A manufacturer wishes to contract a manager for its retail outlet. The profits of thebusiness depend on thestateof the world (휔,distributed uniformly on[0,1]) and theeffort(푒) supplied by the manager. Effort is costly; there is a cost included in the profitfunction휋(푒,휔)=퐴푒휔−푒2In addition, the manager incurs a personal cost of훽푒and has an outside offer worth푈̅≥0.After the profits are earned, both the manager and the manufacturer learn the stateand the manager’s effort (휔and푒).Assume that퐴= 30,훽= 0.25and푈̅= 50.a.If the manufacturer could observe the state (휔)in advance, what would theoptimal contract be (assume that the manufacturer must hire a manager)? [5marks]b.Now suppose that the manager does not observe the state휔until after thecontract is signed, but does learn the state before choosing푒.Also assume thatthe manufacturer cannot observe anything in advance, and only observesprofit afterwards, and therefore offers a profit-sharing contract that pays themanager a proportion휎of profit. Set up the firm’s optimisation problem andfind the optimal profit-sharing level and expected payoffs to the firm and themanager. [15 marks]c.Describe in words what how to set up the problem if the manager observedthe state before signing the contract. What you would expect to happen to thepayoffs of the two parties? [15 marks]d.Now suppose that (as in part a) the manager does not observe the state휔untilafter the contract is signed, but faces no personal cost (훽= 0)and has nooutside option. The firm can choose to audit the state and the manager’s effortafter the manager reports the profit earned by the firm. This audit will cost퐶푎= 100.If the manager reports profits of휋, the firm will get a payoff of휋ifthis exceeds a threshold or trigger level휋∗; otherwise, if the firm conducts anaudit, they will learn the true profit, the state and the manager’s effort. Youmay assume that if the manager is found to have supplied profit-maximisingeffort for the state, the manger gets a fixed payment of푈̅= 0; otherwise, themanager is fined an amount퐹> 0and the firm gets all the profit (but not thefine).Setuptheproblemandthenfindtheaudittrigger휋∗andthecorresponding levels of effort supplied by the manager in each state.[15marks]