ps4sol_eep101+econ125_sp 2014

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Spring 2014 EEP101/ECON125 Environmental Economics

Problem Set 4Due 05/01/14 at the beginning of lecture (3:30pm)

Please submit your problem set through bCourses.

Problem 1. (Payment for Ecosystem Services)

Consider a government program to retire agricultural land for the provision of environmentalservices, specifically erosion reduction and water quality improvement. The total budget ofthe program is $30,000. In the relevant region, the land types, their respective acreages, valueof environmental services and cost to retire, are presented in the following table:

Land Type Acreage ES ($/acre) Cost ($/acre)

A 1500 24 16

B 4000 6 5

C 1500 11 10

D 2000 22 11

(a) What acreage of each type of land would the program retire if its target is to maximizethe number of acres retired? What are the net benefits of such a target?

Answer: In this case, you go for the cheapest land first, which is land typeB. Buying all of it costs $20,000, which leaves $10,000 to be used for the nextcheapest land, which is land of type C. With $10,000 you can buy 1000 acresof land type C. The net benefits of such a policy would be: 4, 000!$6+1000!$11"$30, 000 = $5,000.

(b) What acreage of each type of land would the program retire if its target is to maximizeits net benefits? What are the net benefits of such a target?

Answer: In this case, you go for the land with the highest benefit/cost ratio.This is land of type D (ratio of 2). All land of type you will cost $22,000,which will leave $8,000 to buy the next best land in terms of benefit/costratio, which is land of type A (ratio of 1.5). With $8,000, one can buy 500acres of type A land. The net benefits would be: 2000 !$22 + 500 !$24 "$30, 000 = $26, 000.

(c) Now suppose that land of type B is owned by poor land owners while poor workers areemployed on land of type D. Which outcome (a or b) would be most beneficial to eachof these groups and why?

Answer: In this context both groups prefer the outcome from part a), sincepoor land owners would benefit from having their land retired (type B), whilepoor workers would rather see their land not retire (type D), such that theydo not lose their jobs.

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(d) The problem has been implicitly assuming that erosion prevention and water qualityimprovement services are bundled together. Explain the pros and cons of the bundling marketarrangement in this problem.

Answers: Pros: Bundling is good because it lowers transaction costs by havingtwo services provided in the same market. Also, it makes monitoringand enforcement easier because the same good environmental practices(like planting trees) can contribute to both services (water quality improvementand erosion reduction). Cons: Distribution of ES over locations is not even. Bundling could reduce the WTP of peoplewho could benefit differently from each environmental service and hence itreduces the provision of environmental services. If services were to beunbundled in 2 different markets, a greater budget could be raised to pay for water quality anderosion prevention separately.

(e) Suppose the spatial arrangement of the agricultural land is as depicted below. Supposealso that the environmental services for erosion and water quality remain the same, butthat there is an extra environmental service of $3,000 if all the retired land is contiguous(i.e. adjacent), because it will only provide habitat for foxes (an endangered species inCalifornia) if all the retired land is adjacent. Give the new land retirement by type thatmaximizes net benefits (including fox habitat) and the level of those net benefits.

C A

Answer:

Using land type A and C: One would first retire land type A because ithas the highest benefit/cost ratio (1.5 versus 1.1 for C). Buying all oftype A land costs $24,000, which leaves $6,000 for type C. With $6,000, onecan buy 600 acres of type C land. The net benefits of such a plan are:1500 !$24 + 600 !$11 + $3, 000 "$30, 000 = $15,600.

Using land type B and D: One would first retire land type D because it hasthe highest benefit/cost ratio (2 compared to 1.2 for B). Buying all oftype D land costs $22,000, which leaves $8,000 for type B. With $8,000, onecan buy 1600 acres of type B land. The net benefits of such a plan are:2,000 !$22 + 1600 !$6 + $3,000 "$30, 000 = $26,600.Note that the second option is better. It is also important to note thatthis second option gives higher net benefit than that in part b which was $26,000.

B D

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Problem 2 (Climate Change)

Answer the following parts in no more than one paragraph each. (NOT and essay!)

Solutions to this question are not exhaustive, but only example. Other answers may be correct.

a) List and briefly describe four ways in which climate change will affect agriculture.

1. Pest effect: Warming climate will increase pest populations, which may reduce yields;2. Fertilization effect: Higher levels of carbon will increase yields;3. Daylight effect: Increased sun in some areas will increase yields;4. Protein effect: Increased carbon, while increasing yields, will reduce the amount of proteinproduction.

b) List three ways in which agriculture might adapt to climate change.

