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Berkeley ENVECON C101 - EEP 101 Problem Set 4

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EssayEEP101/ECON 125 Professor Zilberman GSIs: Alix, McKim, Schoengold Problem Set #4 Due Tuesday, April 23rd (Assignments turned in after the beginning of lecture will not be graded) “Now I’ll tell you,” he says, with his teeth sounding gray, “how the Lorax got lifted and taken away… It all started way back… Such a long, long time back… Way back in the days when the grass was still green And the pond was still wet And the clouds were still clean, And the song of the Swomee-Swans rang out in space… One morning, I came to this glorious place. And I first saw the trees! The Truffula Trees! The bright-colored tufts of the Truffula Trees! Mile after mile in the fresh morning breeze. And under the trees, I saw Brown Bar-ba-loots frisking about in their Bar-ba-loot suits As they played in the shade and ate Truffula Fruits. From the rippulous pond came the comforting sound Of the Humming-Fish humming while splashing around. But those trees! Those trees! Those Truffula Trees! All my life I’d been searching for trees such as these. The touch of their tufts was much softer than silk. And they had the sweet smell of fresh butterfly milk. I felt a great leaping of joy in my heart. I knew just what I’d do! I unloaded my cart. In no time at all, I had built a small shop. Then I chopped down a Truffula Tree with one chop. And with great skillful skill and with great speedy speed, I took the soft tuft and I knitted a Thneed! … A Thneed’s a Fine-Something-That-All-People-Need! It’s a shirt. It’s a sock. It’s a glove. It’s a hat. But it has other uses. Yes, far beyond that. You can use it for carpets. For pillows! For sheets! Or curtains! Or covers for bicycle seats! The Lorax said, “Sir! You are crazy with greed. There is no one on earth who would buy that fool Thneed. But the very next minute I proved he was wrong. For, just a that minute, a chap came along, And he thought the Thneed I had knitted was great. He happily bought it for three ninety-eight… from The Lorax by Dr. Seuss Essay 1. Suppose that you lived such a long, long time back, and the Lorax hired you to put the world back on track. He asked you, he said, just to get the job done, but mostly ‘cuz you’d taken EEP 101. Your assignment, he cried, jumping up and down in a fury, was to give him advice, and do it in a hurry. “What should I do?” he moaned, his voice filled with dismay, “travel cost, interviews or willingness to pay? I need an answer, and I need it quick, I must convince the Once-ler, whose head is so thick, that the Truffula trees, the swans and Humming-Fish, are worth more than his profits, his short-term benefits.” Share the knowledge that you’ve learned in this class, to help the Lorax to get out of this morass. Don’t cover just the options that he mentioned, but go beyond them as well and touch on other inventions. Being thickheaded, the Once-ler will require, at least 3 methods (or more if you desire). Valuation, we’ve learned, is quite tricky stuff, so be careful to point out where there might be fluff (i.e., the advantages and pitfalls of each technique). Explain in an essay (keep it short and succinct), how to measure benefits of the natural environment.Numerical Problems 2. Suppose now that the Once-ler is a short-lived sort of guy, he lives only two periods, and after that says good-bye. Like all beings in the world (or so we assume), he maximizes utility ‘til the day of his doom. Consume he does, and consume he must, all the Truffula trees, right down to the dust. Their stock is given, 3000 at first, and utility depends on him quenching his tree-thirst: U )ln()( TT = Take note in this problem that the stock of the trees does not grow over time, they’re like oil, coal or a mineral mine. Given this information, plus a four- percent interest rate, answer the following questions, and don’t turn this in late: In the interest of clarity and saving of time, the remaining instructions will not rhyme. a. Solve for the Once-ler’s consumption in period zero and period one. b. Assuming that dynamic efficiency is met, derive the rate of change in marginal benefits (price) from one period to the next. c. Solve for the multiplier and interpret the solution. d. Now suppose that interest rates increase to eight percent. Calculate consumption in the two periods. e. Now suppose you are in a different situation, where the interest rate is four percent, but the Once-ler lives for T periods, where T is a finite number. Derive the optimal path for prices (marginal benefits). g. In a sentence or two, but in no more than three, write why and how interest rate changes change your consumption of trees (We couldn’t resist). h. Suppose the Once-ler discovers a synthetic substitute for Truffula tufts in Thneed production. What will happen to the rate of tree extraction? Justify your response. 3. Suppose now that the Truffula trees can grow. Indeed, they have a growth rate which is described by the equation g(S) = 4S - 0.0004S2. Each Truffula tree produces one Thneed of value $3.98, but the per Thneed cost of production (the marginal cost) changes with the number of trees: C(X,S) =10,000/S, where S is the total number of trees and X the total number of Thneeds. For this problem, assume a zero interest rate. a. Graph the growth rate as a function of stock size. b. Calculate the maximum sustainable stock level if there is no harvesting of Truffula trees. c. Figure out the maximum sustainable yield and the stock level that supports it. d. Assume that the Once-ler is a profit-maximizer and calculate the optimal steady state stock and harvest levels. e. Suppose now that, as the story goes, as he himself tells the story: “I rushed ‘cross the room, and in no time at all, built a radio-phone. I put in a quick call. I called all my brothers and uncles and aunts and I said, “Listen here! Here’s a wonderful chance for the whole Once-ler Family to get might rich!” We are assuming that, because the Once-ler family is so large and selfish, this situation leads to an open access solution. Please calculate the harvest and stock levels in this


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Berkeley ENVECON C101 - EEP 101 Problem Set 4

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