Attached are some questions below. Try and provide solutions for these.

4. (40 Minutes - 20 Points) Consider the following model in which a worker's choice of health play may signal his health to his insurance company. Suppose nature first chooses the health of the worker choosing @ ( {healthy, not healthy). Assume that the probability that the worker is healthy is q. Player 1 observes whether he is healthy and then chooses a, I from her savings so that her wealth at t + 1 is my+1 = " (wt - 2,) if her wealth at t is wy and she consumes r, at t. (b) Find a sophisticated-optimal consumption strategy for her in which the self at any given date s consumes yes. Compute the constant y and briefly verify that this is indeed a subgame-perfect equilibrium of the multi-agent game. (c) For 8