PROJECT FINANCE SET 1

Problem 1

Suppose the inverse supply and demand functions in the borogove market are given by the following functions:

Demand: P = 150 – 6Q + 0.02Q2 for 0 < Q < 25 Supply: P = 50 + 0.75Q + 0.02Q2 for 0 < Q < 25

where Q is the units of borogove produced or consumed per year, and P is dollars/unit.

Suppose also that the production of borogove emits pollution. The externality of the pollution associated with each additional borogove has rising marginal damages such that:

MED = 0.12Q

with Q defined as before. Assume that the rate of emissions per unit of borogove is fixed (or invariable).

a.       What level of borogove will the unregulated market produce? What will be the price of borogove in the unregulated market?

b.      What is the socially optimal level of borogove production?

c.       What is the potential net social gain from correcting the pollution externality and producing borogove at the optimal level?

d.      Suppose the legislature passes a regulation that shifts borogove production to the socially optimal level. What is the net present value of correcting the externality over the first twenty years of the program? Use a social discount rate of 5%.

Problem 2

Consider a case where there are three firms contributing to the pollution of the Cabernet airshed. Their demand functions for the right to pollute are given as follows:

Firm A: Q = 64 – P Firm B: Q = 32 – 1/3P Firm C: Q = 30 – 2/3P

where Q is the amount of pollution in tons per year and P is the willingness to pay in dollars per ton.

a.       Draw the individual and aggregate demand functions for the right to pollute in the Cabernet airshed (Hint: Note that the aggregate is not a simple summation. If this problem gives you trouble, you may want to review the tutorial on aggregating cost and demand curves that is on the class web site).

Emissions Demand Curves for Individual Firms and Industry Aggregate

b.      What is the total amount of unabated air pollution in this airshed?

c.         Now draw the marginal abatement cost (MAC) curve.

d.      Suppose that the Cabernet environmental agency determines that the MED function for emissions is MED = 50 for the entire range of emissions. Draw the marginal abatement benefit (MAB) curve onto the MAC curve

e.       What is the efficient level of abatement in this case?  The efficient level of emissions?

f.        What is the total cost of abatement to reach the efficient level of emissions?

Aggregate Marginal Abatement Cost Curve And Marginal Abatement Benefit Curve with Total Abatement Cost

g.       What is the allocatively efficient level of abatement for each firm? What is the total cost of abatement to each firm?

Problem 3

Adapted from problem 5, p111 in text

The Great Fracking Natural Gas company has just established a new well in the ranching community of Grassville, USA. It turns out that some of the chemicals used in the Fracking process are contaminating the groundwater. The total damage to ranchers due to livestock losses from drinking the water is 50p2, where p is the level of pollution in this case. The

total damage to families who must travel to town and purchase clean water each month is 300p2. The marginal savings to Great Fracking for being allowed to pollute is 4000 – 40p.

a.       Find the aggregate (including both types of consumers) marginal damage for the public bad.

b.      Graph the marginal savings and aggregate marginal damage curves with pollution on the horizontal axis.

c.       How much will Great Fracking pollute in the absence of any regulation or bargaining? What is this society’s optimal level of pollution?

d.      Starting from the uncontrolled level of pollution calculated in part (c), find the marginal willingness to pay for pollution abatement, A, for each consumer class (abatement reduction in pollution; zero abatement would be associated with the uncontrolled level of pollution). Find the aggregate marginal willingness to pay for abatement.

e.       Again starting from the uncontrolled level of pollution, what is the firm’s marginal cost of pollution abatement?  What is the optimal level of A?

Are the problems of optimal provision of the public bad (pollution) and the public good (abatement) equivalent?  Explain why or why not.

Problem 4

Consider two adjacent businesses: a music studio and a tutoring center. Rock music from the studio can be heard in the tutoring center, causing concentration difficulties for its patrons. The table below shows the total value of each business at various levels of noise. Assume the owners of the two organizations can bargain costlessly.

a)              If the music is legal, what is the outcome of the situation, in terms of the level of noise? What is the potential range of payments that might be made and by whom?

b)             If the music is illegal (restricted to 10), but enforcement is only in response to complaints, how does your answer in part (a) change?

