Economics and the Environment

                     Homework #1: Answers

 

  1. Do the following using the various tools suggested in the question:

 

a. Using supply and demand, explain how the Brazilian government exemption of agriculture from taxation contributes to deforestation of the Amazon rainforest. (Note: Exemption of agriculture from taxation means that there will be an increase in demand by non-farmers for regular agricultural land. Farmers will move off regular agricultural lands and go to the rainforest where agricultural land is cheaper. Why is it cheaper? Because government taxes unimproved land in the Amazon at a higher rate than improved land. This gives settlers an incentive to cut down the trees to lower their taxes.)

 

The key here is to notice that land in the Amazon and regular agricultural lands outside the Amazon are rather poor substitutes, but substitutes nonetheless. An increase in demand for regular agricultural lands by businessmen seeking tax shelters means that the price of these lands has declined considerably for businessmen (but has risen considerably for farmers). That can be seen by the movement along the original demand curve in the graph which establishes the price PB and the shift in the demand curve yielding the price PF for farmers. Since the price of regular agricultural land has risen for farmers many of them will seek out a cheaper substitute, land in the Amazon. The demand for land in the Amazon increases as a result of the government’s tax exemption policy for agriculture. 

 

b. Suppose that (1) investment projects in the Amazon are eligible for a 75% tax credit by the Brazilian government; (2) a particular project develops land for 100 farms with the cost of clearing the land and building roads of $1,000 per farm; and (3) each farm would generate a net revenue stream whose present value is $400. Explain whether this project would be built in the absence of the tax credit and how the introduction of the tax credit affects this decision. Then show a supply-demand graph which illustrates this situation.

 

These data indicate that the cost of developing farmland in the Amazon is $100,000 while the benefits of developing such land is $40,000. This project would not be undertaken in the absence of the tax credit since it would impose net costs of $60,000 on the owners. But the tax credit lowers the costs to private parties to $25,000 (the developers are NOT bearing the full costs of their actions) and makes the project feasible by generating $15,000 in net benefits for the developers.

The graph with the original supply and demand (D and S0) indicates that the land in the Amazon would not be developed. But the tax credit (read subsidy) to developers (who are suppliers of land) will shift the supply curve to S1 thereby making it feasible to develop.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c. Suppose a cement plant emits dust which settles on nearby properties and causes various amounts of damage. Use a supply and demand framework to show the following:

   

(1) Show what kind of tax must be imposed to eliminate the externality. What kind of welfare loss is associated with such a tax? Show and explain.

 

A tax that drives output to zero will eliminate the pollution. Such a tax will shift the supply curve to the left as shown on the graph above. Since output is significantly below its optimal level, there is a welfare loss associated with the tax. That is, the tax has driven resources out of the current market into their next best alternative uses–which are a lower valued use than their current use. Note that it is not worthwhile to eliminate pollution in this case because of the welfare loss; what such a result tells us is that eliminating pollution yields declining benefits while we must incur increasing costs to eliminate a given amount of pollution. At some point the gain in environmental value is not worth the sacrifice of other goods. (NOTE: Can you illustrate the case where it is worthwhile to eliminate the pollution?)

 

 

 

2.   Using information from the Stroup and Shaw article and the in-class discussion of subsidies do the following:

 

a. Stroup and Shaw argue that farm subsidies are one of the major reasons why wetlands are converted to farmlands. Show and explain how this occurs and why a welfare loss occurs.

 

Assume agricultural markets are in equilibrium at price P0 and quantity Q0. Then farm subsidies are introduced in the form of direct payments or target pricing so that farmers receive the price PTAR, consumers pay the price PCON, and farmers are paid a subsidy of (PTAR - PCON)Q1. This means that farmers are willing to produce more than they did in equilibrium (Q1 – Q0). To produce more farmers must use more marginal lands (as they move up the supply curve land cultivated becomes more marginal—that is it is more difficult and costly to grow crops on) such as wetlands (which ordinarily would not make good farmland). Such subsidies produce a welfare loss because the extra resources used to produce (Q1 – Q0) have a higher value elsewhere. The subsidy, in effect, diverts resources into a lower valued use. Another way to see this would be to realize that the resources used in agriculture because of the subsidy would be in some other (higher valued) use in the absence of the subsidy. In this way subsidies to agriculture act as a tax on the rest of the economy and cause the destruction of wetlands.

 

 

b. Be sure you can explain how the combination of farm subsidies and acreage restrictions can lead to excessive pollution of streams and groundwater.

 

See Stroup and Shaw article, pp. 55-56.

 

c. Stroup and Shaw argue that water subsidies to farmers in California cause many farming activities to move to California from other parts of the country (Midwest and South). Show how these subsidies result in a welfare loss and explain how it occurs.

 

Cotton and rice are typically grown in warm moist environments (such as the Mississippi delta) not the desert. But the BR’s policy of making the desert bloom makes growing water intensive crops (such as rice and cotton) in California more feasible; in fact, farmers pay only 15% of the capital cost and none of the operating costs of the water they receive. Stroup and Shaw note that such crops would not be grown in California in the absence of water subsidies. This means that some production of these crops has been diverted from the South and Midwest to California which means resources have been drawn into lower valued uses on land that would otherwise be arid and barren.

