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Suppose that it costs $400 per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. On an average day, the total weight of mushrooms M found at Pt. Reyes is M=100x-x^2 pounds ,where X is the number of people mushroom hunting on that day. Chanterelles can be sold for $90 per pound. How many more people will go mushroom hunting than is socially optimal?

Sagot :

Answer: 48

Explanation:

Firstly, we need to solve the marginal product which will be:

= dM/dx

= d(100x - x²)/dx

= 100-2x

At socially optimal level, it should be noted that:

Price × Marginal Product = Cost

90 × (100-2x) = 400

9000 - 1800x = 400

1800x = 9000 - 400

1800x = 8600

x = 8600/180

x = 47.77

x = 48

Therefore, the optimal number of workers will be 48.

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