Question

The total dollar value of bison killed from Huntington Forest is , where is the number of bison killed. The marginal cost of killing bison is 0. What is the optimal bison-killing tax (per bison) to avoid the tragedy of the commons in this forest

Answer 1

Question:

The total dollar value of bison killed from Huntington Forest is
`f(b) = 53b - 1.3b^2` , where b is the number of bison killed. The marginal cost of killing bison is 0. What is the optimal bison-killing tax (per bison) to avoid the tragedy of the commons in this forest

Answer:

26.5

Step-by-step explanation:

Given:

`f(b) = 53b - 1.3 b^2`, where b is the number of bison killed.

Marginal cost, MC = 0

The socially efficient level: π=f(b)-MC(b)

π = 53b - 1.3b²

`(d\pi)/(db) = 53 - 2.6b = 0`

`2.6b = 53`

`b = (53)/(2.6) = 20.38`

For tragedy of commons:

AR = AC = 0

`AR = (f(b))/(b) = 53 - 1.3b`

`b' = (53)/(1.3) = 40.77`

For imposed tax, t, we have:

AR = AC = 0 + t, where b = 20.38

53 - 1.3b = t

At
`b = b' = 20.38`

Let
`(53)/(2.6)` represent b

`53 - 1.3b = t`

`53 - 1.3((53)/(2.6)) = t`

`53 - 0.5(53) = t`

`53 - 26.5 = t`

t = 26.5

Therefore, optimal bison-killing tax = 26.5