Note: An asterisk (*) indicates that the problem has an accompanying Excel file on the Web page http://www.aae.wisc.edu/chavas/risk.htm.

• *1. Consider a public choice concerning the design and financing of a project involving two individuals, i = 1, 2. The project consists in a public good x that affects the welfare of each individual and that generates uncertain returns that are redistributed to the two individuals. The investment cost is [2 x] while the investment gross return is [(8 x ? .4 x ²) e/10] where e is a discrete random variable that can take any of 10 possible values, e _j = j, j = 1, 2, , 10.

• Each individual behaves in a way consistent with the expected utility hypothesis with a utility function U _i( w _i, x, e) = ? exp( ? w _i) ? a _iexp( ? xe _{j )}, i = 1, 2. The initial wealth w _i for the i ^th individual is: w ₁ = 1 and w ₂ = 0. The preference parameter a _i is: a ₁ = 2 and a ₂ = 1. The i ^th individual s subjective probability of state j is p _ij = .1; i = 1, 2; j = 1, 2, , 10.

  1. Characterize a Pareto optimal design of the project, assuming that both