Finance Contract Theory

Principal is interested in buying lake. The revenues of operating the lake as a camping site are determined by the weather (a random parameter w distributed uniformly on [0,1]) and by the development programme d. The revenue function is wd, the cost of development is ((d^2)−1)/2 and the agent outside option is x>0. Principal needs to specify a contract paying the agent an amount π (if the site produces revenue R, the principal gets R−π and the agent get π). Suppose that the agent have to accept or reject the contract before observing w, but choose the development programme after observing it.

First assume that the principal can observe the revenue R but cannot separately observe d or w. You may assume that the contract takes the form π=aR where a is a (not necessarily positive) parameter. Find the agent optimal development as a function of a, x and R, and use this to compute the value of a that maximises the investor’s expected utility. Also, find the optimised expected value of the lake as a function of x.

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