1. [Lecture 10-21 Discounting] Oil production has been proposed for an area along the coast off Southern California. Oil production would jeopardize the use of beaches along 10 miles of coast which are a major venue for surfing, bathing and other beach activities. The beach recreation runs to about 500,000 visitor days a year. Oil production would greatly reduce beach use, lowering it to about 100,000 visitor days. The oil production would last for 15 years. After that, the oilfield will have been depleted and oil production activities will cease. Once the oil production ends, beach visitation would partially recover, averaging about 350,000 visitor days per year. If there is no oil production, it is expected that beach recreation will continue at its present level indefinitely. Environmental economists studying beach recreation in Southern California have estimated that the value of an average trip to the beach in Southern California, in terms of the average consumer’s surplus, is about $16 per visitor day. Oil production is expected to earn profits of $12 million per year for the 15 years of the oil production. In the following calculations use an interest rate of 5%.
(a) If mining starts now, what is the present value of the profit from oil production?
(c) If oil production is delayed and starts in five years time instead of now, what is the present value as of now, of the profit from oil production?
(d) If there is no oil production, what is the present value of beach recreation in the area?
(e) If oil production starts now, describe the time profile of the beach recreation that will occur in the area. What is the present value of this recreation?
(f) If oil production is delayed and starts in five years time instead of now, describe the time profile of the beach recreation that will occur in the area. What is the present value of this recreation?
g) If oil production starts now, what is the present value of the combined sum of economic flows that will occur – the profits from oil production plus the value of recreation?
h) If oil production starts is delayed and starts in five years time instead of now, what is the present value of the combined sum of economic flows that will occur – the profits from oil production plus the value of recreation?
i) Given three policy options – oil production starts now, oil production starts in five years time, or no oil production ever – which is the best option from an economic perspective?
For the following, see Lecture 10-28
2. What economic return does a person earn if he owns a non-renewable resource (e.g., a deposit of coal) and he lets the resource stay undisturbed for an extra year? What economic return does a person earn if he owns a renewable resource (e.g., a forest) and he lets the resource stay undisturbed for an extra year? What economic return does a person earn if he owns a Rembrandt painting and he holds on to the painting for an extra year? Suppose a person owns quantities of all three types of resources – he owns a number of coal deposits, a number of forests, and a number of old master paintings. What economic rule should he follow in balancing his portfolio of assets?
3. Consider a non-renewable resource. There are two periods, now and later. The demand curve in each period (t = 1, 2) is Qt = 10 - Pt. The stock of the resource is 10 units. Extraction costs are approximately zero. The interest rate is 4 percent.
(a) A market equilibrium requires identifying price and quantity at all times. What are the four variables for which we need to find numerical values to find the equilibria?
(b) To find these four unknowns, we need four equations. These equations are (i) the two demand curves, (ii) the Hotelling price path, and (iii) a summing-up condition that says that the quantity used in both periods sums to the stock. Write down those four equations.
(c) Solve the four equations by substitution to find the equilibrium quantity harvested in each period and the equilibrium market price in each price. What is the solution (round your answers to two decimal places).
(d) In this solution, does price rise with the interest rate?
(e) In this solution, does quantity demanded increase or decrease between the two periods?
(f) What is the discounted present value of the producer’s profit over the two periods?
(g) What happens to the solution if the interest rate is 10% -- how do the answers in part (c) change?
(h) What happens to the solution in part (c) if, while the interest rate is 4%, the demand curve in the second period is Q2 = 15 – P2 ?
4. If there is a non-zero marginal cost of extraction, c, what is the formula for the rate at which the price of extracted resource changes over time? Does it grow at a rate equal to, higher than, or lower than the rate of interest?
For the following, see Lecture 10-30.
5. World consumption of oil has risen from about 78 million barrels/day in 2003 to 87 million barrels/day in 2013. US consumption of oil was about 20 million barrels/day in 2003 and about 19 million barrels/day in 2013. Canada’s consumption was about 2.2 million barrels/day in 2003, and 2.4 million barrels/day in 2013. Canada’s production of oil was about 3 million barrels/day in 2003 and 3.9 million barrels/day in 2013. If the Keystone pipeline is built, an additional 1 million barrels/day of new, relatively high-CO2 intensity oil would eventually be produced in Canada and imported into the US.
(a) What has happened to the world price of oil since the beginning of this year? Since about 2000? What factors might explain those trends?
(b) How well does the Hotelling Rule explain the trajectory of the price of oil since 2000?
(c) Suppose the Keystone pipeline is built and comes into operation. What do you think would happen to the price of oil in the US? Explain the reason for your answer.
(d) Suppose the Keystone pipeline is not built: Canada goes ahead and produces the new, relatively high-CO2 intensity oil and exports it by tanker to Asia instead of the US. What do you think would happen to the price of oil in the US? Explain the reason for your answer.
(e) Suppose the Keystone pipeline is not built and Canada does not produce the new, relatively high-CO2 intensity source oil. What do you think would happen to the price of oil in the US? Explain the reason for your answer.
6. Explain how the Hotelling Rule applies when the non-renewable resource is owned by a monopolist rather than a price-taking industry. How does the monopoly ownership affect the amount of resource extracted in the early years? How does it affect the price at which the extracted resource is sold in the early years? How does it affect the length of time before the non-renewable resource is exhausted?
7. What is a “backstop technology” in the context of the management of a non-renewable resource?
8. Suppose you own a shallow on-shore oilfield and a deep off-shore oil field. They both contain the same amounts of oil. How would you exploit those two resources? Would you extract some oil from each oilfield every year, or would you do something different? If so, what? Why?
9. [Lecture 11-4/6] There is a fishery for halibut in Alaska. The growth equation for change in the stock of biomass over time, St+1 – St,, is given by the equation
St+1 -St =G(St ) = 0.2St[1-St/400]
Let Ht denote the harvest in year t.
(a) When St = 100, what is the annual growth in the stock?
When St = 150, what is the annual growth?
When St =200, what is the annual growth?
When St =250, what is the annual growth?
When St = 300, what is the annual growth?
When St = 350, what is the annual growth?
When St = 400, what is the annual growth?
When St = 450, what is the annual growth?
(b) What is the carrying capacity of the resource?
(c) What is the maximum amount of harvest that can sustainably be achieved (i.e., the maximum sustainable yield, MSY)?
(d) What level of stock generates this MSY harvest?
(e) What is the mathematical relationship that must hold between Ht and St in a steady-state situation?