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. Feel free to include Excel graphs as images to help explain your answers. You must also submit your Excel spreadsheet on Canvas.

Competing Uses of the Ocean

Coastal-dwelling Canadians are beginning to expand their jurisdiction out into the Pacific Ocean. Currently, the ocean is only suitable for two activities: seaweed farming and fish farming. Seaweed farming depends on the depth of the ocean, so it is better situated closer to the coast (where the ocean is less deep). In contrast, fish farming does not depend on how far it takes place from the coast. The Government of Canada has created ocean parcels that are 1-mile in length that can be used for either seaweed or fishing farming, extending out to 15 miles from the coast. In the following questions, you will determine the optimal use of these ocean parcels and whether a competitive market will allocate these ocean parcels efficiently.

For the questions below, let  denote the number of miles an ocean parcel is from the coast (i.e.,  = 1, 2, 3, ..., 15) and let  = 0.05 be society’s annual discount rate. Note that ocean devoted to seaweed farming permits a single harvest per year; thus, land devoted to seaweed farming should be discounted using discrete time.  Fish, on the other hand, grow continuously; thus, ocean devoted to fish farming should be discounted using continuous time. Initially, all ocean parcels are immediately ready for seaweed farming; ocean devoted to fish farming, in contrast, must incur a fixed cost of stocking pens with juvenile fish.

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)?

Part A: The seaweed farmer’s problem [7.5 points]

Consider the seaweed farmer’s problem of allocating workers to an ocean parcel that is  miles off the coast. Suppose

that seaweed farming production decreases the further away a parcel is from the coast, and has a production function of

i) [3.5 points]   Find the optimal number of workers  for a parcel that is  miles away from the coast. Hint: your answer will not be a number; it will be a function of  .

ii) [4 points]   Calculate the net present value (NPV) of a parcel that is  miles from the coast and devoted to seaweed farming in perpetuity (i.e., for infinitely many years). Hint: your answer will still be a function of  .

Part B: The fish farmer’s problem [7.5 points]

Now consider the fish farmer, whose problem consists of stocking a pen with a fixed amount of juvenile fish and choosing the optimal length of time to let the fish grow before harvesting them. Once the fish have been harvested, a new cycle can begin —i.e., the pen can be restocked with juvenile fish, who are left to grow until they too are harvested. These cycles can be repeated infinitely many times over the lifetime of the ocean parcel. Suppose a pen at time  produces a harvestable biomass equal to () =  + 2 −  3 . Let  be the price of fish (per unit of biomass) harvested from the pen, which is assumed to be constant over time. For simplicity, assume that harvesting costs are equal to zero. An ocean parcel devoted to fish farming incurs a fixed cost of  > 0 at the beginning of each cycle to restock the pen with fish. Since fish farming does not depend on the depth of the ocean floor, its production process does not depend on how far away a parcel is from the coast.

For the following questions, use the parameter values  = 75,  = 1,  = 0.01,  = 50,   = 1,  = 45, and  = 0.04.

i) [3.5 points]   Use the fish farmer’s first order condition to explain the marginal benefits and marginal costs associated with the decision of when to harvest fish. Then use Excel to find the fish farmer’s optimal cycle length  and the NPV of an ocean parcel devoted to fish farming.

ii) [4 points]   While fish farming is an efficient way of producing ocean-based protein, it has the unfortunate conse- quence of harboring and spreading disease to wild populations of fish. Suppose that the per-period damages to society of disease increase with the length of the cycle and are equal to   . How does the optimal cycle length and NPV of fish farming for society compare to the fish farmer’s optimal cycle length and NPV? Use the first-order condition for society’s problem to explain your answer and use Excel to determine society’s optimal cycle length and NPV for fish farming.

Part C: The ocean economy over space [7.5 points]

Let’s now consider how ocean parcels are allocated to the two different activities that we investigated above, seaweed farming and fish farming, assuming that the fish farmer does not internalize the damages associated with the spread of disease to wild populations.

i) [2 points]   Suppose the market for ocean parcels is perfectly competitive. Over what distance from the coast  would we expect the ocean to be devoted to seaweed farming? What about fish farming?  Show your work and explain your answer.

ii) [2 points]   How does ocean use in the competitive market compare to the use of the ocean that is optimal for society? Explain your answer.

iii) [3.5 points]   Suppose that society and the seaweed farmer have the same value for the ocean that is devoted to sea- weed farming. What is the NPV of the ocean to society if the allocation of ocean parcels is determined by a competitive market? How does this compare to society’s NPV of the ocean if the ocean is used to maximize social welfare? Hint: You can round your answers from Parts (i) and (ii) above to the nearest integer.

Part D: Ocean Policy [7.5 points]

Suppose that the Government of Canada has decided to be proactive in protecting it’s wild fish populations from disease. In particular, the government has recognized that fish farmers are not internalizing the damages associated with disease spreading to wild fish populations as a result of their farming operations.

i) [3.5 points]   The government hires a recent graduate from UC Berkeley.  Based on his superb training in natural resource economics, he recommends implementing a site tax/subsidy on fish farming that incentivizes farmers to choose a cycle length that is equal to the optimal cycle length from society’s perspective. What would the value of such a site tax/subsidy be (approximately)? Is the advisor’s policy a good recommendation? Explain your answer.