A government department is interested in persuading a private investor to buy the Britvolt battery plant, which is otherwise facing closure. The value of operating the plant will be determined by investor's stake and market forces (a random parameter distributed

uniformly on [0, 10]). The revenue function is = , the cost of the rescue plan is and

the investor's outside option is > 0. The government needs to specify a contract paying the investor an amount - if the site produces value , the government gets and the investor gets . Suppose, moreover, that the investor must accept or reject the contract before observing , but chooses after observing .

a. First assume that the government can observe but cannot separately observe or . You may assume that the contract takes the form = where is a (not necessarily positive) parameter. Find the investor's optimal development as a function of , and , and use this to compute the value of that maximises the government's expected utility. Also, find the optimised expected value of the Britvolt plant (sum of expected payoffs to the government and the investor) as a function of . [12 marks]

b. How (if at all) would your answer differ if the investor observed before accepting or rejecting the contract? [You need not solve this explicitly, but should clearly show how you would solve the problem.] [10 marks]

c. Now suppose that the government can either choose a contract that depends on ( = ) or one that depends on ( = ) but not both. In other words, it must pay off the investor