A price-taking firm in the X industry has the following (pre-tax) total short-run cost function: TC = 50 +30Q + Q^2. Price equals $130. The government is considering the following taxation policies: (a) A per-unit tax of $20/unit, (b) A tax of profit of 50% or (c) A lump-sum tax of $10. Fill in the blanks below. (Assume the firm still faces a price of $130 after a tax is imposed).
Profit-maximizing SR quantity prior to any tax (show the pre tax total profit function) = ?
Profit-maximizing SR quantity under the profit tax = ?
Profit-maximizing SR quantity under the excise tax = ?
Profit-maximizing SR quantity under the lump sum tax = ?