Suppose that daily profit of a small mobile phone kiosk is higher when the kiosk’s employee, Joe, works harder. If Joe works hard, the kiosk’s profit is 1000 with probability of 0.8 and 500 with a probability of 0.2. If Joe is instead lazy, the profit will be 500 with a probability of 0.8 and 1000 with a probability of 0.2. The firm’s owner, Selena, has two choices: she can offer Joe a flat wage of $150 or a contract where Joe’s wage is 0 if profits are low and 255 if profits are high. Of course, Joe does not like to work hard. He pays an effort cost of $150 if he works hard.
a. Draw the sequential game tree for this incentive problem between Joe and Selena.
b. What is the equilibrium of the game? Does Selena’s wage offer based on profits induce Joe to work hard? Explain the intuition in no more than 4 sentences.