Problem 5

Problem 2, p114 in text

Consider a pollution problem involving a paper mill located on a river and a commercial salmon fishery operating on the same river. The fishery can operate at one of two locations: upstream (above the mill) or downstream (in the polluted part of the river).

Pollution lowers profits for the fishery: without pollution, profits are $300 upstream and

$500 downstream; with pollution, profits are $200 upstream and $100 downstream. The mill earns $500 in profit, and the technology exists for it to build a treatment plant at the site that completely eliminates the pollution, but at a cost of $200. There are two possible assignments of property rights: (i) the fishery has the right to a clean river and (ii) the mill has the right to pollute the river.

a.       What is the efficient outcome (the maximum of total joint profit)?

b.      What are the outcomes under the two different property rights regimes, when there is no possibility of bargaining?

c.       How does your answer to (b) change when the two firms can bargain costlessly?

Problem 6

Problem 6, p115 in text

A beekeeper and a farmer with an apple orchard are neighbors. This is convenient for the orchard owner since the bees pollinate the apple trees: one beehive pollinates one acre of orchard. Unfortunately, there are not enough bees next door to pollinate the whole orchard and pollination costs are $10 per acre.  The beekeeper has total costs of

TC = H2 + 10H + 10 and marginal costs MC = 10 + 2H where H is the number of hives. Each hive yields $20 worth of honey.

a.       How many hives would the beekeeper maintain if operating independently of the farmer?

b.      What is the socially efficient number of hives?

c.       In the absence of transaction costs, what outcomes do you expect to arise from bargaining between the beekeeper and the farmer?

d.      How high would total transaction costs have to be to erase all gains from bargaining?

Problem 7

Adapted problem 1, p132 in text

Assume an economy of two firms and two consumers. The two firms pollute. Firm one has a marginal savings function of MS1(e) = 18 – 2e where e is the quantity of emissions from the firm. Firm two has a marginal savings function of MS2(e) = 12 – e. Each of the two consumers has marginal damage MD(e) = 0.5e, where e in this case is the total amount of emissions the consumer is exposed to.

a.      Graph the firm-level and aggregate marginal savings functions.

b.       Graph the aggregate marginal damage function.

c.       What is the optimal level of pollution, the appropriate Pigouvian fee, and emissions from each firm?

Problem 8

Assume that there are two firms each emitting 40 units of pollutants into the environment for a total of 80 units in their region. The government sets an aggregate abatement standard of 30 units. The polluters' total abatement cost functions are as follows:

Polluter 1: TAC1 = 450 + 4.6(A1)2 + 0.20(A1)3 Polluter 2: TAC2 = 370 + 10.2(A2)2 + 0.20(A2)3

where Ai = the amount of abatement by polluter I and costs are in dollars.

a.       Suppose the government allocates the abatement responsibility equally such that each polluter must abate 15 units of pollution. Graphically illustrate this allocation and analytically assess the cost implications (i.e., use the above formulas in a mathematical

analysis). Your analysis should include the total cost to each firm, the marginal cost to each firm, and the total cost to society.

b.      Now, assume that the government institutes an emission fee of $900 per unit of pollution. How many units of pollution would each polluter abate? Is the $900 fee a cost-effective strategy for meeting the standard? Explain.

c.       What allocation of abatement responsibility will reach the abatement goal of 50 units at the lowest social cost? What will be the MAC for each firm and for society under this optimal allocation?

