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(e) Explain how someone who looked at Hoglund's and Skoglund's corn yields and their fertilizer inputs but couldn't observe the quality of their land, would get a misleading idea of the productivity of fertil- izer. Fertilizer did not cause the entire difference in yield. The best land got the most fertilizer. 19.10 (0) A firm has two variable factors and a production function, ((31, 12) = 2 27 . The price of its output is 4. Factor 1 receives a wage of w and factor 2 receives a wage of 12. (@) Write an equation that says that the value of the marginal product -1/2 1/4 of factor 1 is equal to the wage of factor 1 20 2 06 = Wj and an equation that says that the value of the marginal product of factor 1/2 -3/4 2 is equal to the wage of factor 2. 21 2 = W2. Solve two equations in the two unknowns, a, and ry, to give the amounts of factors 1 and 2 that maximize the firm's profits as a function of w and wa. This gives r1 = 8/(wiway) and x3 = 4/(wfwi) . (Hint: You could use the first equation to solve for r as a function of z, and of the factor wages. Then substitute the answer into the second equation and solve for ry as a function of the two wage rates. Finally use your solution for zo to find the solution for 21.) (b) If the wage of factor 1 is 2, and the wage of factor 2 is 1, how many units of factor I will the firm demand? 1 . How many units of factor 2 will it demand? 1. How much output will it produce? 1 . How much profit will it make? 1