A monopoly firm has a marginal cost of = 12 + 6. They serve a market with demand function = 150 2, and associated marginal revenue of = 150 4. Suppose that a per unit tax is imposed on the firm's output. a. Determine the monopolist's updated marginal cost as a function of the tax, . (*Hint: think about how a $ per unit tax will impact the firm's per-unit costs.) b. Derive reduced form equations for the profit-maximizing values of and in terms of the tax . c. Use the reduced form equations to predict the and values when = $8 .