Economic calculate problem set

ECON 456 San Diego State University Abman Fall 2020

Econ 456 - Problem Set 3

1. Suppose you are in charge of a forestry operation in the Pacific Northwest. Trees on your property grow according to the table below (which relates time to timber volume). This type of timber sells for $2 per board foot in the market, clearing your land will cost you $450 (regardless of the volume when you clear) and your land is worth $850 when cleared. The market interest rate is 12%.

T Volume (Year) (Board feet)

1 150 2 300 3 650 4 800 5 900 6 1,000

(a) What is the optimal (profit maximizing) year to cut your trees? What is the present value of the profits earned in that year?

(b) Find the rotation age that maximizes average annual yield (tMSY )

(c) Suppose a developer offered you $1,500 for your land today (with the trees on it). Should you sell your land or keep it, and harvest timber at the optimal time, and sell your land for the $850 it is worth after the rotation?

(d) Suppose a local mountain biking association offered to pay you and annual amount to keep the trees standing on your land (because they like mountain biking on trails with the trees). What is the minimum amount they would offer you to choose to delay your harvest until year 5, rather than the year you found in part (a)?

2. Suppose a rockfish fishery is characterized by the following equations for sustainable yield (SY ) and total cost (TC):

SY = 60E − 3E2

TC = 9E

The market price for one ton of rockfish is $3.

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(a) Find the level of effort that produces the maximum sustainable yield (EMSY ).

(b) Find the efficient level of effort for the fishery (E∗).

(c) Find the open-access equilibrium for the fishery (EOA).

(d) Graph the sustainable revenue curve and the total cost curve. Identify all points listed in parts (a) - (c).

(e) Find the maximum annual resource rent possible in the rockfish fishery.

(f) Suppose the fishery is currently open access. Regulators are worried that the cur- rent fishery is poorly managed and thus propose that nets may no longer be used to fish and all fishing must be done via longline fishing. This technique is more costly to fisherman and now doubles the cost of a unit of effort (such that it is now $18 rather than $9). What is the effect of this new regulation? What would we expect the new equilibrium effort level to be? Is this policy efficient? Why or why not?

3. Suppose the pacific sablefish fishery is characterized by the following equations for sus- tainable yield (SY ) and total cost (TC):

SY = 100E − 2E2

TC = 12E

The market price for one ton of sablefish is $2.

(a) Find the level of effort that produces the maximum sustainable yield (EMSY ).

(b) Find the efficient level of effort for the fishery (E∗) and the total rents under this level of effort.

(c) Find the open-access equilibrium for the fishery (EOA).

(d) Suppose lower gas prices make it cheaper for fishermen to power their boats. The new lower gas prices drop the cost of a unit of effort to $4 (down from $12). What would be the new open access equilibrium level of effort? Would fishermen be bet- ter off under this new equilibrium rather than the equilibrium found in part (c) with the higher effort cost? What would be the new efficient level of effort for the fishery? If the efficient level of effort could be enforced, how much more rent would

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there be relative to the potential rent from part (b)?

4. Two halibut fisherman each receive a certain share of the total allowable catch (TAC) at the beginning of the fishing season. These two fishermen differ by experience; the fisher- man with the high-level of experience has a lower marginal cost than the fisherman with the low experience. The low marginal cost fisherman (denoted L) has a marginal cost of catching fish of 2∗q and the high marginal cost fisherman (denoted H) has a marginal cost of catching fish of 5∗q where q refers to tons of halibut. The market price for hal- ibut is $500 per ton. Suppose a regulator has decided to limit the tons of halibut that can be fished in a given year to 100 tons and issues permits at the beginning of the season.

(a) Suppose the regulator were to issue 50 permits to each fisherman for the season and they can not trade the permits. What will the total profits from the halibut fishery be this year under this allocation?

(b) If the regulator had information regarding the marginal cost of each fisherman, how many permits would she issue each of the fisherman in order to maximize total prof- its from the halibut fishery this year? What are the total profits from this optimal allocation? Why do they differ from the profits in the allocation described in part (a)?

(c) Suppose 50 permits were allocated to each fisherman, but they can trade permits amongst each other. How many would each of them end up with after this bar- gaining has taken place? How much would fisherman L be willing to pay for the additional permits (those he buys beyond the 50 permits he is allocated)? How much would fisherman H be willing to accept to sell these permits?

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