Percentage tax on hamburgers

in the last video on taxing hamburgers I did a somewhat artificial thing where I text hamburgers with an absolute dollar amount typically consumption taxes are a percentage of the of the actual price of the good so for example sales taxes might be 8% or 9% of whatever you are buying so let's think about how the supply curve is perceived by the consumers would look if we had a percentage tax so now our government instead of chart it started taxing one dollar per hamburger let's say that their tax is and I'll make it big just to make it clear so that we can so we can see the result of it let's say their tax is twenty percent of the price twenty percent of the price of the hamburger so let's think what's going to happen just like we saw in the last video in order for producers to even think about producing that first hamburger they need to get two dollars per hamburger for it because that's their opportunity cost using those same inputs that same labor and resources they could produce their other opportunity would give them at least $2 so you have to give them at least two dollars in order to focus on hamburgers and every incremental hamburger after that the opportunity cost goes more because now they'll be using things that are slightly less suited for making hamburgers and maybe slightly more suited for making other things now at that very first hamburger you need to get two dollars for it from the supplier point of view but from the consumer point of view they can't just pay two dollars for it they're gonna have to pay two dollars plus twenty percent of the two dollars so twenty percent of two dollars is forty cents so from the consumers point of view I'll do it in blue they're gonna have to pay about two dollars and forty cents and instead of and right over here if you want to get the suppliers to produce about two and a half million hamburgers per day they're going to have to get especially for those those that those incremental hamburgers in order to get these the you know the the two and a half million hamburger produced you're going to have to give three dollars per hamburger for the supplier but the consumer is not going to be able to pay three dollars they're gonna have to pay three dollars plus twenty percent so that's three dollars and sixty cents so that will put us right about right about there and if you go further instead of four dollars so if you want the producers to produce right around right around four million hamburgers per day you'd have to pay them four dollars but the consumers would have to pay 20% more than that so they're gonna have to pay for 80 and so what you're going to see is from the consumers point of view the demand the supply curve I should say is going to look something like this it's not going to shift it's not going to shift a fixed amount up it's going to fix it's going to shift 20 percent up so let me do that pleat let me so it's going to shift something like that so for lower values it's going to shift a less absolute amount because 20 percent of $2 is less than 20 percent of $3 which is less than 20 percent of $4 so as we have more quantity and more price it'll shift up more and more because 20 percent because 20 percent will then become a larger absolute amount so the shift would look something like this but at any given point at any given point that is 20 percent that is 20 percent 20 20 percent is 2 it's 20 percent higher then the price that the suppliers then the producers would see so it's going to be 20 percent higher than say $6 zero so this is going to be a dollar 20 higher but you have the same exact phenomenon that we saw in the previous video in the previous video this entire area this entire area was the surplus that both of the consumers and the producers share now now the equilibrium quantity is less now the equilibrium quantity is less it's going to move right over there because we have this new curve so our new equilibrium quantity is over here so neither the consumers nor the government know there nor the producers are going to be able to take advantage of this of this surplus which was there when you didn't have the taxation so this is why taxation is generally considered inefficient and obviously you have to do some of it but it's generally inefficient it reduces some level of economic activity at least if you make us all the assumptions in this model and you have this deadweight loss the surplus that can't be that can't be had by anyone so there you still have a you still have a wait deadweight loss and if you look at the revenue that the government will now have it will still be it'll still be this quantity so it looks like our equilibrium quantity is now three million hamburgers per day which is about what we got in the last one and obviously I'm not doing this very precisely and it's going to be 60 cents so 20 percent times three dollars is 60 cents so the height is going to be 60 cents so this height right over here is 60 cents and the width right over here is three million hamburgers so it's going to be 60 cents per hamburger which is 20 percent of its price per hamburger per hamburger times times three million hamburgers three million hamburgers gives us gives us one point eight million dollars million dollars per day and just like the previous one now the producers surplus has shrunken the producers surplus is now just going to be this area right over here the producer surplus is just going to be that area right over there and the consumer surplus has also been shrunken it's been bitten into by the tax revenue so obvious revenue and the deadweight loss takes from both the producer and the consumer surplus