0.06-0.01*C. Using this equation and adjusted levels of travel cost, we can calculate the predicted level of visitors with a fee of $1: Zone Travel cost ($) Population Visitor/population Visitors 1 1+1 50000 0.04 2000 2 2+1 25000 0.03 750 3 3+1 12500 0.02 250 4 4+1 6000 0.01 60 5 5+1 8000 0.00 0 6 6+1 10000 0.00 0 Total 3060 So now we get 3060 visitors when an admissions fee of $1 is imposed. Do this for fees from 1 to 6 and we arrive at the following demand schedule: Price 0 1 2 3 4 5 Total 4075 3060 2125 1250 500 0 Visits 2.2 Given the results from 2.1, you estimate the inverse demand curve as P = 6 (1/815)*Q where P is the admission fee and Q is the number of visitors. Using this fact and the information above calculate the daily value of keeping the land as a park.
You can still get an approximation of surplus by solving for each level visitors per day when the entrance fees are 0, 1, 2, 3, 4 and 5. This is what I found: P 5 4 3 2 1 5001250 2125 3060 4075 Here, an approximation of the area under this curve is simply: $4075+$3060+$2125+$1250+$500 = $11,010 per day. Alternatively, you could have plugged in values of P = 0, 1, 2, 3, etc to get this demand schedule: Price 0 1 2 3 4 5 6 Total 4890 4075 3260 2445 1630 815 0 Visits Note that your results will differ slightly depending on which method you use but both methods are correct. Here, an approximation of the area under this curve is simply: $4890+$4075+$3260+$2445+$1630+$815 = $17,115 per day. 2.3 Using an interest rate of 5%, please compute the present value of the benefits the park delivers from year 1 on (Hint: the present value of an annualized benefit in perpetuity is annual return divided by the interest rate). You may assume that each year's benefits are 365 times the daily benefit and arrive in a single payment: e.g., the annual value for year 1 is 365 times the daily value and arrives in one payment at t=1. That is, you do not need to worry about the timing of daily payments within the year. Answer: You will get: 365 days x $11,010 per day = $4,018,650 per year. So, the annualized value is: $4,018,650 / 0.05= $80,373,000. Note this is an underestimate since we calculated an approximation If you use the provided equation, you get, 365 days x $17,115 per day = $6,246,975 per year. So, the annualized value is: $6,283,475 / 0.05= $124,939,500. Note this is an underestimate since we calculated an approximation
2.4 If a developer would be willing to pay $28 million for the land, and conversion would eliminate the benefits of the park starting in year 1, what should be done? Explain. Answer: The present value of the land as a park is larger than the value that a developer would give. Therefore development is not recommended. Our analysis is also an underestimate so we are undervaluing the land. Note that since we use TCM, we may even be undervaluing the park because non-use value is not included. 3. Fecal coliform is a significant water pollutant that is affecting water quality in Lake Erie. Some policymakers would like to reduce fecal coliform levels in the lake but before they can do that, they need an assessment of the value of such a project to the nearby houses along the lake. If you were tasked to derive the value of reducing fecal coliform, what is the most appropriate valuation technique given that you have a large amount of budget and sufficient time to conduct a thorough study? Describe in detail how this valuation technique is conducted for this particular situation. Enumerate the advantages and disadvantages of this technique for this case. There are two options: hedonic pricing method or defensive expenditure method. If hedonic pricing is used data needs to be gathered on a proxy market. Here, it could be the housing market. We need to get data on house values along with the characteristics of each house such as size, number of rooms, etc. We also need neighborhood characteristics and characteristics of the individual buyer. The most important data is the level of fecal coliform exposure in each housing location. After all the data is gathered, estimate a hedonic pricing model to derive the marginal effect of fecal coliform on house value along with all other regressors. Using this measure of the marginal effect, estimate the demand for environmental quality where the measure of environmental quality is the difference between maximum fecal coliform exposure and the current level of fecal coliform. The area underneath the demand curve bounded by the target environmental quality level is a measure of benefits of reducing fecal coliform. Main advantage: This technique uses real data from a market and is flexible. Disadvantages: assumes housing market is in equilibrium always. If defensive expenditure is used data needs to be gathered for items used to reduce fecal coliform exposure. We need to survey households around the lake to see what items they purchase to avoid fecal coliform exposure. The most important data is the level of fecal coliform exposure in each housing location. We also need characteristics of the individual buyer. After all the data is gathered, estimate a model looking at the determinants of defensive expenditure spending to derive the marginal effect of fecal coliform on defensive expenditure value along with all other regressors. Using this measure of the marginal effect, estimate the demand for environmental quality where the measure of environmental quality is the difference between maximum fecal coliform exposure
and the current level of fecal coliform. The area underneath the demand curve bounded by the target environmental quality level is a measure of benefits of reducing fecal coliform. Main advantage: This technique uses real data from a market and is flexible. Disadvantages: there may be multiple uses for some of the things purchased. Does not consider value of households moving away.