BPP Field Exam 2007 Answers

C.2: Contracting with and without commitment

C2 (a)

According to John, a fully specified algebraic solution is not necessary. We simply need to note that there will be efficiency for the low type (high cost) and the high type (low cost) will earn an information rent. The "key tradeoff" driving the structure of the contract is: Efficiency at the low end vs paying information rent at the high end.

Note that this is an "indirect" mechanism.

The solution is given by [math]\max_{t_{H},t_{L},q_{H},q_{L}}[\sum_{i=0}^{\infty}[\delta^{i}(0.5(u(q_{H})-t_{H})+0.5(u(q_{L})-t_{L}))]][/math]

C2 (b)

This is a direct mechanism, which is equivalent to the indirect mechanism above. This is a trick question because they're equivalent.