# period 1 utility
u1i <- function(sigma_hat, tau, s = s, delta= delta) {
if(sigma_hat == y_L) {
y = Eu2i(0, tau, mean_y)
} else if(sigma_hat == y_H) {
y = Eu2i(r(lambda), tau, mean_y)
}
(s + delta) * u2i(tau, y, mean_y)
}
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