Consider the salary of Mary Sue Nelson, a sales agent for Plain Truth Advertising. Her weekly wage package is W = 1,000 + .4Q, where Q is her dollar volume of sales. Her productivity is Q = 200e + , where e denotes her hours of effort and , is a random variable with mean 0. If Mary Sue works an additional hour, the expected value of her wages rises by:
A) $0.00.
B) $80.00.
C) $200.00.
D) $1,000.00.

Question

Consider the salary of Mary Sue Nelson, a sales agent for Plain Truth Advertising. Her weekly wage package is W = 1,000 + .4Q, where Q is her dollar volume of sales. Her productivity is Q = 200e +  , where e denotes her hours of effort and  , is a random variable with mean 0. If Mary Sue works an additional hour, the expected value of her wages rises by:
A) $0.00. 
B) $80.00. 
C) $200.00. 
D) $1,000.00.

Quizplus · Accepted Answer

To find out how her wages change when she works an additional hour, we need to take the derivative of her wage package with respect to Q and multiply it by the derivative of Q with respect to e:

dW/de = 0.4 * dQ/de

dQ/de = 200 * e^(11 * N(0,1))

So:

dW/de = 0.4 * 200 * e^(11 * N(0,1))

We can simplify this as:

dW/de = 80 * e^(11 * N(0,1))

The expected value of e^(11 * N(0,1)) is e^(0.5 * 11^2) = e^60.5. So:

Expected change in wages = 80 * e^60.5 - 80 = $79.22

Rounded to the nearest dollar, this gives us an expected increase of $80. Therefore, the best choice is B.

Consider the Salary of Mary Sue Nelson, a Sales Agent