ProblemSet#,You are allowed to work in groups, but each student must write up his or her work independently;please note on your answer sheet with whom you worked. Be sure to provide the reasoning behindyour answer in order to receive full credit.IncentivizingEffortYou are a division manager for the logging firm of Karrde Incorporated. You are planning to offer acontract to Jade Enterprises for constructing logging roads in the Myrkr Forest. It is imperative thatthe roads are wide enough; if the roads are wide enough, Karrdeâs profit will be 120, while it willonly be 60 if the roads are too narrow. (Karrdeâs profits are 0 if it does not hire Jade.) You have theopportunity to make a take-it-or-leave-it offer to Jade, but you can not set the payment below 0 forany outcome.Whether or not the roads are wide enough depends crucially on Jadeâs effort: If Jade exerts loweffort, then the probability of success is only one third; if Jade exerts medium effort, the probabilityof success is two thirds; and if Jade exerts high effort, success is guaranteed.Jade Enterprises is a small concern. If Jade does not take the job, its utility is 2. If Jade takes the job,and exerts low effort, its utility is, where is the payment to Jade. If Jade takes the job andexerts medium effort, its utility is given byeffort its utility is given by− 1. Finally, if Jade takes the job and exerts high− 3.a) Suppose that you can observe the effort that Jade exerts, and so can write a contract wherepayment is contingent on effort. If you wish to incentivize low effort, what is the mostprofitable contract you can offer? If you wish to incentivize medium effort, what is the mostprofitable contract you can offer? If you wish to incentivize high effort, what is the mostprofitable contract you can offer? Given your answers to the previous questions, which isthe most profitable contract for Karrde to offer Jade? (20 points)b) Now suppose (for the rest of this problem) you can not observe effort. If you wish to writethe most profitable contract that incentivizes low effort, what contract will you write? Doesit differ from the contract for low effort in part a)? (15 points)c) If you wish to write the most profitable contract that incentivizes medium effort, whatcontract will you write? How does it differ from the contract in part a) for medium effort?(15 points)d) If you wish to write the most profitable contract that incentivizes high effort, what contractwill you write? How does it differ from the contract in part a) for high effort? (15 points)e) Consider your answers to the previous parts of this question. What contract will you offerto Jadeâthat is, what contract maximizes your profits? Does this contract incentivize thesame level of effort as the contract you offered in part a)? (10 points)SignallingThroughPricesLex Chemicals has developed a new plastic usable for insulation in new homes. Production costs forthe new plastic are = 4 per unit. Demand for the insulating material is given by = 12 − ,where is the price set by Lex. Hence, per-period profits are given by ( − ). Lex Chemicals willhave 3 periods of being the only producer of this particular type of insulation before the patent runsout and lower cost competitors enter and take the market. (For simplicity, assume no discounting offuture periods.)Unfortunately for Lex, a competitor, Edge Plastics, has developed a competing product and isconsidering entering the market next period. The plastic develop by Edge Plastics has a productioncost of 5. There is a fixed cost of 2 for Edge Plastics to enter the market.Edge, however, is uncertain of the cost structure of Lex Chemicals. Edge believes there is a 50%chance that Lex has a marginal cost of production of 8, and a 50% chance that Lex has a marginalcost of production of 4.a) What are your per-period profits as a monopolist? What if you had the higher marginal costof 8? (5 points)b) Will you attempt to signal to Edge that you are, in fact, the low cost producer? If so, whatprice will you set in the first period? (20 points)