Question

Suppose working hard costs botanists a monetary equivalent of $200. The labor market for botanists is so small that, if they were ever out of job, they will be unemployed and get paid $1000 per month through government unemployment compensation. Because most botanists do what they love, they are largely unmonitored by the employer, and thus faces a very low probability of 0.1 to be detected for shirking on job. Compute the wage at which level the botanists should be indifferent between working hard and shirking (i.e., if they are paid even just $0.0000001 more, they will choose to work hard, and if paid $0.0000001 less, will choose to shirk).

*** HERE IS A SIMILAR SAMPLE PROBLEM/NOTES: **

Threat to termination as an incentive: prospect of being fired incentivizes agent to work

Let’s examine a simple model:

Work hard puts physical/emotional strain on agent, equivalent to $50 (so if possible it should be reduced or avoided)

Agent paid wage of W, but if fired, will be paid at best at W*; not working hard has a p chance to be detected. If firm is really good at detecting shirking, p can be as high as 0.9; otherwise p can be low, such as 0.1

Decision to work hard results from simple benefit-cost analysis

Payoff from working hard: W-50; payoff from not working hard: pW*+(1-p)W

Will work hard if W-50>pW*+(1-p)W=>p(W-W*)>50 Intuition: when cost of shirking (p(W-W*)) is greater than cost of working hard ($50), will not shirk

Answer 1

Given the information about botanists:

cost of working hard= $200

the p= probability of detection in shirking on job =0.1

then the 1-p= probability of not detecting in shirking=1-0.1= 0.9

if out of job/unemployed, govt gives unemployment compensation= $1000

To find: W = wages such that botanists are indifferent between shirking and working hard

indifference occurs when: E(shirking job)=E(working hard)

the i.e expected utility of shirking and working hard are equal.

Expected Utility(shirking job)= p*(no compensation) + (1-p)*(compensation)

=0.1 * $0 + 0.9 * $1000 = $900

E(working hard) = W- cost of working hard = W - $200

Equating these two :

$900 = W - $200 implies W = $900+$200 = $1100

Hence, wage of botanists is $1100 such that they will be indifferent in working hard and shirking on job.