Question

2. Suppose there are two firms that emit pollution. The abatement cost of firm 1 is \frac{1}{2}(\theta_1 - x_1)^2 where $\theta_1$ is a constant and $x_1$ is firm 1's emissions of pollution. Likewise, the abatement cost of firm 2 is \frac{1}{2}(\theta_2 - x_2)^2. a) Determine the marginal abatement cost functions for firm 1 and firm 2 (give a mathematical description). b) Suppose we want the total emissions of pollution to be limited to $x$, and we are going to do this by placing a tax $t$ on emissions. What $t$ should we select? c) Now suppose we want $x = 0$ (we want zero pollution.) What $t$ should we select?

          2. Suppose there are two firms that emit pollution. The abatement cost of firm 1 is \frac{1}{2}(\theta_1 - x_1)^2 where $\theta_1$ is a constant and $x_1$ is firm 1's emissions of pollution. Likewise, the abatement cost of firm 2 is \frac{1}{2}(\theta_2 - x_2)^2.
a) Determine the marginal abatement cost functions for firm 1 and firm 2 (give a mathematical description).
b) Suppose we want the total emissions of pollution to be limited to $x$, and we are going to do this by placing a tax $t$ on emissions. What $t$ should we select?
c) Now suppose we want $x = 0$ (we want zero pollution.) What $t$ should we select?

2. Suppose there are two firms that emit pollution. The abatement cost of firm 1 is (1)/(2)(θ1 - x1)^2 where θ1 is a constant and x1 is firm 1's emissions of pollution. Likewise, the abatement cost of firm 2 is (1)/(2)(θ2 - x2)^2.
a) Determine the marginal abatement cost functions for firm 1 and firm 2 (give a mathematical description).
b) Suppose we want the total emissions of pollution to be limited to x, and we are going to do this by placing a tax t on emissions. What t should we select?
c) Now suppose we want x = 0 (we want zero pollution.) What t should we select?

Added by Karen P.

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