The Whiskey Rebellion Math Challenge!!! Alexander Hamilton set up the whiskey excise tax (an excise tax is a tax on goods within a country) after completing some detailed mathematical calculations. He knew that if a still had a certain size cooker that it could produce a certain number of gallons of whiskey at a time. He made calculations on how many gallons could be produced over the course of a month working full time (meaning when 1 batch of whiskey was finished that another would be started almost immediately after it). He also based his calculations on the still working for 4 months out of the year (this was the average amount of time a distillery would work at making new whiskey). Hamilton s goal was a tax of $.09 per gallon of whiskey. Producers of whiskey had 2 payment options: 1. Pay a one-time fee (based on the size of your cooker ) for that year in advance. The fee would be based on 4 months of production. OR 2. Pay $.09 per gallon of whiskey that you produced. If you lived in a town or city, you could choose either of the 2 payment options above. If you lived in a more remote, rural area you had to choose option 1 (because it was almost impossible for a government representative to be able to check how many gallons you were actually producing). Though Hamilton said he believed this approach to be fair, how could this plan favor a large producer of whiskey compared to a smaller producer of whiskey? 1. Consider the case of a still that has the capacity to make 12 gallons of whiskey in 1 batch. According to Hamilton s formula he assumed it would make 15 batches (or 180 gallons) in 1 month. He multiplied this by 4 months production (the average) and got 720 gallons and then multiplied this by $.09 per gallon and got $64.80. This was the flat fee an owner could pay. a. What if the owner lived in a town and ran the still for 5 months at the same capacity what would his tax per gallon be? Which tax option should the man choose? FLAT FEE or $.09/GALLON What would be his tax per gallon based on the option chosen? b. What if a small producer in a rural area could only produce for 2 months what would his tax per gallon be? Which tax would he pay? FLAT FEE or $.09/GALLON What would be his tax per gallon be based on the option chosen?
ANSWERS The Whiskey Rebellion Math Challenge!!! Alexander Hamilton set up the whiskey excise tax (an excise tax is a tax on goods within a country) after completing some detailed mathematical calculations. He knew that if a still had a certain size cooker that it could produce a certain number of gallons of whiskey at a time. He made calculations on how many gallons could be produced over the course of a month working full time (meaning when 1 batch of whiskey was finished that another would be started almost immediately after it). He also based his calculations on the still working for 4 months out of the year (this was the average amount of time a distillery would work at making new whiskey). Hamilton s goal was a tax of $.09 per gallon of whiskey. Producers of whiskey had 2 payment options: 1. Pay a one-time fee (based on the size of your cooker ) for that year in advance. The fee would be based on 4 months of production. OR 2. Pay $.09 per gallon of whiskey that you produced. If you lived in a town or city, you could choose either of the 2 payment options above. If you lived in a more remote, rural area you had to choose option 1 (because it was almost impossible for a government representative to be able to check how many gallons you were actually producing). Though Hamilton said he believed this approach to be fair, how could this plan favor a large producer of whiskey compared to a smaller producer of whiskey? 1. Consider the case of a still that has the capacity to make 12 gallons of whiskey in 1 batch. According to Hamilton s formula he assumed it would make 15 batches (or 180 gallons) in 1 month. He multiplied this by 4 months production (the average) and got 720 gallons and then multiplied this by $.09 per gallon and got $64.80. This was the flat fee an owner could pay. a. What if the owner lived in a town and ran the still for 5 months at the same capacity what would his tax per gallon be? Which tax option should the man choose? FLAT FEE or $.09/GALLON
HE SHOULD CHOOSE THE FLAT FEE. DOING THE MATH WE SEE THAT THIS MAN PRODUCES FOR 5 MONTHS AT THE GIVEN RATE. THIS MAKES HIS PRODUCTION 900 GALLONS (5 MONTHS X 180 GALLONS PER MONTH). IF HE CHOSE TO PAY $.09 PER GALLON HIS COST WOULD BE $81. CHOOSING THE FLAT FEE OF $64.80 SAVES HIM MONEY. What would be his tax per gallon based on the option chosen? HIS TAX PER GALLON [REMEMBER THAT PER BASICALLY MEANS DIVIDED BY ] WOULD BE CALCULATED BY TAKING HIS TOTAL TAX PAID ($64.80) AND DIVIDING THAT BY THE TOTAL NUMBER OF GALLONS HE PRODUCED (900 GALLONS). THE ANSWER TO THIS WOULD BE $.072 [OR 7.2 CENTS] PER GALLON. b. What if a small producer in a rural area could only produce for 2 months what would his tax per gallon be? Which tax would he pay? FLAT FEE or $.09/GALLON THIS QUESTION IS A LITTLE TRICKY IN THAT THE FARMER HAS TO CHOOSE THE FLAT FEE BECAUSE HE IS IN A RURAL AREA (re-read the explanation in the handout, if necessary). IF HE ACTUALLY HAD A CHOICE, HE WOULD SAVE MONEY BY PAYING THE RATE OF $.09 PER GALLON BECAUSE HE ONLY PRODUCES FOR 2 MONTHS. HIS TOTAL TAX DOING THIS WOULD ONLY BE $32.40.
