Question

3. A private investor is interested in taking over the Hinckley Point C reactor. The revenues of operating the plant are determined by the electricity demand (a random parameter w distributed uniformly on [O,1]) and by the quality of nuclear fuel d provided by an overseas supplier. The revenue function is od, the cost of fuel quality is and the supplier's outside option is U- 0. The investor needs to specify a contract paying the supplier an amount π (if the reactor produces revenue R, the investor gets R-π and the fuel supplier gets π. Suppose, moreover, that the fuel supplier has to accept or reject the contract before observing ω, but chooses the fuel quality after observing it. First assume that the investor can observe the revenue R but cannot separately observe d or a. You may assume that the contract takes the form π-αR where α is a (not necessarily positive) parameter. Find the fuel supplier's optimal quality as a function of α, U and R, and use this to compute the value of α that maximises the investor's expected utility. Also, find the optimised expected value of the reactor as a function of U. a. b. How (if at all) would your answer differ if the fuel supplier observed o before accepting or rejecting the contract? (you should set up the problem, but do not have to solve it explicitly). Now suppose that the investor can choose a contract that depends on ω (π-αω) or on d (t-ad) but not both. In other words, they must pay off the fuel supplier before observing the value of revenue R. As before, the fuel supplier accepts or rejects the offer before observing o. Which would the investor prefer to observe? C.

Answer 1

a) 1) Value of = d²-1/2*R-U/ $\omega$ .  As cost of fuel quality was coincided with R (Revenue) will be deducted from the Utility (U) function in order to get investors utility is maximized. 2) Optimised expected value of the reactor = $\pi$ / $\omega$ *U, whereas income amount is deducted from formal parameter which multiplied into U function to give a expected Value.

b) The Supplier will not have an Optimal utilisation if he follows the Parameter set by the investor $\omega$ . Assuming the fact that the Value of is < U. Let us create a problem in the following the way assuming the above facts.

What will be the Actual Marginal cost of Suppliers things remaining the parameter value $\omega$ and Value of keeping constant.

c) As it was previously stated Optimised expected value of the reactor will fetch good revenue, then investor prefer the first option ( $\pi$ = $\omega$ ) than the second option.