Question

In: Economics

At the Santa Barbara fishing hole, people come from all around to catch fish to sell...

At the Santa Barbara fishing hole, people come from all around to catch fish to sell at the fish market.
The total number of fish caught is F = 10x-x2
where x is the number of fishermen. Suppose it costs
each person $20 a day to fish and that fish sell for $10 each at the market. At the social optimum,
how much would it hurt all the other fishermen (combined) if one more person started fishing?
(a) $30
(b) $20
(c) $10
(d) $40

Answer D=40

could you please explain in detail?

Solutions

Expert Solution

Soln. At social optimum, marginal social benefit = marginal social cost

Let no of fisherman = 2

Therefore, no of fish caught = 10*x - x2 = 10*2 - 22 = 16

Total sale of the market = 10*16 (price of each fish is $10 and total no of fish is 16) = $160

Total cost of the market = 20*2 (cost for each fisherman to fish is $20 and total fisherman is 2) = $40

Benefit of market = total sale - total cost

= $160 - $40 = $120

Combined benefit of all the fisherman = $120

Benefit of each fisherman = 120/2 = $60

Now, let 1 extra fisherman added.

Therefore, total no of fisherman = 3

No of fish caught = 10*3 - 32 = 30 - 9 = 21

Total sale of the market = 10*21(price of each fish is $10 and total no of fish is 21)= $210

Total cost of the market = 20*3 (cost for each fisherman to fish is $20 and total fisherman is 3) = $60

New benefit of market = total sale - total cost

= $210 - $60 = $150

Benefit of each fisherman = 150/3= $50

Loss of each fisherman = $60 - $50 = $10

Combined loss = 2*20 = $20

  


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