ECON 101 Professor Vogel Additional practice questions - Fall 2017 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 :c, where a; can be equal to O, 1, or 2. The cost of the investment is 932. If the worker works for the rm, the investment generates a return for the rm equal to 435. If the worker decides to work on his own, the investment generates a return equal to 23;, and the worker keeps this return. The threestage game proceeds as follows. First, in stage 1, the worker decides how much to invest; namely, whether to invest a: = 0, cc = 1, or at = 2. Second, in stage 2, after having observed the worker's choice 33, the rm offers 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 2:0. The payoffs of the rm are the revenue generated by the worker minus the worker's wage (that is, 435 w) if the worker accepts the rm's offer; zero if the worker rejects the rm's offer. The payoffs of the worker are the income (w if he accepts the rm's offer; 21c if he rejects the rm's offer) minus the cost of investment $2. Draw the game tree. What is the SPNE? What is the outcome that results given this equilibrium? Suppose that if indierent, the worker accepts the rm '3 oer. Question 2: Now change the game in Question 1 as follows. First, in stage 1, the worker decides a: (a: = 0, a: = 1, or :c = 2). Second, in stage 2, the worker makes an offer to the rm about his salary w 2 0. Last, in stage 3, the rm observes a: and w and decides whether to accept the worker's oer (that is, hire the worker) or reject the worker's offer (that is, not hire the worker). Suppose that if indz'erent, the rm accepts the worker's oer. Everything else is identical