1. Farmers will change inputs use and switch crops;2. Redesign and reconstruction of water systems;3. Some areas near the tropics will be deserted; some areas close to the poles will be farmed.

c) Two countries (A and B) use the hedonic price method to evaluate the impacts thatclimate change will have on them. We assume the rents in each country take the form:r=100t"t2, where r is rent in dollars and t is temperature in degrees Fahrenheit.Furthermore, we know that if temperature is increased by 20% in each country, thencountry A is going to gain and country B is going to lose from the climate change. Butwe do not observe the initial temperature (before climate change) in each country. Oneand ONLY one of the following four statements is true about the two countries. Pleasefind out the true statement and very briefly explain your reasoning.

Statement 1: The initial temperature in country A must be less than 50 degrees.

Statement 2: The initial temperature in country B must be greater than 50 degrees.

Statement 1 is the true statement. Given the functional form of the rent function, weknow that the rent is maximized when temperature is 50 degrees. Moreover, the marginalrent is r=100-2t. Thus, whenever the initial temperature is less than 50, the marginal rentis positive which means that there is a possibility for gaining from climate change.

However, a possibility for gaining means that even if the initial temperature is less than50, there are also chances that a country with less than 50 degrees initial temperaturewould lose from the climate change. For example, say the initial temperature in country Bis 49 degrees, the rent is r=4900-492=2499. After the climate change, temperature incountry B becomes 49*1.2=58.8 degrees. The new rent is 100*58.8-58.82=2422.56. Socountry B is still losing even if the initial temperature is below 50. This is acounterexample for Statement 2.

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Problem 3. Biotech:

A farmer produces using the local variety of seeds. His profits are given by:

#(s) = py(s)(1 "d) "c(s)

p is the price (US$ per ton) the farmer receives for his crop, y(s) is the potential output (in tons),which depends on the quantity of seeds used (s), d is the damage function, and c(s) is the cost ofthe seeds. Assume there are no other costs involved in the production of this crop. For this

production method, which we will call traditional", let !!!! ! !!and c(s) = 50sAssume that with the traditional seeds that the farmer currently uses, 40% of the crop is damaged.The price is US$150 per ton.

(a) Find the optimal value of s and the maximum profit level.

Answers: The farmer maximizes profits, given by:

!!!! ! !"# !!!!!! ! !"!!!

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(b) A biotechnology firm develops a seed that produces ! ! !!!The cost is the same as thetraditional type of seeds, 50s, but the farmer has to pay a flat fee to have access to the new seeds.In other words, the cost is c(s) = 50s + F, where F can be interpreted as a fixed cost. What is themaximum value of F for which the farmer will choose the GMO variety?

Answers: Now, the farmer maximizes profits, given by:

! ! ! !"# !! !!! ! !"! ! !!!

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!" !!

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We need to compare the profits from this part with the profits from part a, and ensure they willbe at least as large:

! !!! !"# !!! ! !!!" ! !" !!!" ! ! ! !"!!

! ! !"!!

(c) Now, the farmer realizes that demand for the crops used with the new seeds is different, but itis unknown. The best available studies imply that the price will be US$100 with a probability of50% and US$150 with a probability of 50% (the price for the crops with the traditional seed isstill US$150). If F is US$25, will the farmer adopt the new seeds, or will he keep the traditionalseeds?

In this case there is uncertainty, so the farmer maximizes the expected profits. They are given by:

E[#(s)] = E[py(s)(1 d) c(s)]

= E[py(s)(1 d)] E[c(s)]

=E

[p]y(s)(1 d

) c

(s)

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The farmer will keep the traditional seeds.

(d) Now, the biotech company develops an improved version of the seed. The variable cost is

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higher, at c(s) = 60s and the expected price for the crops grown with this seeds is US$150 per ton.The main novelty is that this variety improved the resistance of the crop to natural damage. Thedamage function is such that 20% of the crop will be damaged with a probability of 80%, and 30%will be lost with a probability of 20%. If F is US$30, will the farmer adopt this new variety ofGMO seeds, will he adopt the seeds from part (d), or will he keep the traditional seeds?

"#$% &'( )*+(,&-.*&/ +#0(1 2,#0 &'( 3-0-4( 2)*+&.#*5 6'( (78(+&(3 3-0-4( .1

E[d] = .2 .8 + .3 .2 = .22

E[1 d] = 1 E[d] = 0.78

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ps4sol_eep101+econ125_sp 2014

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