Consider the salary of Mary Sue Nelson, a sales agent for Plain Truth Advertisin

Question

Consider the salary of Mary Sue Nelson, a sales agent for Plain Truth Advertising. She has an effort cost of C = e2 and she a reservation wage of $1,500 so that wage package is W = 1,500 + .2 Q where the CEO sets the incentive at .2 and Q = 200 e. If the CEO increases the incentive from .2 to .25, what happens to the Nelson's effort? Will profits rise or fall?

I need a detailed answer, show every steps.

This is the right answer, I need the mathematical explanation:

Therefore her effort increases. Expected output goes up to Q =5,000. Expected wages are 2,750. Expected profit will rise in this case to 2,250.

Explanation / Answer

Clearly, her effort increases as she is gaining more incentive and the expected profit will also increase

Expected Output = Q

Profit= P=W-C

= 1500+.25Q-e^2

= 1500 +50e-e^2

For maximum Profit,

dP/de=0

= 50-2e=0

=e=25

Therefore,

Expected Output= 200e= 5000

Expected Wages= 1500+0.25*Q= 1500+1250= 2750

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