Question 1: A worker and a rm interact as follows. The worker decides how much to invest in developing his skills. The level of investment is denoted by :1], where a; can be equal to 0, 1, or 2. The cost of the investment is 952. If the worker works for the rm, the investment generates a return for the rm equal to 495. If the worker decides to work on his own, the investment generates a return equal to 2x, and the worker keeps this return. The three-stage game proceeds as follows. First, in stage 1, the worker decides how much to invest; namely, whether to invest 50 = 0, x = l, or m = 2. Second, in stage 2, after having observed the worker's choice at, the rm oers a wage w 2 0 to the worker. Last, in stage 3, the worker decides whether to accept or reject the offer. If he accepts, he receives the wage w. If he rejects, he works on his own thereby making 233. The payoffs of the rm are the revenue generated by the worker minus the worker's wage (that is, 4x w) if the worker accepts the rm's offer; zero if the worker rejects the rm's olfer. The payos of the worker are the income (7.0 if he accepts the rm's offer; 25:: if he rejects the rm's offer) minus the cost of investment m2. Draw the game tree. What is the SPNE? What is the outcome that results given this equilibrium? Suppose that if tndierent, the worker accepts the firm '3 offer