9. Consider a profit-maximizing firm with the production function y' = f (x1, x2), facing output price p and factor prices w, and w. Suppose this firm is taxed according to the total cost of factor 2, i.e., tax = 1w2x2. (a) Derive the factor demand functions; i.e., show where they come from, etc. Are these choice functions homogeneous of any degree in any of the parameters? (b) Show that if the tax rate rises, the firm will use less of factor 2. (c) Show that 8x1/21 = w28x;/aw, (d) Suppose that factor 1 is held fixed at its profit-maximizing level. Show that the response of factor 2 to a change in the tax rate is less in absolute value than before. 9. Consider a profit-maximizing firm with the production function y' = f (x1, x2), facing output price p and factor prices w, and w. Suppose this firm is taxed according to the total cost of factor 2, i.e., tax = 1w2x2. (a) Derive the factor demand functions; i.e., show where they come from, etc. Are these choice functions homogeneous of any degree in any of the parameters? (b) Show that if the tax rate rises, the firm will use less of factor 2. (c) Show that 8x1/21 = w28x;/aw, (d) Suppose that factor 1 is held fixed at its profit-maximizing level. Show that the response of factor 2 to a change in the tax rate is less in absolute value than before