Bioeconomics of an open-access fishery


The data for this project summarize annual yields, fishing effort levels and dockside prices (in 1976 dollars) for mid-Atlantic yellowfin hake.  (This species subsequently collapsed from overfishing and is no longer commercially important.)  Import these data to Excel.  Create an effort-squared column adjacent to the effort column, and use these data to estimate an effort-yield function of the form Y = α1E + α2E2 (check “Constant is Zero” to force a zero intercept: no effort, no yield).  Create an XY plot of actual yield points and the predicted yield function against effort. 

Calculate the maximum sustainable yield (MSY) level and the value EMSY that maximizes Y.   If the effort-yield function is quadratic, what are the general formulas for calculating EMSY and MSY?  (The actual yields above MSY were not sustainable.) 

Use the data to estimate an inverse market demand function for this species of the form P = β0 + β1Y.  Plot the actual price points and the predicted price line against yield.

Further down in your spreadsheet, enter effort levels from 0 to 1000 in increments of 25. Use your estimated effort-yield function to calculate predicted yield for each effort level.  Use your estimated inverse demand function to calculated predicted price and total industry revenue for each yield.  Assuming a cost of $0.55 per unit of effort, calculate industry total cost and average cost per pound for each yield level.

Use these data to plot yield, TR, TC and industry profit as functions of effort.  What levels of E and Y would maximize industry profit?  TR has (or should have) two peaks; explain why.  There are (or should be) three zero-profit points where TR = TC.   If this is a competitive fishing industry, what is the most likely long-run equilibrium point?  Explain.

The average cost function is the industry’s long-run inverse supply function.  Create an XY plot of predicted demand price and average cost as functions of yield.  The backward-bending supply function intersects demand at three points.  Calculate the consumer surplus for the high-yield and low-yield equilibrium points.  Explain why the middle equilibrium point is unstable.

In hindsight, a tax on fishing effort might have kept harvests at safe levels and maintained the long-term viability of the stock.  What minimum tax per unit effort would have likely prevented this industry from crossing the threshold (the unstable middle equilibrium point) to severe overfishing and eventual collapse?  What tax per unit effort would have sustained effort and yields at the maximum profit point?  (Hint: all profits would have been captured by the tax.)