Needful Things sells cursed antiques (A) using two inputs: labor (L), and the owners' time (T). The shop's production function is A=L1/4T1/4. Needful Things sells cursed antiques in a competitive market at a price of $100. Labor costs $P per unit, and the owner's time costs $1 per unit. a. Write down Needful Things' profit function. (2 points) b. Suppose in the short run, the owner's time is fixed at T=16. Find the first order condition for the short-run profit maximizing amount of labor. (2 points) c. Solve for the amount of labor that the shop uses in the short run to maximize profit as a function of P. Is your answer consistent with the law of demand? Explain. (4 points) d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizing amounts of both inputs. (2 points) e. Solve for the amount of labor and time that Needful Things uses to maximize profit in the long run. (4 points)