FARE*2700 Lab 3

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University of Guelph *

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2700

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Economics

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Feb 20, 2024

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Department of Food, Agricultural and Resource Economics University of Guelph, FARE*2700 Survey of Natural Resource Economics Fall 2023 Lab 3 –Take-Home Assignment Due by: 12:30 pm on November 22, 2023 (Late submission will NOT be accepted) Please submit your work as a single PDF file. (70 Marks in Total) 1. (12marks) To answer the following , please refer to Question #1 in-class portion of Lab (6 marks) If the fixed supply of water is 20 units, what is the efficient allocation for person A? What is the efficient allocation for person B? Explain. Efficient allocation occurs when MC = MB, and in this case MC = 5. For person A, inverse demand function is P = 15 – 2Q. By replacing the price with the marginal cost, 5, Person A’s efficient allocation is 5 = 15 – 2Q, and Q is found to be 5. For person B, inverse demand function is P = 25 – 2Q, and by substituting in 5, Q is found to be 15. Thus, the efficient allocation when fixed supply of water is 20 units is 5 for A and 15 for B. (6 marks) If the fixed supply of water is 4 units, what is the efficient allocation for person A? What is the efficient allocation for person B? Explain. In this case, since only 4 units of water are being supplied, the higher value of water for each person must be considered in the efficient allocation. For person A: For Person B: When Q = 1, P = 13 When Q = 1, P = 23 When Q = 2, P = 11 When Q = 2, P = 21 When Q = 3, P = 9 When Q = 3, P = 19 When Q = 4, P = 7 When Q = 4, P = 17 In this case, Person B values the water more highly than Person A because their willingness to pay for each quantity of water. For each price point while demand = 4, Person B is willing to spend more than Person A, which means that the highest value of water comes from only giving all four units of water to Person B. Thus, efficient allocation for Person A is 0 and Person B is 4. 2. (30marks) A forestry firm hired you, an economist, to consult on the optimal harvest age for a stand of trees. The forester has the secure private property rights to the stand, so rights are enforceable, exclusive, and transferable. He plans to harvest only once (i.e., this is a single harvest scenario).
a. (18 marks) The forester needs to determine when to harvest the trees. You are provided with the following information: Calculate the present value of net benefits for each harvest age and state which one would you recommend. At age 30, Total Timber Value = Volume * Price = $30,000 Total Harvest Cost = Volume * Harvesting Cost = $6,000 Initial Planting Cost = $1000 Total Discount = Volume * Discount Rate = $450 Thus, Profit = $30,000 – Total Cost = $30,000 – ($6,000 + $1,000 + $450) = $22,550 At age 50, Total Timber Value = Volume * Price = $36,000 Total Harvest Cost = Volume * Harvesting Cost = $7,200 Initial Planting Cost = $1000 Total Discount = Volume * Discount Rate = $540 Thus, Profit = $36,000 – Total Cost = $36,000 – ($7,200 + $1,000 + $540) = $27,260 Since other parameters stay the same, volume of timber heavily increases the profit when at age 50. Thus, I would recommend harvesting at age 50. b. (4 marks) Does it affect the recommended harvest age if the planting cost is reduced to $700? Explain. Since the planting cost would be reduced in both age groups, reducing the planting costs does nothing to actually change the amount of profit gained between the two harvesting ages. Even if Planting cost was $700, the profit at age 30 would be $22,850, and the profit at age 50 would be $27,560. Both profits simply increased by 300. More on next page!
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