In the labor supply model of chapter 1, assume a utility function u(x, x) = x^-x, where (0, 1).

(a) Derive a condition on such that the consumer participates in the labor force.

(b) Assume that there are N consumers for whom is a realization of a uniform distribution on [0, 1], which is independent across consumers. Determine the expected labor force participation rate in that population.