4. [25 Points] A rm has a production function y = f (LK) = L1/3K2/3 where input prices are 10;, = $4 and nix = 8. (a) [5 Points] Graph the rm's isoquant corresponding to its output of y = 100. What is the technical rate of substitution (TBS) at the point (L,K) = (4, 10). Is L = 4, K = 10 is a. cost minimizing bundle? Explain your answer. (13) [5 Points] In short-run, if the quantity of capital xed, i.e.K = K. What is the firm's short-run total cost function as a function of if and y? (c) [5 Points] What is its short run marginal cost function? What is its short run average cost function? (d) [10 Points] Calculate the rm's conditional demands for capital and for labor7 given that it produces some level of y in the long-run by using the Lagrangian method. Find the rm's longrun cost function