Four brothers share a forest with 2,000 acres of trees. To preserve the forest, the government promises to pay the group $400,000 minus $200 per acre of trees that has been cut down (this money will be split evenly among the brothers.) Each brother can cut down and sell trees for $100 per acre.

What is the symmetric Nash equilibrium quantity of cut tree acres per individual?

a. 0 acres
b. 100 acres
c. 1,000 acres
d. 500 acres

Question

Four brothers share a forest with 2,000 acres of trees. To preserve the forest, the government promises to pay the group $400,000 minus $200 per acre of trees that has been cut down (this money will be split evenly among the brothers.) Each brother can cut down and sell trees for $100 per acre.

What is the symmetric Nash equilibrium quantity of cut tree acres per individual?

a. 0 acres
b. 100 acres
c. 1,000 acres
d. 500 acres

dtan5457 · Answer

btw for part 1 of this question I found that not cutting any acres would maximize the profit of the group, if that is helpful...

dtan5457 · Answer

@ganeshie8 @Directrix @Hero @Abhisar

dtan5457 · Answer

I WILL FAN AND MEDAL HELP ME

anonymous · Answer

Nash equilibrium I believe is when everyone acts in their own self interest, which may or may not be in the interest of the entire group

jtvatsim · Answer

Seems to me that the "best situation" for each individual would be to cut down as many tree acres as possible.

dtan5457 · Answer

The answer is apparently 500 acres, but why? I don't know

jtvatsim · Answer

That's what I got as well.

jtvatsim · Answer

Like "uhhhh" said, a Nash Equilibrium is the "greedy solution" when each individual maximizes their profit.

dtan5457 · Answer

mind explaining?

jtvatsim · Answer

Sure thing.

jtvatsim · Answer

The brothers profit from two sources: 1) the government funds, and 2) cutting down trees.

jtvatsim · Answer

All of these funds will be divided evenly (presumably) since each individual wants to maximize their profit.

jtvatsim · Answer

Therefore, looking at the profits relative to ONE BROTHER:

P1 = (400,000 - 200a)/4  (from the government divided among 4)
and
P2 = 100a (from the trees)

jtvatsim · Answer

The total profit for one brother is given by
P1 + P2 = (400,000 - 200a)/4 + 100a = (400,000 + 200a)/4

jtvatsim · Answer

From the form of the profit, it is apparent that "a" should be made as large as possible

jtvatsim · Answer

There are only 2000 acres for all 4 brothers, so each can get 500. This is the maximum value of a, and therefore, the maximum profit.  In other words, the brothers should completely destroy the forest.

jtvatsim · Answer

Does that make sense?