# Optimal rate of harvest | Concept of optimal depletion and its conditions

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Hello Friends, welcome to my website Khan Study. In today’s article we are going to know about Optimal rate of harvest (Concept of optimal depletion and its conditions) . So let’s discuss in details.

## Optimal rate of Harvest

In population ecology and economics, the optimum sustainable yield is the level of effort that maximises the difference between total revenue and total cost.

In other words, where marginal revenue equals marginal cost, at that level we get optimum rate of harvest. The optimum rate is the harvest level that produces the largest annual net benefits. Let us assume that-

• The resource (Fish) price is constant.

• The marginal cost of fishing effort is constant.

• The amount of harvest per unit of effort expanded is proportional to the size of the resource stock. Now, we introduce the level of exploitation (harvest) of the resource from assumption 3 we can write-

X = Y/E —— (i)

Alternatively we can write –

E = Y/X ——- (ii)

Where, E = Effort

X = Resource stock

Y = Harvest

From equation (ii) it is cleared that bigger the effort (E), larger will be the harvest (Y) but lesser is the resource stock (X).  Now equation (ii) we can be written as –

Y = EX —– (iii)

## Economically Optimal rate of Harvest with diagram

In the following figure, on OX axis we measure resource stock (Fish Population) and on OY axis we measure growth and harvest.

We assume that X min = X0. The choice of effort (E) will determine the equilibrium harvest (Y) and the stock level (X). Where Ex in equation (iii) is equal to the growth of the resources we attain the equilibrium rate.

In the above figure, Y1 along the line E1X will mean that harvest is greater that sustainable yield Y1 and the stock will decline to X1.

A harvest level below Y1 along E1X will be less than the yield and in this case the stock will grow to X1 again. In the above figure Ym is the maximum sustainable yield of the resource Xm.

Similarly, EmX is the maximum sustainable effort level from the figure it is cleared that Ym > Y1, it means sustainable yield is greater than the equilibrium yield (optimum level of yield).

Similarly, on OX axis maximum sustainable resource stock (X1). Thus the figure shows that as the yield rate falls the resource stock increases.

### Optimal Depletion

The optimum rate is the rate where the harvest rate is equal to the stock level of the resource. The optimal depletion condition can be stated as follows –

X = Y/E

⇒ Y = EX

This is called the condition of optimal rate of depletion. If Y > EX, then there is degradation of the resources. Again if EX > Y, then there is surplus of resources which will regenerate the resource base.

#### Conclusion

So friends, this was the concept of Optimal rate of harvest (Concept of optimal depletion and its conditions). Hope you get the full details about it and hope you like this article.

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