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Calculating the Effects of a Specific, Indirect Tax - YouTube
Channel: Jason Welker
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[Music]
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in this next video we're going to do
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some analysis that is really only
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applicable to IB higher-level economic
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students or other introductory students
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who are learning about linear equations
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in markets for particular Goods so we're
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looking at the same graph actually as we
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did in our previous two videos showing
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the market for cigarettes in this
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instance though we've now applied linear
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equations to these graphs so the demand
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curve here is represented by the
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equation QD equals 50 minus 4p and the
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supply curve is represented by the
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equation Q s equals negative 7.5 plus
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7.5 P now we're going to make the same
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assumption that we did in the previous
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two videos that the government decides
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to levy a $2 per pack tax on the market
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for cigarettes which will have the same
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effect that it did in previous videos
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which was it will decrease the supply
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curve for cigarettes by shifting the
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marginal cost up by two dollars per pack
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however now rather than just simply
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drawing the increase in the marginal
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cost and the decrease in supply we're
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going to apply this $2 tax to our
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equation here and come up with a new
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supply equation for cigarettes
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knowing that following the tax producers
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of cigarettes we'll be receiving two
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dollars less for every pack then the
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price that consumers pay knowing that
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it's quite simple to come up with the
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new supply equation here's our original
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supply equation the assumption is that
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this $2 tax will be subtracted from the
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price that consumers pay knowing this we
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can come up with the new supply equation
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the new supply equation will be Q s
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equals negative 7.5 plus 7.5 times P
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minus 2 now the minus 2 here represents
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the $2.00 tax since the price consumers
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pay is $2.00 greater than the price that
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producers will get to keep now that we
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have a new supply equation we can simply
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by this and find out mathematically what
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our new equilibrium price and quantity
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will be let's simplify this equation now
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Q s now equals negative 7.5 plus 7.5 P
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minus 15 of course we took the 7.5 and
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multiplied it by negative 2 and we took
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the 7.5 and multiplied it by the P to
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come up with this new equation let's
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simplify this again we know that now Q s
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equals negative 7.5 plus 7.5 P minus 15
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we can simplify this so quantity
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supplied now equals negative 22.5 plus
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7.5 P now we have our new supply
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equation and of course the next step
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would be to find the price intercept of
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the new supply curve so that we can draw
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it more accurately on a graph on the
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right to find the price intercept we
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must set the quantity equal to 0 and
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solve for P so let's do that now we've
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got 0 equals negative 22 point 5 plus
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7.5 P simplify again we see that 22.5
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equals 7.5 P and if we divide both sides
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by 7.5 we get the p-intercept 22.5
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divided by 7.5 equals 3 this tells us
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where our new supply curve will begin it
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will begin at a quantity of 0 and a
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price of 3 of course this makes total
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sense because it was a $2.00 tax after
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all and the original supply curve had a
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P intercept of 1 therefore the new
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supply curve will have a P intercept of
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1 plus the $2.00 tax so our new supply
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curve will be sloping upwards starting
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at a price intercept of 3 but notice
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that since it is a specific tax and not
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an ad valorem tax the slope of the new
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supply curve is the same as the slope of
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the original supply curve determined by
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the responsiveness of producers to price
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changes or the D variable in our
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equation
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so it's still a constant slope from the
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original supply curve so we've now got
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our new supply with tax curve the price
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intercept is three now we can take this
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new supply equation equate it to our
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original demand equation since there's
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been no change in demand to find more
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accurately the new equilibrium price so
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now let's take our new supply equation
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of negative twenty two point five plus
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seven point five P and set it equal to
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our original demand equation of fifty
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minus 4 P to solve for the new
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equilibrium price that consumers will
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pay and from that we can actually
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determine very easily the new price that
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producers will get to keep so to solve
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for our new equilibrium price we can
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simply add four P to both sides and we
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get that eleven point five P equals and
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we can add twenty two point five to both
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sides so we get seventy two point five
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and if we divide both sides by eleven
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point five we can solve for our new
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equilibrium price which is six dollars
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and thirty cents so if you recall from
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our original video lesson on the effect
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of an excise tax on the market for
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cigarettes we estimated that it was
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around six dollars and 20 cents based
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only on a graphical analysis but here we
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can see more accurately using our new
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linear supply equation that the actual
