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?
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Ответ:
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.
Ответ:
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