(12 pts, Chapter 4) Consider the following questions on labor demand. (a) Prove graphically that a profit maximizing firm will hire labor where the marginal product of labor is equal to the wage rate. (b) Among other things, the new health care legislation will tax sun-tanning booths. That is, every time you use sun-tanning booth services, the salon must pay a federal government tax. What should happen to the demand for labor at sun- tanning salons? Prove your assertions graphically. 3 (c) Suppose that the production of a firm is given by the cobb-douglas form: Y z(K).40(N).60. Using the above production function, plot output for where z = K 1 at various levels of labor. Find and plot the marginal product of labor. Is it positive and diminishing? (d) Using the above production function, plot output for where z 2, K = 1 at various levels of labor. Given the rise in z, what should happen (and why) to the demand for labor? Explain. (12 pts, Chapter 4) Consider the following questions on labor demand. (a) Prove graphically that a profit maximizing firm will hire labor where the marginal product of labor is equal to the wage rate. (b) Among other things, the new health care legislation will tax sun-tanning booths. That is, every time you use sun-tanning booth services, the salon must pay a federal government tax. What should happen to the demand for labor at sun- tanning salons? Prove your assertions graphically. 3 (c) Suppose that the production of a firm is given by the cobb-douglas form: Y z(K).40(N).60. Using the above production function, plot output for where z = K 1 at various levels of labor. Find and plot the marginal product of labor. Is it positive and diminishing? (d) Using the above production function, plot output for where z 2, K = 1 at various levels of labor. Given the rise in z, what should happen (and why) to the demand for labor? Explain