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equilibrium price paid by consumers
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following the $2 excise tax is six
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dollars and thirty cents now we should
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be able to fairly easily solve for the
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new equilibrium quantity as well by
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plugging the price of six thirty into
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one of the two equations so let's do
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that now we can see if the quantity
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demanded is going to equal fifty minus
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four times six dollars and thirty cents
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so the new quantity demanded that
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supplied should be 50 minus that's
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twenty five point two which equals
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twenty four point eight thousand
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cigarettes so we've actually got a new
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equilibrium quantity here more accurate
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we did in our original version of this
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video lecture when we did not use the
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linear equations we can see that
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following the two dollar attacks on each
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pack of cigarettes the quantity Falls to
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twenty four point eight thousand
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cigarettes at a price of six dollars and
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thirty cents now it should be very
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simple to determine the price that
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producers get to keep following this
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excise tax and we do that by subtracting
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two dollars the two dollar tax which
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must be paid from the price that
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consumers pay therefore the two dollar
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tax has to be subtracted here and we can
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see very easily that the price that
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producers get to keep which is
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determined by the original supply curve
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is four dollars and thirty cents now
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again of course to conclude our analysis
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we can actually calculate the amount of
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consumer tax burden which is represented
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by this rectangle as explained in a
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previous video lecture and we can
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calculate the amount of producer tax
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burden as well producer tax burden of
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course is represented by the green
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triangle I'm sorry the green rectangle
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here below the original price and above
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the new price kept by producers
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now to do this we can simply find out
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how much per pack each consumers pain
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and multiply this by the number of packs
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being consumed so we know that the per
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pack tax paid by consumers is the new
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price of six dollars and thirty cents
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minus the original price of five dollars
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so it's one dollar and thirty cents and
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we know that consumers are buying twenty
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four point eight thousand packs so to
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find the actual amount of consumer tax
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burden we can simply take twenty four
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point eight and multiply it by the per
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pack tax burden and we get a consumer
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tax burden of thirty-two point two four
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and of course this is thousands of
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dollars we can see that consumers are
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going to end up paying thirty two point
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two four thousand dollars towards this
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tax
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now we can do similar analysis to find
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out how much of the total tax will be
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paid by producers so let's now apply the
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per pack producer tax burden which since
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consumers are paying 130 producers must
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be paying per pack $2 the full amount of
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the tax - the producers tax are - the
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consumers tax burden
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so it's 0.7 dollars or 70 cents and we
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know they're twenty four point eight
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thousand packs being sold times the
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producer tax per pack burden and we see
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that the total tax burden paid by
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producers is equal to seventeen point
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three six of course this is thousands of
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dollars so seventeen thousand three
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hundred and sixty dollars represented by
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this area here now wouldn't it also be
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nice if we could determine the total
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amount of tax revenue generated from
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this tax well that should be quite easy
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now because we know how much tax would
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be paid by consumers and we know how
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much tax would be payed by producers and
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as we learned in previous videos the
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total amount of tax revenue is equal to
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the sum of the consumer burden and the
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producer burden so all we need to do is
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take the consumer burden of thirty-two
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point two four thousand and add the
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producer burden of seventeen point three
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six thousand and very easily we can come
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up with the total amount of tax revenue
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generated which is forty-nine thousand
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and six hundred dollars forty nine point
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six thousand dollars so we can see that
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the total amount of tax revenue
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generated is the sum of the consumer tax
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burden of 32 thousand two hundred forty
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dollars and the producer tax burden of
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seventeen thousand three hundred sixty
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dollars which is 49 thousand six hundred
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dollars this is how much tax will be
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raised from a $2.00 per pack cigarette
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tax shared between consumers and
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producers again since demand for
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cigarettes is relatively inelastic we
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found that the blue rectangle
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representing consumer burden was larger
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than the green rectangle representing
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perdu
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to burden now all of we've all that
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we've done is applied our linear
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equations to find the actual equilibrium
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price and quantity resulting from the
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$2.00 tax and using that simple using
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those simple equations we could quite
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easily come to the amount of tax revenue
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generated
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