1. The production technology is given by q = K1/4 L1/4 E1/4 where output is represented by q, capital by K, labor by L, and energy by E. The input prices are respectively denoted by r, w, and u. Capital is a fixed input in the short run: K = K. Find the short-run variable cost function. a. Write an expression that gives the expenditure on capital. b. Write the expressions that give the expenditures on energy and on labor. c. Write the expression that gives the total expenditure on the three inputs. d. Recall that capital is a fixed input and that energy and labor are variable inputs. Write an expression that gives variable expenditure (on the variable inputs). e. Consider a given level of output, q0, and all combinations of the variable inputs that will produce q0: q0 = K1/4 L1/4 E1/4. Set up the Lagrangean function for the problem to minimize the variable cost of producing q0 = K1/4 L1/4 E1/4. f. Derive the first-order conditions. g. Solve the first-order conditions for the expansion path. h. Solve for the short-run cost-minimizing demands for labor and energy. Show all steps in your work. i. Solve for the short-run