12. did it cost too much This is a continuation of problem 11 above. Everything remains as before, except the probabilities are given by x1/g x1/b x2/g x2/b

π(x, y|H) .2 .3 .2 .3

π(x, y|L) .7 .1 .1 .1

(a) Determine an optimal contract. Explain your finding.

(b) Now is signal y = g or b informative about cost? Explain your reasoning.

(c) Why is it possible to have an information source that is useful for contracting purposes in the presence of output, yet useless in forecasting what that output will be?