 

 

 

d. People who build on coastal barriers where destructive storms frequently occur receive numerous subsidies that allow them to rebuild in the same place as often as they want. Show how this results in excessive development in such dangerous areas and how a welfare loss occurs (otherwise called a major misallocation of resources).

 

Before subsidies are introduced housing on coastal barriers has a higher price because of higher insurance costs or extra construction measures needed to make homes more storm-proof. This is reflected in the price difference P2 – P1. Now introduce a subsidy for homeowners who build on coastal barriers (in the form of subsidized flood insurance or post-disaster aid that reduces the costs of rebuilding in the same place again and again). This reduces the price they must pay from P2 to P1. The size of the subsidy they receive is P3 – P1. This subsidy increases the amount of development in storm-prone areas by shifting the demand curve to the right (the subsidy goes to the homeowner) and getting suppliers (developers) to increase the quantity of housing there. Resources are thus diverted from building in safer areas into a lower valued use on coastal barriers (causing the supply curve of housing in safe areas to shift to the left and prices of homes in safer areas to increase).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 3. Use the Coase Theorem to solve the following problems and explain your answer.

 

     a. Suppose a cement factory and a laundry are located near one another. The paper mill (PM) has initial profits of $300,000 and the downstream farmer (F) $100,000 when neither has taken action to clean up the water. The farmer incurs damages from the water pollution of $25,000, the farmer’s costs of cleaning the water are $15,000, and the paper mill’s costs of installing pollution control equipment are $35,000. Fill in the table and then show the results of applying the two property rules: Rule #1-the property rights to pollute the river belong to the PM; Rule #2-the farmer has property rights to the river and may sue to recover damages.

 

 

Not Clean Water (F)

Clean Water (F)

Not Clean Water (PM)

F = $100,000

PM = $300,000

F = $110,000

PM = $300,000

Clean Water (PM)

F = $125,000

PM = $265,000

NOT RELEVANT

    

     Rule #1: The Farmer knows he will lose if he goes to court so he simply cleans up the water himself. We have arrived at the efficient solution where the low cost avoider has acted and the profits are jointly maximized at $410,000.

 

     Rule #2: The Paper Mill knows it will lose if the farmer takes it to court so it negotiates an out of court settlement.  The maximum price the PM is willing to pay is $25,000 while the minimum price the farmer is willing to accept is $15,000. They negotiate a settlement whereby the PM pays F $20,000 for the right to pollute. Note that this solves the pollution problem since F has sold the property right to pollute to the PM. Profits for PM = $300,000 - $20,000 = $280,000; profits for F = $100,000 - $15,000 + $25,000 + $20,000 = $130,000. Once again the efficient result has been achieved with F acting (the low cost avoider) and joint profits maximized at $410,000.

 

     Both rules produce the efficient outcome so the Coase Theorem is satisfied.

 

 

 

 

     b. Suppose the initial data on profits from part a. is the same but the paper mill drastically increases its pollution. The farmer incurs damages from the water pollution of $50,000, the farmer’s costs of cleaning the water are now $40,000, and the paper mill’s costs of installing pollution control equipment are still $35,000. Fill in the table and then show the results of applying the two property rules: Rule #1-the property rights to pollute the river belong to the PM; Rule #2-the farmer has property rights to the river and may sue to recover damages.

 

 

 

Not Clean Water (F)

Clean Water (F)

Not Clean Water (PM)

F = $100,000

PM = $300,000

F = $110,000

PM = $300,000

Clean Water (PM)

F = $150,000

PM = $265,000

NOT RELEVANT

    

     Rule #1: The Farmer knows he will lose if he goes to court so he makes the following deal with the PM. The maximum he is willing to pay the PM is $40,000 (why?) and the minimum the PM will accept is $35,000 (why?). They bargain and reach agreement at $37,500 where both parties are better off. F = $100,000 - $37,500 + $50,000 = $112,500 and PM = $300,000 + $37,500 - $35,000 = $302,500. Joint Profits are maximized and low cost avoider (PM) acts.

 

     Rule #2: The Paper Mill knows it will lose if the farmer takes it to court so it simply installs the pollution control equipment. F = $150,000 and PM = $265,000. Joint profits are maximized and low cost avoider (PM) acts.

 

     Both rules produce the efficient outcome so the Coase Theorem is satisfied.

 

 

 

 

 

 

 

 

 

 

 

 

 4. Using the concept of marginal user cost developed in class do the following: In a three period model, suppose that U1 = $10, U2 = $12, U3 = $13, and r = 10%. Explain what must be done to achieve a dynamically efficient allocation of a resource over three time periods. Show your work.

 

The condition for dynamic efficiency is

 

                    U1        U2

              U0 = =   

                   1 + r   (1 + r)2

 

But

 

             U1        

            = $10.91

           1 + r  

 

And

 

             U2

          = $10.74 

           (1 + r)2

 

 

This state of affairs implies that reducing current production of the resource will raise U0; increasing production of the resource in periods two and three will lower U1 and U2 (noting that proportionately more resources should be shifted to period two than period three as the user cost in this period has farther to decrease).