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Berkeley ENVECON C101 - EEP 100 Problem Set 3

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EEP101/ECON125 Spring 99Prof D. ZilbermanTA's: Malick/Marceau3/9/991PROBLEM SET 3Due Tuesday, March 16, 1999, in class(Late assignments will not be graded)1. Assume that Y is produced using flood irrigation. Let the irrigation efficiency, (effectiveinput / applied input) be h. Px is the price of input water (X) and Py is the price of thecrop. The production function for Y is given by,Y = (hX)βwhere β is a positive parameter.(a) Before using any numbers, i. Write down the profit maximization problem.ii. Solve for the optimal amount of X, as a function of Px , Py , h, and β.(b) Assume that Px = $80, Py = 500, and β = 0.75. Also, assume there are two possibleirrigation technologies: Furrow irrigation (h= 0.6 ) and drip irrigation (h = 0.9 ).i. For furrow irrigation, 1. Calculate the input demand for X .2. Calculate the output supply of Y.3. Calculate the profits.ii. For drip irrigation, 1. Calculate the input demand for X .2. Calculate the output supply of Y.3. Calculate the profits.Summarize your results in a table.EEP101/ECON125 Spring 99Prof D. ZilbermanTA's: Malick/Marceau3/9/992iii. If the grower is currently using furrow irrigation and the cost of converting to dripirrigation is $5,000 dollars (the fixed cost of the equipment plus the cost of learninghow to farm with drip irrigation), will the grower switch to drip irrigation? iv. Is it possible for the grower to use more water under a higher precision irrigationsystem? Explain why or why not. Does the grower in part i. use less water with thehigher precision system?2. This question was inspired from the article “Steep Prices at Tea Garden” by Yumi Wilson,which appeared in the SF Chronicle on 02/26/99 [http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/02/26/MN102467.DTL] You don’t need thearticle to complete the numerical exercises below. It may serve you as background readingfor the essay question. (This is not necessary, though.) Note: You are not asked to explainyour answers to parts a - g of this question. You are required to SHOW YOUR WORK.Save your explanations for the essay that follows.Every year, there are two categories of potential visitors to the Japanese Tea Garden in SanFrancisco’s Golden Gate Park: tourists and locals. There are also two types of locals: thosethat place a “high” value on their visit to the Garden and those that place a “low” value ontheir visit to the Garden. Imagine, for the time being, that there could be more than onegarden. The marginal benefit for an individual in each of the three groups of potentialvisitors are given by their demand curves for Q, the number of gardens visited. These are,Tourists: Pt = MBt = 10 - 5Q“high” value locals: Ph = MBh = 20/3 - (4/3)Q"low" value locals: Pl = MBl = 10/3 - (2/3)Q(a) Draw these curves on the same graph. What is the most money each type of visitor iswilling to pay to visit one garden? (b) If there are 15 "high"-type locals, 15 "low"-type locals and 45 tourists, what is theaggregate marginal benefit (AMB) curve for tea gardens? Write the two equations thatdefine the AMB curve and specify the range of Q for which each equation is valid.Graph this AMB curve. (c) Suppose the annual marginal costs of maintaining the gardens are MC = 30 + 315Q.What is the efficient number of gardens, Q*, to provide? What is the total cost ofproviding Q*?EEP101/ECON125 Spring 99Prof D. ZilbermanTA's: Malick/Marceau3/9/993(d) If the entry fee is $2.50, how many visitors will the Garden get? What are the Garden'stotal revenues and total profits under this pricing policy? (e) Suppose the entry fee is increased to $3.50. How many visitors will the Garden get?What is the highest fee the Recreation and Park Commission could charge and notexclude any of the potential visitors? What are the total revenues and profits under bothof these fees? (f) How much of an admission fee would a monopoly concessionaire charge? (g) Could the Garden still cover its costs by allowing locals to enter free but still chargingtourists? Show how it could or could not.3. (Essay Question) Assume that all of the information in the numerical exercise reflects thetrue costs and benefits of the Japanese Tea Garden. Write a brief (less than one page)economics-inspired essay arguing whether or not residents of San Francisco should havefree access to the Garden. At a minimum, you should address whether the Tea Garden is apublic good and what are the net benefits under a free and a fee policy. You may alsochoose to discuss (i) other pricing policies, (ii) who the users will be under each policy, (iii)the quality of the experience under each policy (e.g., crowding), (iv) cost-recovery, (v)concession licensing of the gate and of the teahouse/café, (vi) anything else you think maybe economically


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