1. Suppose that the government imposes a production tax. That is, the firm pays t units of consumption goods to the government for each unit of output that it produces. The firm's problem now becomes to maximize = [zF(K, Nd) tzF(K, Nd)] - wnd with variables as defined in class. Consider the following information: Y = 2K0.3N0.7 and : = 3, K = 4, w = 1, t=0.05. (a) What is the optimal amount of labor for the firm without the tax and what is it after the tax? (6 points) (b) Illustrate the original optimum (with no tax) and the new one (with the production tax) on a graph with costs/revenue on the y-axis and N on the x-axis. Be sure to label your curves as well as distinguishing between the pre-tax and post-tax optimums. (10 points) (C) How much does the firm produce before the tax and how much does it produce after the tax? (5 points) (d) What is the firm's profit before the tax and what is it after the tax? (6 points) (e) Illustrate the effect of this tax on the firm's demand for labor on a graph with the wage on the vertical axis and labor demand on the x-axis. Be sure to include the values you computed for part (a). (3 points) 1. Suppose that the government imposes a production tax. That is, the firm pays t units of consumption goods to the government for each unit of output that it produces. The firm's problem now becomes to maximize = [zF(K, Nd) tzF(K, Nd)] - wnd with variables as defined in class. Consider the following information: Y = 2K0.3N0.7 and : = 3, K = 4, w = 1, t=0.05. (a) What is the optimal amount of labor for the firm without the tax and what is it after the tax? (6 points) (b) Illustrate the original optimum (with no tax) and the new one (with the production tax) on a graph with costs/revenue on the y-axis and N on the x-axis. Be sure to label your curves as well as distinguishing between the pre-tax and post-tax optimums. (10 points) (C) How much does the firm produce before the tax and how much does it produce after the tax? (5 points) (d) What is the firm's profit before the tax and what is it after the tax? (6 points) (e) Illustrate the effect of this tax on the firm's demand for labor on a graph with the wage on the vertical axis and labor demand on the x-axis. Be sure to include the values you computed for part (a). (3 points)