Xavier (a government official) proposes to change zoning law to forbid industrial use (downzoning).Yvonne (a building owner) plans to improve the building for use as a factory. Y must decide how much to invest in improving her building. Let y denote her investment expense that will affect the revenue the building can yield. Y is considering two possible levels of investment: y= 90 or 20. The revenue curve R(y) indicates the revenues obtainable when there is no downzoning, so that the building can be used as a factory.

Assume that R(y= 90) = 400 and R(y= 20) = 300.

Assume that when there is downzoning, the revenues will be zero regardless of investment. At the time of investment, Y believes that there is 40% chance that the government will downzone the area.

Should the government carry out its proposed change, she will lose money on her investment, and a court will then have to decide whether she is entitled to compensation for the loss.

1. Identify the socially efficient level of investment.
2. Assume that the legal rule is: The court declares the change in the government land-use plan to be a taking. Identify Y's optimal investment level under the rule. Is the equilibrium outcome efficient?
3. Now suppose that the legal rule is: The court declares the change in the government land-use plan to be a regulation. Identify Y's optimal investment level under the rule. Is the equilibrium outcome efficient?