Consider the following game between a firm and worker and involving Nature as a player. Firm 1 moves first, offering the worker Contract 1 which pays the worker a wage w-25 regardless of the outcome of the project she develops for the firm or Contract 2, which gives her a wage, w-36 if the outcome of the project is Good and a wage of w-9 if the outcome of the project is Bad. The worker then chooses to Accept or Reject the Contract offered. If rejected, both players earn 0. If Accepted, the worker then decides whether to exert High or Low effort. After the worker has made an effort choice, Nature makes a move. If the worker chose High effort, then with probability 0.9, Nature chooses the Good outcome and with probability 0.1, Nature chooses the Bad outcome. If the worker chooses Low effort, then Nature chooses the Good or Bad outcomes with equal, 0.5 probability. The worker's payoff is: vw -1 ifthe worker chooses High effort Vwif the worker chooses Low effort The firm's payoff is: 90-w 30-w if the project outcome is Good If the project outcome is Bad a. Depict this sequential move game in extensive form. b. Find the subgame perfect equilibrium of this game. c. Consider now the existence of a social security payment that guarantees the worker a payoff of x>0 regardless of whether she works or not. Determine for what value(s) of x the worker would accept a contract to work and choose low effort in equilibrium.