5. [4 + 7 + 4 + 7 = 22 points) Consider XYZ Inc. which uses inputs K (capital), L (labor), and E electricity) to produce output Y according to the production function: Y = f(KL, E) = VK + min{VI, VE} The price per unit of labor is wu = 10, per unit of electricity is we = 2 and per unit of capital is wr = 4. (i) In the short-run, this firm has its level of capital fixed at K*, but can choose labor and electricity as it wishes. Determine the short-run variable cost function c(yo; K*) for this firm. (ii) In the long-run, this firm can also vary its capital level K. If it wishes to produce a level of output yo, what is its optimal choice of capital in the long-run? Also, show that its long-run cost function is given by c(70) = 3y - [Hint: For (ii) make use of the short-run cost function you obtained in ().] (iii) If the price of Y in a competitive market is p, how much will this firm supply in the long run and what will be its profit? (iv) Due to some factors, the price p in the market for Y is uncertain. Specif- ically, it is known that p is distributed uniformly over (40, 100). Before the market price is determined, a buyer comes along offering to buy 10 units of Y at the price of $70 per unit. But XY Z Inc. must sign a clause agreeing to supply exclusively to this buyer and no one else. Will XYZ (which is interested in maximizing its expected profit) agree to this deal? Why or why not? 5. [4 + 7 + 4 + 7 = 22 points) Consider XYZ Inc. which uses inputs K (capital), L (labor), and E electricity) to produce output Y according to the production function: Y = f(KL, E) = VK + min{VI, VE} The price per unit of labor is wu = 10, per unit of electricity is we = 2 and per unit of capital is wr = 4. (i) In the short-run, this firm has its level of capital fixed at K*, but can choose labor and electricity as it wishes. Determine the short-run variable cost function c(yo; K*) for this firm. (ii) In the long-run, this firm can also vary its capital level K. If it wishes to produce a level of output yo, what is its optimal choice of capital in the long-run? Also, show that its long-run cost function is given by c(70) = 3y - [Hint: For (ii) make use of the short-run cost function you obtained in ().] (iii) If the price of Y in a competitive market is p, how much will this firm supply in the long run and what will be its profit? (iv) Due to some factors, the price p in the market for Y is uncertain. Specif- ically, it is known that p is distributed uniformly over (40, 100). Before the market price is determined, a buyer comes along offering to buy 10 units of Y at the price of $70 per unit. But XY Z Inc. must sign a clause agreeing to supply exclusively to this buyer and no one else. Will XYZ (which is interested in maximizing its expected profit) agree to this deal? Why or why not