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### Course: Microeconomics > Unit 4

Lesson 2: Market interventions and deadweight loss- Rent control and deadweight loss
- Minimum wage and price floors
- How price controls reallocate surplus
- Price ceilings and price floors
- Price and quantity controls
- The effect of government interventions on surplus
- Taxation and dead weight loss
- Example breaking down tax incidence
- Percentage tax on hamburgers
- Taxes and perfectly inelastic demand
- Taxes and perfectly elastic demand
- Economic efficiency
- Lesson Overview: Taxation and Deadweight Loss
- Tax Incidence and Deadweight Loss

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# Percentage tax on hamburgers

What would happen if we have a percentage tax instead of a fixed dollar amount. Created by Sal Khan.

## Want to join the conversation?

- Why do you shift the supply curve? Isn't it more intuitive that the demand curve changes?(40 votes)
- the price of the supply is what inherently changes, so the supply curve goes up. the demand then meets that curve at it's equilibrium(36 votes)

- I am not sure about the way you've calculated the revenue of the government. Yes, it was the case for previous video where we can make an assumption that for each sold hamburger government will take the same revenue - and, as a consequence, we could approximate the revenue area as a rectangle - but for the current case it does not hold due to the fact that the revenue (its absolute value) will vary for each sold hamburger. Or may be I am missing something - could you, please, clarify this moment. Thanks!(10 votes)
- That's a good question. What you are missing is that the revenue (its absolute value) will not vary for each sold hamburger in neither of the two videos. It doesn't matter if the tax is in percentage (20%) or in a constant value ( 1$ ) because the price of the hamburger is fixed. No matter how many hamburgers a person buys it will always cost 3$/hamburger, so the 20% tax will be the same for each hamburger ( 0.60$ ). Thus 0.60 * 3m = 1.8 m/day makes sense. I hope it helped you. PS: sorry for my bad English (it's not my mother tongue)(14 votes)

- I am trying to understand why the producer surplus is calculated with the original supply curve instead of the new supply curve? I thought that a government tax would increase cost of production, thus lowering the producer surplus.(10 votes)
- Not quite. It's a tax on sales, not a tax on production. Only the consumers "see" the higher price, and have to pay it (that's why Sal said "the supply curve from the consumer's point of view").

The producers are only indirectly affected by the tax, because due to a higher price the quantity demanded will be less, and therefore they will sell less hamburgers.(11 votes)

- I was just wondering, if the tax rate is 20%, doesn't it mean, that the 20% of the price is the government's revenue? In that case the price would be calculated this way:

$2 / 0.80 = $2.5

Is it correct?(4 votes)- I agree that is how you would solve the problem.(2 votes)

- At4:50, Sal says "the height is 60¢". How can that be figured out?(3 votes)
- His drawing is a little bit "off" but where he says the "height is 60c" he is referring to the amount of tax added on to the price of the burger.

The tax has changed the EQ position: so in order to find the price before tax we use the original purple supply curve. This is because the increased price is 100% due to the tax and not factors affecting supply. Find the new Quantity at the new equilibrium and draw down to the purple supply curve. Draw a line directly left to the price axis to find the price of each hamburger minus the tax. That line, lines up with the price of each hamburger minus the tax on each hamburger.

I think Sal just made up the value of 60 cents for argument's sake. But we can work it out if we are given enough information.

Here's an accurate way to work out how much tax is added:

1. The new EQ looks like it lines up with a P of $4 and a Q of 3 million burgers.

2. We know that price has now increased and quantity demanded has now decreased from the old Equilibrium.

3. The tax was 20% therefore if we divide the new price by 1.2 we can find what the price minus tax is

4. 4 / 1.2 = $3.33. 4 - 3.33 = $0.67 in tax per burger.

5. New EQ price is $3.33 per burger with a tax of $0.67 per burger.

Therefore the height of the dead weight loss is 67 cents and the area of the dead weight loss can be calculated. In the video i'm assuming Sal just gave the dead weight loss an approximate height to explain the theory with nice round numbers.

