ARE/ESP 175 Natural Resource Economics Final Exam, Fall 2023

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Natural Resource Economics

Final Exam, Fall 2023

ARE/ESP 175

Total Points 20

Instructions

This is the second part of your final exam.  It consists of a single problem (with multiple parts) that tests your ability to apply the general concepts tested in Section 1 to solve a specific problem. For each question, be sure to show your work and explain why you are doing what you are doing—how you derived an answer is just as important (if not more) as the answer itself. Answers that are correct but do not show work or explain how they arrived at the answer will only receive partial marks.  The problem makes extensive use of Excel.  Please include Excel graphs as images to help explain your answers (or draw images that resemble your Excel graphs as close as possible). You must also submit your Excel spreadsheet on Canvas.

Oath

The answers below are my own answers. I did not coordinate with anyone else while completing this final exam. Do you attest to this statement (Yes or No)?

Should we be going nuts over almonds?

Almonds have exploded in popularity in recent years due to their proposed health benefits and the growth in plant-based substitutes for dairy and meat products.  As a result, it is not uncommon to see the country side covered with almond trees. While some environmentalists claim that the move towards plant-based products has been positive for reducing greenhouse gas emissions, it has not come without it’s own set of challenges.  In particular, almonds are notorious for being water intensive and wreaking havoc on groundwater supplies in local aquifers. In this problem, we will explore some of these challenges and consider some policy options for addressing the problem.

Note:  I had grand ambitions for this problem,  linking almond farming use to over exploitation of groundwater in aquifers. Unfortunately,I underestimated how hard this problem would be to solve, and in the end,I removed the groundwater portion of the problem from the exam to make it more reasonable.  The consequence of this decision is that the problem I am asking you to solve is pretty mundane, inconsequential, and somewhat boring. My apologies.

Part A: The almond farmer [10 points]

Consider an almond farmer’s problem of choosing the volume of almonds to produce in a given year, which depends on the age of the almond trees and the amount of labor devoted to harvesting almonds from the trees. In particular, suppose that a plot of land devoted to almond farming has a production function of f(t, L) = α(t)L− 1/2L2, where L is the amount of labor, t is the age of the trees, and α(t) represents how tree productivity varies with age. Suppose almonds receive a per-unit price of p in a perfectly competitive market, which is assumed to be constant over time. For simplicity, suppose that the supply labor is perfectly elastic and the per-unit cost of labor is equal to zero.

i) [2 points] Find the optimal amount of labor for a plot of land for a given age of the trees (t).

Hint: Your answer will be a function of t.

ii) [2 points] Derive an expression for almond farming profits for a given age of trees t.

Hint: Use your answer from the previous question.

iii) [2 points] Suppose that almond trees are relatively more productive when they are younger and decline in produc- tivity as they age. In particular, assume that a(t) = evt/2 , where v < 0. Derive an expression for the net present value of almond farming profits for trees left to grow from the age of t = 0 to t = T, assuming that you realize profits from almonds for every instance of t ∈ [0,T].

iv) [2 points] Suppose a farmer incurs a fixed cost of D to plant the trees.  Further suppose (for now) that a farmer is only considering a single rotation of trees. At what age is it optimal to cut the trees, assuming a farmer wants to maximize the NPV from almonds? Explain your answer intuitively and (if possible) mathematically.

v) [2 points] Now suppose that a farmer is considering infinitely many rotations of almond trees. Use a farmer’s first- order condition to discuss the marginal benefits and costs they face when choosing the optimal age (T∗ ) at which to  cut and replace almond trees.  Will a farmer choose a different cutting age when considering infinitely many rotations  compared to just a single rotation? Explain.

Note: You do not need to solve for the optimal cutting age; we’ll do that later.

Part B: Almond Industry Equilibrium [10 Points]

Now suppose there are N identical farms producing almonds. Assume that the age of almond trees across farms is dis- tributed uniformly over [0,T*], where T* denotes the optimal cutting age.

i) [2 points] Derive an expression for the industry supply of almonds as a function of price, Qs (p).

Hint: If g(x) denotes output given an input x and x is distributed uniformly between the values [a, b], then the total amount of dx .

ii) [2 points] Using Excel’s Solver, determine the optimal cutting ageT* that maximizes theNPV from almond farming for the values p = {0.6, 0.7, 0.8, ..., 1.9, 2}. Create two graphs: one that plots the optimal cutting age (y-axis) as a function of almonds prices (x-axis), and another that plots the net present value of a farm (y-axis) as a function of almonds prices (x-axis).  Explain how you determined the optimal cutting age and include a screenshot of your graphs in your answer. Use the following values for the remaining parameters: v = −0.2, T = 0.05, and D = 1.

iii) [1.5 points] In Excel, plot the industry supply of almonds (x-axis) as a function of the almond price (y-axis) assuming that there are N = 4 farms. Explain how you derived your graph and include a screenshot of your graph in your answer.

iv) [1.5 points] Suppose the inverse demand curve for almonds is equal to Qd (p) = 2 − p. What are the equilibrium price and quantity of almonds?

Hint: You do not need to use Solver; you can simply use a graph to come up with an approximate equilibrium price.

v) [1.5 points] Suppose there are no barriers to entry in the almond market.  Do you think the equilibrium price and quantity you identified above represent a long-run equilibrium? Why or why not?

vi) [1.5 points] In the long run, how many almond farms do you expect to exist? At what age will the cut their trees?

Explain.

Hint 1: It turns out that p = 0.5 is the minimum price that an almond farmer would be willing to receive to operate an almond farm.

Hint 2: Don’t use Solver for this question—use the intuition developed in previous questions instead.