Question

The most popular state park in the Craggy Mountains recently re ached the point where a common property resources problem arose — too many people hunted for wild boar each season. The boar population became over hunted and was in peril of exti nction. An economist at the local university studied the probl em for the park management an d estimated the following cost and revenue relationships: Demand: P = 10 - 0.008Q Marginal social cost: MSC = 1.00 + 0.0067Q Marginal private cost: MPC = 1.00 + 0.0010Q. The variable Q represents th e number of boars killed each seaso n and price P is in hundreds ($). a. Determine the equilibrium numb er of boars killed per season, wh en there is unlimited access to the park. b. Determine the per boar fee that must be charged to reduce the h arvest to the efficient level. c. Determine the social cost of unlimited hunting of the boar.

Answer 1

SOLUTION:-

(A). With unlimited access, equilibrium is obtained by equating demand with Marginal Private Cost (MPC).

10 - 0.008Q = 1 + 0.001Q

0.009Q = 9

Q = 1,000

Price = MPC = 1 + (0.001 x 1,000) = 1 + 1 = $2

(B). Social optimum is obtained by equating Demand with Marginal social cost (MSC).

10 - 0.008Q = 1 + 0.0067Q

0.0147Q = 9

Q = 612

Price = MSC = 1 + (0.0067 x 612) = 1 + 4.1 = $5.1

When Q = 612, MPC = 1 + (0.001 x 612) = 1 + 0.61 = $1.61

Required fee to be charged = $(5.1 - 1.61)

= $3.49

(C). Social cost = (1/2) x Difference in Price x Difference in Quantity

= (1/2) x $(5.1 - 2) x (1,000 - 612) = (1/2) x $3.1 x 388 = $601.4