A firm has two variable factors and a production function (21,22) = x/2x}. Please find the marginal product using formulas in the lecture notes by yourself. The price of its output is 4. Factor 1 receives a wage of w and factor 2 receives a wage of u. (a) Write an equation that says that the value of the marginal product of factor 1 is equal to the wage of factor 1: and an equation that says that the value of the marginal product of factor 2 is equal to the wage of factor 2 Solve two equations in the two unknowns, 11 and 12, to give the amounts of factors 1 and 2 that maximize the firm's profits as a function of w and . This gives a =- and xy = (Hint: You could use the first equation to solve for xl as a function of x2 and of the factor wages. Then substitute the answer into the second equation and solve for x2 as a function of the two wage rates. Finally use your solution for 2 to find the solution for x1.)
(b) If the wage of factor 1 is 2, and the wage of factor 2 is 1, how many units of factor 1 will the firm demand?___ How much output will it produce? How much profit will it make? How many units of factor 2 will it demand? 2