Problem 3 Two timber companies sell wood at a price of $4000 per ton. (There are...

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Problem 3 Two timber companies sell wood at a price of $4000 per ton. (There are many other companies in other regions so price does not vary with the two companies' production plans.) They cut down trees in the same forest so chopping off an extra ton of sellable wood gets only more expensive the more wood has already been cut. Formally, firm 1's cost for selling q₁ tons of wood while its competitor sells q2 tons is (9₁ +92)91. Assuming a similar cost function for firm 2, profit functions are thus given by the following formulas: π1 = 4000q₁ 4000g (91 +92)91 π2 = 400092 400092 (91 +92)92 2 (a) (2 pts) What is the SPNE if firm 1 is the leader and firm 2 is the follower? (b) (2 pts) Check whether the outcome resulting from the SPNE computed in (a) is Pareto efficient or not. Problem 3 Two timber companies sell wood at a price of $4000 per ton. (There are many other companies in other regions so price does not vary with the two companies' production plans.) They cut down trees in the same forest so chopping off an extra ton of sellable wood gets only more expensive the more wood has already been cut. Formally, firm 1's cost for selling q₁ tons of wood while its competitor sells q2 tons is (9₁ +92)91. Assuming a similar cost function for firm 2, profit functions are thus given by the following formulas: π1 = 4000q₁ 4000g (91 +92)91 π2 = 400092 400092 (91 +92)92 2 (a) (2 pts) What is the SPNE if firm 1 is the leader and firm 2 is the follower? (b) (2 pts) Check whether the outcome resulting from the SPNE computed in (a) is Pareto efficient or not.

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a To find the Subgame Perfect Nash Equilibrium SPNE in this sequential game we will analyze the game backwards starting with the followers decision Fi... View the full answer