Hope that helps! :)(2 votes)

- How can I calculate the tax revenue? Is there a formula?(3 votes)
- If it's percent then you take that percent of the revenue.(2 votes)

- Would you please explain for what reason we have to calculate the deadweight loss?(3 votes)
- to calculate the loss to the society ( producers & consumers), as none is better off due to the action by government (here taxation by the government)(2 votes)

- Will deadweight loss not be spent on something else or go into savings etc?(3 votes)
- Think of deadweight loss as unrealized potential. By implementing a tax, consumers and producers will both have lower surpluses than they could have in a no tax environment, so the deadweight loss reflects the loss of potential surplus.(1 vote)

- To find the new surplus, why don't we take the area between the new supply curve and the demand curve? Why do we still take the old supply curve?(3 votes)
- we use the old supply curve to calculate the producer surplus only. This is because although consumers are paying more per unit, the producers are still earning the same amount per unit, since the rest is taxes for the government. So, from the point of view of the producers, they are not changing their supply, but consumer demand is decreasing(1 vote)

- From your hamburgers example it can be seen that the Revenue collected from the

one-dollar tax is greater than that from the Sales Tax, so does this trend apply to all kinds of goods ? And should the government use only the one-dollar tax in order to maximize the Revenue ?(2 votes)- The government is not a profit-maximizing firm; it's not looking for revenue. It levies taxes in order to run itself and to provide public goods while mitigating the effects of negative externalities.(2 votes)

## Video transcript

Voiceover: In the last
video on taxing hamburgers, I did a somewhat artificial thing where I taxed hamburgers with an absolute dollar amount. Typically, consumption
taxes are a percentage of the actual price of the goods. For example, sales taxes might be 8% or 9% of whatever you are buying. Let's think about how the supply curve, as perceived by the consumers, would look if we had a percentage tax. Now, our government, instead of taxing $1 per hamburger, let's
say that their tax is, and I'll make it big just to
make it a clear, so we can see the result of it, let's say
their tax is 20% of the price. 20% of the price of the hamburger. 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 $2 per hamburger for it, because that's their opportunity cost. Using those same inputs,
that same labor and resources their other opportunity
would give them at least $2, so you have to give them at
least $2 in order to focus on hamburgers. 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, that very first
hamburger, you need to get $2 for it from the supplier point of view, but from the consumer point
of view, they can't just pay $2 for it. They're going to have to
pay $2 plus 20% of the $2. 20% of $2 is $0.40, so from
the consumer's point of view I'll do it in blue, they're
going to have to pay about $2.40. Right over here, if you
want to get the suppliers to produce about 2.5
million hamburgers per day, they're going to have
to get, especially for those incremental
hamburgers, in order to get 2.5 million hamburgers
produced, you're going to have to give $3 per hamburger for the supplier, but the consumer's not
going to be able to pay $3, they're going to have to pay $3 plus 20%, so that's $3.60, so that will
put us right about there. If you go further,
instead of $4, if you want the producers to produce right around 4 million hamburgers
per day, you'd have to pay them $4, but the
consumers would have to pay 20% more than that, so
they're going to have to pay $4.80. What you're going to see
is, from the consumer's point of view, the supply
curve, I should say, is going to look something like this. It's not going to shift a fixed amount up, it's going to shift 20% up. Let me do that ... It's going to shift something like that. For lower values, it's going to shift a less absolute amount,
because 20% of $2 is less than $20 of $3, which
is less than 20% of $4, so as we have more
quantity and more price, it'll shift up more and more, because 20% will then become
a larger absolute amount so the shift will look
something like this. At any given point, that is 20%. It's 20% higher than the
price that the suppliers and the producers would
see, so it's going to be 20% than $6 there, so this is
going to be $1.20 higher, but you have the same exact phenomenon that we saw in the previous video. In the previous video, this
entire area was the surplus that both the consumers
and the producers share. Now, the equilibrium quantity is less. It's going to move right
over there, because we have this new curve. Our new equilibrium quantity is over here, so neither the consumers,
nor the government, nor the producers are going
to be able to take advantage of this surplus, which was
there when you didn't have the taxation. This is why taxation is
generally considered inefficient. 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 all the
assumptions in this model, and you have this dead weight loss. This surplus that can't be had by anyone, so you still have a dead weight loss. If you look at the revenue
that the government will now have, it will
still be this quantity. It looks like our equilibrium quantity is now 3 million hamburgers per day, which is about what we
got in the last one. Obviously I'm not doing
this very precisely, and it's going to be $0.60,
so 20% times $3 is $0.60, so the height is going to be $0.60. This height right over
here is $0.60 and the width right over here is 3 million hamburgers. It's going to be $0.60 per hamburger, which is 20% of its price per hamburger times 3 million hamburgers,
gives us $1.8 million per day and just like the previous one, now the producer's surplus has shrunken. The producer's surplus
is now just going to be this area right over here. The producer's 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 and the dead weight loss
takes from both the producer and consumer surplus.