Review session for Midterm #1

5.28 Consider Noah’s preference for leisure (L) and other goods (Y), U(L,Y) = L + Y . Theassociated marginal utilities are MU L= 1 and MU Y= 12 L2 Y . Suppose that P Y=$1. Is Noah’ssupply of labor backward bending?If Noah’s wage rate is w, then the income he earns from working is (24 – L)w. Since P Y = 1, the number ofunits of other goods he purchases is Y = (24 – L)w. Also, the tangency condition gives us2Combining the two conditions, w L = (24 − L)w , orY = w . L24L = . Clearly, the amount of leisure thatw + 1Noah consumes decreases with an increase in the wage rate, and this is true no matter what the wagerate is. Since the amount of labor that Noah supplies equals (24 – L), we see that his supply of laboralways increases with an increase in the wage rate. So, his labor supply curve is always positively sloped– that is, it is not backward bending.Chapter 6 Review Questions6.4 Suppose that the production function for DVDs is given by Q=KL 2 ‐L 3 , where Q is the number ofdisks produced per year, K is machine‐hours of capital, and L is man hours of labor.a) Suppose K=600. Find the total product function and graph it over the range L=0 and L=500. Thensketch the graphs of the average and marginal product functions. At what level of labor L does theaverage product curve appear to reach its maximum? At what level does the marginal product curveappear to reach its maximum?Total Product with K=600Total Product35,000,00030,000,00025,000,00020,000,00015,000,00010,000,0005,000,000-0 100 200 300 400 500 600 700Labor19