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.

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