 My Math Forum Derivatives: Chain Rule - Marginal Revenue Product

 Calculus Calculus Math Forum

 June 12th, 2017, 12:04 AM #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 10:55 AM. June 12th, 2017, 10:48 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 Are you sure that a calculus answer is even wanted? I would probably attack this with difference equations rather than derivatives. June 15th, 2017, 08:15 AM   #3
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

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 ^{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. Tags chain, derivatives, marginal, product, revenue, rule Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post green21317 Calculus 1 February 3rd, 2014 04:05 AM li1995717 Calculus 2 October 2nd, 2013 08:31 PM Oranges'n'Lemons Calculus 2 February 17th, 2013 11:18 PM pomazebog Calculus 3 February 8th, 2012 12:52 AM Oranges'n'Lemons Economics 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      