Suppose that a firm’s production function is given by =K0.33L0.67 , where PK=0.33K−0.67L0.67 , and PL=0.67K0.33L−0.33 . a. As L increases, what happens to the marginal product of labor? b. As K increases, what happens to the marginal product of labor? c. Why would MPL change as K changes? Labor and capital are substitutes. Technology makes capital more valuable, so firms use more capital and less labor. Labor becomes more productive when capital increases. Capital crowds out labor. d. As capital increases, MPK , and as labor increases, MPK .

Aproduction line has three machines a, b, and c, with reliabilities of .96, .86, and .85, respectively. the machines are arranged so that if one breaks down, the others must shut down. engineers are weighing two alternative designs for increasing the line’s reliability. plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. in either case, three machines (a, b, and c) would be used with reliabilities equal to the original three. a. compute overall system reliability under plan 1. (round your intermediate calculations and final answer to 4 decimal places.) reliability b. compute overall system reliability under plan 2. (round your intermediate calculations and final answer to 4 decimal places.) reliability c. which plan will provide the higher reliability? plan2plan1