Question: A firm has two variable factors and a production function, f(x 1 , x 2 ) = x 1 1/2 x 2 1/4 . The
A firm has two variable factors and a production function, f(x1, x2) = x11/2x21/4 . The price of its output is 4. Factor 1 receives a wage of w1 and factor 2 receives a wage of w2.
(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, x1 and x2, to give the amounts of factors 1 and 2 that maximize the firm’s profits as a function of w1 and w2. This gives x1 _________ and x2 = ________. You could use the first equation to solve for x1 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 x2 to find the solution for x2.)
(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 many units of factor 2 will it demand ________. How much output will it produce ___________. How much profit will it make ___________?
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