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2. A perfectly competitive firm has a production function f(x1, x2) - X1X2. Input prices are given by W1 = 2 and W2 - 1. a. Does this production function exhibit decreasing, constant, or increasing returns to scale? (1 pt) b. In the short run, input factor 2 is fixed at X2 - 1 and the firm chooses the optimal input quantity xi to minimize the cost of producing output y - 8. Derive xi. (1 pt) c. Calculate the costs Cs associated with the above short-run solution. (1 pt) d. In the long run, the firm chooses the optimal input quantities x; and x2 to minimize the cost of producing output y = 8. Write the Lagrangian function for this firm's long-run cost minimization problem. (1 pt) e. Derive the first-order conditions for this firm's long-run cost minimization problem. (3 pt) f. Solve the above first-order conditions to derive the optimal input quantities x; and x2. (2 pt) g. Calculate the costs c' associated with the above long-run solution. (1 pt)