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

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

$\frac{d\pi}{db} = 53 - 2.6b = 0$

$2.6b = 53$

$b = \frac{53}{2.6} = 20.38$

For tragedy of commons:

AR = AC = 0

$AR = \frac{f(b)}{b} = 53 - 1.3b$

$b' = \frac{53}{1.3} = 40.77$

For imposed tax, t, we have:

AR = AC = 0 + t,  where b = 20.38

53 - 1.3b = t

At $b = b' = 20.38$

Let$\frac{53}{2.6}$ represent b

$53 - 1.3b = t$

$53 - 1.3(\frac{53}{2.6}) = t$

$53 - 0.5(53) = t$

$53 - 26.5 = t$

t = 26.5

Therefore, optimal bison-killing tax = 26.5