My Math Forum Percent Change discrepancy

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 January 1st, 2018, 12:09 PM #1 Member   Joined: Nov 2016 From: USA Posts: 34 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 non-negotiable 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: 1,210 Thanks: 495 Quote:  Originally Posted by Seventy7 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 non-negotiable 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?
Because the increase you are calculating is based on the artist's receipt rather than the sales price.

$0.05 * 10000 = 500.00$

$0.0769 * 6500 = 499.85 \approx 500.00.$

January 1st, 2018, 02:23 PM   #3
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Quote:
 Originally Posted by JeffM1 Because the increase you are calculating is based on the artist's receipt rather than the sales price. $0.05 * 10000 = 500.00$ $0.0769 * 6500 = 499.85 \approx 500.00.$
Is it correct for the artist to think that an extra 7.69% (approx.) arose when the broker lowered the commission rate?

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: 1,210 Thanks: 495 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. Thanks from Seventy7
 January 2nd, 2018, 04:40 AM #5 Global Moderator   Joined: Dec 2006 Posts: 19,983 Thanks: 1853 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: 13,627 Thanks: 954 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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