Changes

To find the equilibrium do the following:#The floor maximizes its utility given its priors about the distribution. Its best guess is the mean and it believes the outcome is in the range of the distribution. <math>p^* = x_f - \overline{w} = - \overline{w}\,</math>. #The committee knows that it can't affect the floors posterior, and so proposes any bill. This is found by taking <math>\mathbb{E}u_f = \mathbb{E}(-(\overline{\omega}+\omega)^2) = -(\mathbb{E}(\omega^2)-\overline{\omega}^2) = -\sigma_{\omega}^2\,</math>. And likewise for the committee. Note that both have informational losses, and the committee has a distributional loss.