Can anyone help me with this question with explanations? (#5-6) A village uses a

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Can anyone help me with this question with explanations? (#5-6)

A village uses a nearby forest to hunt for food, and has no other source of food. The village has the following Value function for hunting: Value 30v -v2 where v represents the number of villagers hunting. For each villager, the marginal 1. Why might the villagers total value from hunting eventually decline as the 2. Find the marginal value gained by an additional villager hunting cost for hunting is MC-4 number of hunters increases? 3. If revenue is divided equally across all villagers who participate in the hunt, find how much value each villager receives as a function of v. (hint: find average value per hunter How many villagers will hunt if the forest is open to anyone who wants to hunt? What will the total profit (value - cost) be? (Recall that with free entry we expect firms to enter until average profit is 0) 5. If the forest were optimally managed, how many villagers would participate in the hunt, and what would be the total profit? 6. Suggest a mechanism through which the village might achieve the optimal num ber of hunters. Be as detailed as possible in defending your mechanism in a few sentences

Explanation / Answer

1) The total value of villagers from hunting decline due to law of diminishing return that states that when more inputs of production such as labor are invested in the production, the total output will start decreasing after a certain level.  

2) Total value of hunting(V) = 30v-v 2

Marginal value of hunting, dV/dv= 30-2v (Taking first order derivative of either side)

At equilibrium point, marginal value of hunting = marginal cost of hunting

i.e., 30-2v = 4 .......(i), which is the marginal value of villager from hunting.

3) Solving (i), we get v =13 , total value of hunting = 30v-v2

Therefore, average value of hunting = (30v-v2 )/v = 30-v = 30-13= 17.

4) Total number of villagers who would participate in hunting = 13

marginal cost is constant. Therefore, marginal cost= average cost = 4

Therefore, total profit = Total value- Total cost = 30v-v2 - 4v= 26v-v2 = 13(26-13)= 169

5) if the forest is optimally managed, then marginal value of hunting = 0

i.e., 30-2v=0 or, v=15  

Therefore, total profit = total value - total cost = 30v-v2 - 4v = v(26-v) = 15*(26-15) = 15*11= 165

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