Question

Suppose that it costs $200 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?

Answer 1

Solution :-

Given

M = ( 100 X - X 2 )

The number of people mushroom hunting on that day. be X

Costs per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. = $200

Selling Price of Chanterelles ( P ) = $90

Now We see the Individuals will go mushroom hunting so long as they receive a positive profit from doing so

Therefore

= ( 100 - X ) * $90 = $200

100 - X = 2.22

X = 97.78

Now , The Social Planner instead seeks to maximize profit ( MTB = MTC )

= $90 * ( 100 X - X 2 ) - $200 X = 0

= 9000 X - 90 X 2 - 200 X = 0

Now with Differentiation

= 9000 - 180 X - 200 = 0

180 X = 8,800

X = 48.89 Units

Hence, 48.89 more people go mushroom hunting than the socially optimal allocation .

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