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January 1st, 2018, 12:09 PM  #1 
Member Joined: Nov 2016 From: USA Posts: 33 Thanks: 1  Percent Change discrepancy
I'm trying to reconcile why these two percent changes aren't agreeing in the end: An artist makes a deal with a sales broker to market and sell a sculpture. The artist agrees to pay a 25% commission charge on the sales price of the sculpture. The gallery where the sculpture is displayed requires a nonnegotiable 10% fee from the sales price (which will be paid by the artist, not the broker). The artist's sculpture sells for 10,000 dollars. From the 10,000 dollar sale, the gallery receives its 10% fee (1000 dollars). The broker is owed 25% of the sale, which is 2500 dollars. That leaves 6500 left for the artist. Wanting more business from the artist, the broker reduces the commission from 25% down to 20% on this sculpture sale (a $2000 commission). The gallery still receives its 10% fee (1000 dollars), so the artist ultimately received 7000 dollar net payment. The artist went from 6500 to 7000. The percent change calculation is: (7000  6500) / 6500 = 7.69% increase. Since the commission had been lowered 5.00%, why didn't this result in a 5.00% increase for the artist? 
January 1st, 2018, 12:23 PM  #2  
Senior Member Joined: May 2016 From: USA Posts: 881 Thanks: 353  Quote:
$0.05 * 10000 = 500.00$ $0.0769 * 6500 = 499.85 \approx 500.00.$  
January 1st, 2018, 02:23 PM  #3  
Member Joined: Nov 2016 From: USA Posts: 33 Thanks: 1  Quote:
Or did this deal simply result in 5.00% increase?  
January 1st, 2018, 05:27 PM  #4 
Senior Member Joined: May 2016 From: USA Posts: 881 Thanks: 353 
When the broker lowered the commission rate by 5% of the gross price, the artist's net receipts rose about 7.69%. It is looking at the same thing from two different vantage points.

January 2nd, 2018, 04:40 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,416 Thanks: 1462 
The broker's commission went from \$2500 to \$2000. The percent change calculation is: ((2500  2000)/2500 = 20% decrease. Why didn't this result in a 5% increase for the artist? 
January 2nd, 2018, 06:57 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,346 Thanks: 728 
You can "complicate!" your problem more by kicking out the gallery and using 9000 as selling price. Then the 2500 fee becomes ~27.8% of 9000, and the reduced 2000 fee becomes ~22.2% of 9000. Ahem! 

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