(15p) Consider a profit-maximizing U.S. monopolistic firm that produces one product, Q at two different plants, one in U.S. (Q1) and the other in Mexico (Q2). The firm faces the inverse demand function P=abQ, where Q=Q1+Q2. The domestic cost function is C1=sQ12 and the cost function in Mexico is C2=tQ22+Q2, where is the U.S. tariff applied per unit produced in Mexico. Mind that production is more expensive in the U.S. than in Mexico, s>t, but there is an import tax. (a) (5p) Write the profit function. Find the profit maximizing first order conditions and the solution to it. What parametric restriction is needed for Q2 to be positive? (b) (4p) Do the comparative static analysis of the total output Q=Q1+Q2 as changes. (c) (4p) Find the second order conditions. What parametric restrictions are needed for the solution to the first order conditions to be a local maximum? (d) (2p) If the firm is working in a perfectly competitive market, i.e. the inverse demand function is not a function of Q, does your answer to (b) change? (15p) Consider a profit-maximizing U.S. monopolistic firm that produces one product, Q at two different plants, one in U.S. (Q1) and the other in Mexico (Q2). The firm faces the inverse demand function P=abQ, where Q=Q1+Q2. The domestic cost function is C1=sQ12 and the cost function in Mexico is C2=tQ22+Q2, where is the U.S. tariff applied per unit produced in Mexico. Mind that production is more expensive in the U.S. than in Mexico, s>t, but there is an import tax. (a) (5p) Write the profit function. Find the profit maximizing first order conditions and the solution to it. What parametric restriction is needed for Q2 to be positive? (b) (4p) Do the comparative static analysis of the total output Q=Q1+Q2 as changes. (c) (4p) Find the second order conditions. What parametric restrictions are needed for the solution to the first order conditions to be a local maximum? (d) (2p) If the firm is working in a perfectly competitive market, i.e. the inverse demand function is not a function of Q, does your answer to (b) change