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READING: BH 379 - 398 Stock Resources These are resources that endure - they last a long time (eg trees) or forever (eg coal) if the resource is not...

Hi, I have a question regarding #3. I am just not sure how to do the problems after a. I have attached the Lecture notes as well. Thank you. 

READING: BH 379 - 398
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1 ECN 445 SPRING 2016 PROBLEM SET 4 Due by the close of business on Thursday April 21, 2016 1. [Lecture 3-15 Discounting, slides 2-7] Mining is being proposed for Wonderful Wilderness. This area provides great outdoor recreation for backpacking. The mining would last for 12 years. During that period, mining would reduce backpacking visits from its current level of 12,000 recreation visitor-days per year to 4,000 days per year; after the mining ends, recreational use would partially rebound to 7,000 days/year into perpetuity. If the mine is not opened, recreational use is expected to continue at current levels into perpetuity. In what follows, use a 4% discount rate. (a) If one day of backpacking is worth $50, what is the present value of recreation in the area if it is not mined? (b) If it is mined, what is the present value of the recreation that will occur during the period when it is mined? (c) If it is mined, what is the present value (as of now) of the recreation that will occur after the mining ends? (d) Combine your answers to parts (b) and (c): what is the present value of the recreation that will occur from now onwards if mining is allowed? Mining is expected to bring profits of $650,000 million/year for the 12 years of the mining operation. (e) What is the present value of mining if it is allowed (excluding the value of recreation)? (f) What is the total present value of the area if mining is allowed including the value of recreation? (g) Should mining be allowed? (h) In general – without doing the detailed calculations -- explain how your answer to (g) might be different if a discount rate of 12% were used, instead of 4%. 2. [Lecture 3-17, Introduction to Resource Economics] (a) Give examples of a renewable resource versus a non-renewable resource. How do they differ from an economic perspective? (b) Is there any similarity between owning a Rembrandt painting and owning a non-renewable resource? Explain the reason for your answer. (c) What about owning a Rembrandt painting versus owning a renewable resource – is your answer different than for part b? Explain the reason for your answer. 3. [Lecture 3-22 & 29, Nonrewable Resources (especially pp 14-20, 29-32, and 36-45).] Consider a non- renewable resource. There are two periods, now and later. The demand curve in each period ( t = 1, 2) is Qt = 200 - 2 Pt . The stock of the resource is 20 units. Extraction costs are approximately zero. The interest rate is 5 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 equilibrium? (b) Assume production costs are zero. What is the algebraic formula for the Hotelling Rule in this case? (c) Assume production involves a constant marginal cost of $c per unit of the resource extracted. What is the algebraic formula for the Hotelling Rule in this case?
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2 (d) Explain the economic logic underlying the Hotelling Rule? (e) Assume a production cost of $c per unit of the resource extracted, as in (c). To find the values of the four variables identified in (a), we need four equations. These equations are (i) the two demand functions, (ii) the Hotelling rule, and (iii) an adding up condition that the total extracted in the two periods just equals the total stock. Write down those four equations. (f) Assume that c = $3. Solve for the equilibrium values of P 1 , P 2 , Q 1 and Q 2 . (g) In this solution, does price rise at the rate of the interest rate? If not, why not? (h) In this solution, does the quantity extracted decline over time? (i) What is the discounted present value of the profit over the two periods? 4. [Lecture 3-31] (a) If an industry owning a non-renewable resource acts monopolistically, how does the time pattern of resource price, p t , differ from that when the industry acts as a price-taking, competitive industry? How does the time pattern of extraction, y t , differ? What about the date when all of the resource has been extracted – does that differ? How about the total discounted present value of profit to the industry over the life of the resource – does that differ? (b) A non-renewable resource firms owns two deposits of copper, where the potential amount of copper in the deposits are the same but one is located at a shallower depth and has a lower cost of extraction. How would you exploit those two resources? Would you extract some copper from each deposit every year, or would you do something different? Describe the extraction strategy you would employ, and the underlying economic rationale. (c) In the context of a non-renewable energy resource, what is a “backstop” technology? How does the existence of a backstop technology for generating energy affect the price today of coal? [Lecture 4-2, slides33-38] (d) Has the world price of oil risen, from 1950 to now, approximately at the interest rate, as a simple version of the Hotelling rule would suggest? (e) If not, what is an economic explanation of the price of oil over the last 15 years? [Lecture 4-7 & 12] 5. There is a fishery for sardines in Monterey Bay. The growth equation for change in the stock of biomass over time, S t+1 – S t ,, is given by the equation 1 ( ) 0.2 1 500 t t t t t S S S G S S    Let H t denote the harvest in year t. (a) When S t = 250, what is the annual growth in the stock? When S t = 300, what is the annual growth? When S t = 350, what is the annual growth? When S t = 400, what is the annual growth? When S t = 450, what is the annual growth? When S t = 500, what is the annual growth? (b) What is the carrying capacity of the resource?
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sol to Q#1 and Q#3.pdf

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