What would be his tax per gallon be based on the option chosen? SINCE HE MUST CHOOSE THE FLAT FEE OF $64.80 THEN HIS TOTAL TAX PER GALLON WOULD BE $64.80 DIVIDED BY HIS TOTAL GALLONS PRODUCED (360 GALLONS). THIS WOULD EQUAL $.18 PER GALLON. THE FINAL QUESTION IS: DOES THE TAX SEEM FAIR? MOST PEOPLE WOULD SAY NO BECAUSE, AS SHOWN IN QUESTION B ABOVE, PEOPLE IN THE MORE RURAL AREAS OR THE FRONTIERS HAD NO CHOICE IN HOW TO PAY THE TAX. THIS COULD RESULT IN THEM ACTUALLY HAVING TO PAY TWICE AS MUCH (OR POSSIBLY EVEN MORE) TAX PER GALLON. FOR QUESTION B, THE FARMER PAID $.18/GALLON TAX-- THIS IS TWICE AS MUCH AS HAMILTON SAID HIS TAX GOAL WAS. MEANWHILE, IN QUESTION A, A LARGER PRODUCER WAS ACTUALLY ABLE TO REDUCE HIS TAX PER GALLON TO 7.2 CENTS PER GALLON. IT IS EASY TO UNDERSTAND WHY MANY WHISKEY PRODUCERS ON THE FRONTIER WERE UPSET BY THE LAW. ADDITIONAL PRACTICE PROBLEMS BELOW...
Ia. CALCULATE THE FLAT FEE DUE ON A STILL THAT HAD A 4 GALLON COOKER. TRY TO CALCULATE THIS ON YOUR OWN (BUT ANSWER & EXPLANATION ARE BELOW) FIRST: REMEMBER THAT THE FLAT FEE IS BASED ON WHAT HAMILTON THOUGHT THE AVERAGE PRODUCER WOULD MAKE AND WHAT HIS BASIC TAX GOAL WAS. BECAUSE OF THIS, THE ONLY THING THAT CHANGES IN SOLVING WHAT A FLAT FEE WILL BE IS THE SIZE OF THE COOKER. (LOOK BACK TO THE HANDOUT FOR MORE EXPLANATION, IF NECESSARY.) YOU NEED TO MULTIPLY 4 THINGS TOGETHER TO GET THE FLAT FEE: 1. SIZE OF THE COOKER IN GALLONS (THIS IS THE ONLY THING THAT CHANGES). 2. AVERAGE NUMBER OF BATCHES MADE PER MONTH (ALWAYS 15). 3. AVERAGE NUMBER OF MONTHS OF PRODUCTION (ALWAYS WILL BE 4). 4. HAMILTON S GOAL OF A TAX PER GALLON (ALWAYS $.09).
SO THE EQUATION TO SOLVE FOR THE FLAT FEE (FOR ANY STILL) IS ALWAYS: Size of cooker X 15 X 4 X.09 = FLAT FEE SO FOR THE EXAMPLE PROBLEM ABOVE WITH A 4 GALLON COOKER YOUR EQUATION WOULD BE: 4 X 15 X 4 X.09 = $21.60 FLAT FEE = $21.60 Ib. NOW LET S PRETEND THIS STILL S OWNER LIVED IN A TOWN AND ACTUALLY PRODUCED FOR 7 MONTHS OUT OF THE YEAR. BECAUSE HE LIVES IN A TOWN HE HAS A CHOICE OF PAYING THE FLAT FEE OR PAYING $.09 TAX PER GALLON (SEE HANDOUT FOR MORE EXPLANATION, IF NECESSARY). OBVIOUSLY, HE WOULD LIKE TO PAY WHICH EVER IS THE LOWEST AMOUNT. DETERMINE WHETHER THIS STILL OPERATOR SHOULD PAY THE FLAT FEE OR THE $.09 PER GALLON. WORK THIS OUT ON YOUR OWN.
ANSWER AND EXPLANATION ARE BELOW FOR THIS 4 GALLON STILL, WE HAVE ALREADY CALCULATED THE FLAT FEE-- WHICH IS $21.60. HOW MUCH WOULD HIS TAX BE IF HE PAID $.09 PER GALLON? WELL IF IT IS $.09 PER GALLON, WE NEED TO DETERMINE HOW MANY GALLONS HE ACTUALLY PRODUCED. THE INFORMATION WE NEED TO SOLVE THIS IS: 1. SIZE OF THE COOKER IN GALLONS (WE KNOW THIS ONE IS 4). 2. AVERAGE NUMBER OF BATCHES MADE PER MONTH (ALWAYS 15). 3. ACTUAL NUMBER OF MONTHS OF PRODUCTION (7 MONTHS FOR THIS PERSON). THE EQUATION TO DO THIS WOULD LOOK LIKE THIS: Size of cooker X 15 X number of of months of actual production FOR THIS PROBLEM, IT WOULD BE: 4 X 15 X 7 = 420 GALLONS PRODUCED HE HAS AN OPTION OF PAYING $.09 FOR EACH ONE OF THESE GALLONS. THAT WOULD BE 420 X $.09 = $37.80 FLAT FEE = $21.60
$.09 PER GALLON TAX = $37.80 HE WOULD OBVIOUSLY CHOOSE TO PAY THE FLAT FEE OF $21.60. Ic. KNOWING THE TAX TO BE PAID ($21.60) AND THE GALLONS PRODUCED (420), WHAT WOULD BE HIS TAX PER GALLON? CALCULATE YOUR ANSWER: (ANSWER/EXPLANATION GIVEN BELOW) REMEMBER THAT TAX PER GALLON MEANS THE TAX PAID DIVIDED BY THE NUMBER OF GALLONS PRODUCED. THEREFORE, THIS WOULD EQUAL $21.60/420 GALLONS = $.051 OR 5.1 CENTS PER GALLON