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Question 1 Suppose the polluting firm has a cobb-douglas production function Y = =KoNI-a with capital and productivity fixed. The government gives the firm a choice: pay a (pro- portional) tax 7 per unit of output or hire additional workers to clean up the pollution. Suppose that the pollution is such that the firm would have to hire a additional workers in order to clean up the pollution generated by each unit of output, and assume that these additional workers are hired in the same labor market as the production workers. (a) Suppose the firm chooses to pay the proportional tax, set up the firm's optimization problem and solve for the optimal hiring M and the maximal profit III. (b) Suppose the firm chooses to hire workers instead to clean up the pollution. Set up firm's optimization problem and solve for optimal hiring N2 and the maximal profit II2. (c) Under what conditions, if any, would the firm prefer to hire more workers instead of paying the tax