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June 12th, 2017, 12:04 AM   #1
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Derivatives: Chain Rule - Marginal Revenue Product

All answers involve a unit of dollars, so you must enter your answers accurate to two decimal places!
A factory owner who employs m workers finds that they produce

q = 1.8m(1.8m+18)^3/2 units of product per day.

The total revenue R in dollars is

R=1544q / (344448+4q)^1/2

(a) From the fact that
revenue = (price per unit)*(number of units)
it follows that
R=(price per unit)*q

So when there are 10 workers, the price per unit is 2.5733 dollars.

(b) When there are 10 workers, the marginal revenue is 2.52 dollars/(one unit of product).

(c) The marginal-revenue product is defined as the rate of change of revenue with respect to the number of employees. Therefore,
marginal-revenue product=dR/dm

If q and R are given as above then, when m = 10, the marginal-revenue product is ? dollars/(one worker). This means that if employee number 11 is hired, revenue will increase by approximately ? dollars per day.

Can't seem to find the answer for c.

Last edited by skipjack; June 12th, 2017 at 10:55 AM.
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June 12th, 2017, 10:48 AM   #2
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Are you sure that a calculus answer is even wanted?

I would probably attack this with difference equations rather than derivatives.
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June 15th, 2017, 08:15 AM   #3
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Quote:
Originally Posted by theguest View Post
All answers involve a unit of dollars, so you must enter your answers accurate to two decimal places!
A factory owner who employs m workers finds that they produce

q = 1.8m(1.8m+1^3/2 units of product per day.

The total revenue R in dollars is

R=1544q / (344448+4q)^1/2

(a) From the fact that
revenue = (price per unit)*(number of units)
it follows that
R=(price per unit)*q
So ^{3/2} P" /> where P is the "price per unit".

Quote:
So when there are 10 workers, the price per unit is 2.5733 dollars.
Well, the formula above says that ^{1/2}}= 18(36)^{3/2}P" /> or so that P= 0.24357 not 2.5733.
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