A monopoly firm faces a demand curve given by P = 80 – Q and has a cost curve given by TC = 0.6Q^2. Specify and demonstrate its optimal output, price, and profits. Now suppose a specific tax of $16 per unit produced is imposed upon this firm; specify and demonstrate how this tax affects the firm’s optimal output, price and profits. Suppose instead a fixed “franchise tax” of $160 is levied upon the firm; specify and demonstrate how this tax affects the firm’s optimal output, price, and profits. Finally, suppose a “corporate profits tax” of 50% is levied upon the firm; specify and demonstrate how this tax affects the firm’s optimal output, price, and profits.