Example 10

EXAMPLE 10 Fishing and Logging

In this model, we assume that the cost of harvesting a unit of the population decreases as the size of the population increases. This is the familiar principle of economy of scale. For example, the same fishing effort yields more fish when fish are more abundant. Similarly, a logger’s harvest costs per tree are less when the trees are clumped together. This is the logger’s motivation to clear-cut large stands. What would a sustainable-yield harvesting policy be?

The cost curve slopes downward and to the right, as in Figure 23.14. The size of the population from which 1 unit is harvested is shown on the horizontal axis. The (average) cost of harvesting a single unit is measured on the vertical axis.

An optimal sustainable-yield harvesting policy depends on the relation between price and costs. There are two cases, as shown in Figure 23.15 on the next page, for a fixed price level.

Figure 23.14: Figure 23.14 The unit cost, as a function of population size, for fishing or logging.

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Figure 23.15: Figure 23.15 The unit cost, unit revenue, and unit profit of harvesting 1 unit, as a function of population size, for fishing or logging. (a) The market price is below the harvesting cost for all population sizes. (b) The operation is profitable for populations above a certain minimum size.

The unit cost curve lies entirely above the unit price line (Figure 23.15a). The revenue received for a harvested unit is less than the cost of harvesting it, no matter how large the population. It is impossible to make a profit.
The unit cost curve intersects the unit price line (Figure 23.15b). Above a certain population size, the price for a harvested unit is more than the cost of harvesting it, so profit is possible. Some population size, the economically optimal harvest, gives a maximum net profit. That harvest is lower than the maximum sustainable yield but leaves a greater number to reproduce for next year.