Consider a binary choice to allow or not the emission of pollutants. The cost to consumers of allowing the pollution is C = 2,000, but this cost is only observable to the consumers. The benefit for the polluter of allowing the externality is B = 2,300, and only the polluter knows this benefit. Clearly, optimality requires this externality is allowed, since B > C. However, the final decision must be based on what each party chooses to reveal.
a. Construct a tax-subsidy revelation scheme such that it is a dominant strategy for each party to report truthfully their private information.
b. Show that this revelation scheme induces the optimal production of the externality.
c. Show that this revelation scheme is unbalanced in the sense that the given equilibrium reports the tax to be paid by the polluter is less than the subsidy paid to the pollutee.