Homework answers / question archive / Oregon State University Department of Applied Economics AEC 351 Homework 5  Suppose that growth rate of the Atka mackerel (Pleurogrammus monopterygius) stock in the Western Aleutian Islands fits a logistic function, with parameter values listed in Table 1 below

Oregon State University Department of Applied Economics AEC 351 Homework 5  Suppose that growth rate of the Atka mackerel (Pleurogrammus monopterygius) stock in the Western Aleutian Islands fits a logistic function, with parameter values listed in Table 1 below

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Oregon State University

Department of Applied Economics

AEC 351

Homework 5 

1. Suppose that growth rate of the Atka mackerel (Pleurogrammus monopterygius) stock in the Western Aleutian Islands fits a logistic function, with parameter values listed in Table 1 below.

 

1. 1. What is the stock level that corresponds to maximum sustainable yield (MSY)? Depict your solution on a graph with growth on the vertical axis and the stock level on the horizontal axis.

 

Table 1. Parameter values

Parameter	a	K	q	p	w
Value	.8	3,000	0.025	100	400
Units	1/year	tons	1/trip	$/ton	$/trip

 

2. Now assume that there is a single decision maker (a hypothetical “sole owner”, or perhaps a cooperative) empowered to choose the level of effort for the fishery. The vessel has cost per-unit of effort equal to w and earns landings price p for Atka mackerel harvested (see Table 1).

 

1. 1. What level of effort (trips/season) will the decision maker select for the fishery in equilibrium? Use the bioeconomic functions provided in Table 2 below to calculate your answer. Explain your reasoning.

 

1. 2. On a graph with dollars on the vertical axis and effort on the horizontal axis, depict your answer to problem #2.

 

Table 2. Bioeconomic functions of aggregate effort

Sustainable stock
Sustainable harvest rate
Total revenue
Total cost
Average revenue
Average cost	w
Marginal revenue
Marginal cost	w

 

1. 1. 1. of 2

 

 

3. Consider a scenario where the Western Aleutian Island Atka mackerel fishery is open access, with all current and potential participants facing the same landing price and sharing vessel 1’s cost structure.

 

1. 1. What level of effort will be active in this fishery in equilibrium under open access? Explain your reasoning.

 

1. 2. On a new graph with dollars on the vertical axis and effort on the horizontal axis, depict your solution to problem #3.a.
2. 3. Taking your graph from problem #3.b, add the solutions to problems #1.a. and #2.a (making adjustments as necessary so all solutions are in the same units). If the three solutions you draw differ, explain how and why.

 

1. 1. 2. of