Question

1. Suppose a manager hires a technician to operate the machine for $5000 per month. The firm’s monthly revenue depends on only two factors: (1) luck and (2) effort exerted by the technician. The probability of having good luck and that of having bad luck are both 0.5. The technician can choose to exert high effort or low effort, depending on which option maximizes his monthly income. Assume that low effort does not cost the technician while high effort costs him $1000. Below is the firm’s payoff table:

	Good luck (50% chance)	Bad luck (50% chance)
Low effort	24,000	12,000
High effort	40,000	24,000

1. If the technician is paid with a fixed amount of $5000 per month, which level of effort would he choose? Provide your reasoning.
2. What is the corresponding expected revenue for the firm?
3. If the manager tries to improve the firm’s expected revenue by offering a pay for performance scheme, why do you think this may or may not work to exert high effort from the technician?
4. If the pay for performance scheme is listed as the following:

(1) If the revenue is below or equal to 24,000, then the technician receives $5000.

(2) If the revenue is larger than 24,000, then the technician receives $5000 plus a bonus of X dollars.

If the bonus is 3000 dollars, would it encourage the technician to put in high effort? Make sure you support your answer with numerical values.

5. Continue the pay for performance scheme. What is the minimum amount of bonus so that the technician is willing to exert high effort?

Answer 1

a) If technician is paid fixed $5,000 / month. Then he would chose low effort it cost nothing to him - net income would be $5,000. While high effort will cost him $1,000 - net income would be (5,000-1,000) = $4,000. Hence he would chose low effort

b) Since the technician would chose the low effort as discussed above.

Expected revenue for the firm = Good luck chance* low effort payoff with good luck + Bad luck chance * low effort payoff with bad luck

= 0.5 * 24,000 + 0.5 * 12,000 = 18,000

Expected payoff to firm = $18,000

c) Offering incentives work high effort will only work if the extra effort incentives are higher than the cost of high effort ($1,000) to technician and percentage sharing of additional payoff with the firm is good number (for example 50:50 sharing)

d)

Expected payoff under high effort = 40,000 *0.5 + 24,000 * 0.5 = $32,000

Technician's net extra payoff = incentive - extra cost for high effort = 3,000 -1,000 = $2,000

Extra net payoff to technician % of additional payoff generated by firm= 2000/ (32000-18000) = 14%. Hence it might not encourage the technician to put high effort although he is extra net $2,000 for high effort

$3,000 additional incentives for at least $24,000 target is higher than the cost $1,000 for higher.

Hence offering the