3. The manufacturing of Styrofoam coffee cups causes damage to a local river when the manufacturing plant produces more than 500 units in a period. To discourage the plant from producing more than 500 units, the local community is considering placing a tax on the plant. The long-run cost curve for the firm is: C(g. f) = 1500+tq, where q is the number of coffee cups produced and it is the per unit tax on paper production. The relevant marginal cost curve is: MC(q. f)=+t. If the manufacturing plant can sell all of its output for $1 what is the firm's optimal output if the tax is set at zero? What is the minimum tax rate necessary to ensure that the firm produces no more than 500 units? How much are the firm's profits reduced by the presence of a tax?