My Math Forum Derivatives: Chain Rule - Marginal Revenue Product

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 June 11th, 2017, 11:04 PM #1 Newbie   Joined: Jun 2017 From: vancouver Posts: 3 Thanks: 0 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 09:55 AM.
 June 12th, 2017, 09:48 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,047 Thanks: 430 Are you sure that a calculus answer is even wanted? I would probably attack this with difference equations rather than derivatives.
June 15th, 2017, 07:15 AM   #3
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Quote:
 Originally Posted by theguest 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 $\frac{1544q}{(344448+ 4q)^{1/2}= 1.8m(1.8m+ 1^{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 $\frac{15440}{(34448^{1/2}}= 18(36)^{3/2}P" /> or $26.306= 108P$ so that P= 0.24357 not 2.5733.

 Tags chain, derivatives, marginal, product, revenue, rule

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