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Consider a Stackelberg duopoly with a homogeneous product where market demand is given by P =...

Consider a Stackelberg duopoly with a homogeneous product where market demand is given by P = 1 - Q = 1 - q1 - q2. Firm 1 produces one unit of output using one unit of labor and one unit of a raw material. Firm 2 produces one unit of output using two units of labor and one unit of the raw material. The unit costs of labor and the raw material are w and r respectively. The timing of the game is as follows: t=1: Firm 1 purchases its inputs and produces output q1, which is observed by Firm 2. t=2: Firm 2 purchases its inputs and produces output q2, which is observed by Firm 1. t=3: Both firms sell their output and payoffs are realized. 1. Compute the SPNE and SPNE outcome of the game. 2. How does Firm 1's profit vary in the price of labor w? Can you give some intuition for this result?

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Firm 1's profit is negatively related to w. As w rises, firm 1's payoff fall in every game.

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