3.Crown Cork and Seal company makes metal cans for soft drinks suppliers like Coke. Suppose the production equipment at Crown was specialized for the production of Coke and not suited for other drinks. The cans used by Coke, generate a revenue of $2,000 for Coke. Crown can invest in equipment to make better quality cans that retain the carbonation of the beverage better. The investment costs $1,000 and Coke earns higher revenues of $3,600. Letre (0.1) represent Crown's decision to invest in the new equipment; x = 0 means no investment, and x 1 represents new investment. Let ye (0, 1) represent Coke's decision to buy from Crown. Let p represent the price at which Coke buys cans from Crown. The timeline of decisions is as follows. Crown decides whether to use the old equipment (x = 0) or to invest in the new equipment (x 1). Crown and Coke negotiate a price p for the cans and then Coke decides whether to buy from Crown (y-1) or not (y = 0). Let us call Crown, Player 1 and Coke, Player 2. The payoffs to each player, given x, y, and p are as follows: u(x,y.p) py-$1,000x u2(x.y.p) $3,600xy+$2.000 (1-x)y-py Assume that bargaining weights for each player are = = 1 a. Fill in the payoffs to each player and the joint payoffs for each value of x and y in the table below. r y 0 0 0 1 1 1 0 1 UI 2 V -U1 +12 b. Find the outcome in terms of x' and y' that maximizes the joint payoff. Suppose Crown did not invest in the new equipment, i.e., x=0. C. What are the disagreement payoffs, d.d? d. What is the surplus that Coke and Crown split between each other and what is the price, p? e. What is the payoff to Crown given p obtained in part d)? Suppose Crown invested in the new equipment, i.e., x-1. f. Redo parts c) to e). g. Comparing Crown's payoff from x 0 with its payoff from.x-1, what is Crown's best decision in terms of investment. h. Explain the "hold-up" problem that arises in part g). L Suppose Coke and Crown vertically integrated, would the hold-up problem exist? Why or why