Problem 9

Suppose the state is trying to decide how many miles of a very scenic river it should preserve. There are 10,000 people in the city, each of whom has an identical inverse demand function given by p = 36 – 0.08q, where q is the number of miles preserved and p is the per-mile price he or she is willing to pay for q miles of preserved river.

a.       If the marginal cost (dollars per mile) of preservation is p = 2500 + 8q2, how many miles would be preserved in an efficient allocation?  Round to three decimal places.

b.      What would be the marginal value of saving the last mile up to the efficient allocation?

c.       What would be the total costs of preservation?

Total cost is the area under the marginal cost curve up to the quantity produced (or in this case preserved). On the graph below, this is Area C. So to find this, integrate the marginal cost function between 0 and the efficient allocation, 31.777 miles.

The total cost function is thus 2500q + (8/3)q3.  This gives us a total cost of

d.      How large would the net benefits be

Problem 10

The marginal private cost of the production of stooges is described by the following equation, where Q is the quantity of stooges produces.

MPC = 8 + 0.8Q

Unfortunately, the production of stooges has a detrimental impact on the environment, estimated by the following damage function:

MD = 1.2Q

The private market demand for the production of stooges is described by the following equation:

MPB = 80 – 4Q

The government decides to set a Pigouvian tax to account for the environmental damages caused by stooges. What is the optimal Pigouvian tax? What is the expected government revenue generated from this tax?

Problem 11

Suppose the individual demands for wetlands (a pure public good) by the four citizens in a town are given by

Q1  = 10 - P Q2 = 5 - 0.1P Q3 = 7 – 0.2P Q4  = 12 - 0.5P

where Qi is the quantity of wetland demanded by individual i, p is individual i’s price (or willingness to pay) for wetlands.

a.       Diagram the individual demand curves and the societal demand curve for wetlands.

b.      Suppose there is a constant marginal cost of 65 to supply wetlands. What is the socially optimal level of wetlands?

Problem 12

Suppose that a chemical manufacturing plant is releasing nitrogen oxides into the air, and these emissions are associated with health and ecological damages. Economists have estimated the following marginal costs and benefits for the chemical market, where Q is monthly output in thousands of pounds and P is price per pound.

Marginal Social Benefit [MSB]=50-0.4Q Marginal Private Cost [MPC]=2+0.4Q Marginal Environmental Cost [MEC]=0.2Q

Your job is to:

a)              Find the competitive equilibrium quantity (Q0) and price (P0).

b)             Find the efficient equilibrium quantity (Q1) and price (P1).

c)               Draw a graph of this market, showing the MSB, MPC, MSC curves, Q0, Q1, P0, and P1.

d)             Find the dollar value of a Pigouvian tax that would achieve the efficient equilibrium.

Problem 13

Suppose there is a firm in the town of Oakley that pollutes the water of the town’s lake. The damages to the town from the pollution, and the cost to the firm of cleaning up the pollution, are shown in the following figure.

a.       What does the Coase Theorem tell us to expect if an alienable right to prevent pollution is given to the town?

b.      What level of pollution will emerge from a Coasian bargain? Provide a numerical answer.

c.       What is the range of payments the firm might make to the town following a mutually agreeable bargain? Provide a numerical answer.

d.      How does your answer change if the initial property right in pollution is given to the firm? Provide a numerical answer.

Problem 14

An unregulated industry produces zappas and sells them in a competitive market. The inverse supply function for the firm in this market is:

P = 6 + 2Q

where P is the price per unit of zappa produced (dollars/zappa) and Q is the number of zappas produced per year. The elasticity of supply (Es) is 2.125. The elasticity of demand (Ed) is -4.25.  The equilibrium price in the unregulated market is 34/3 dollars/zappa.

a.       What is the function describing the demand in the unregulated market?

b.      What is the consumer and producer surplus in the unregulated market?

Now suppose the production of zappas produces emissions that cause people to freak out. To address the emissions problem, suppose the government sets a regulation that increases the cost of production of zappas by 2 dollars/zappa.

c.       What is the new equilibrium price and quantity? What assumption(s) did you make when determining these values?

d.      Ignoring the benefits associated with the emission reduction, what is the change in consumer, producer, and social surplus?