Things can get a little confusing

when we put a tax on a market.

So today we're going to sort out

what happens.

First keep track of

what's on the axis of your graph.

We're using our typical market graph.

So we have quantity

on the horizontal

and dollars per unit price

on the vertical.

The type of tax

we want to model

is a per unit tax.

It's not a percentage

of the consumers expenditure.

It's a specific dollar amount

for each item sold.

An example would be the $0.18 per gallon

Federal tax on gasoline

or the $2 or $3 per pack taxes

many states put on cigarettes.

Since we have dollars per unit

on the vertical axis and our tax

is also dollars per unit

that tax shows up

as a vertical interval

on our graph.

The bigger the per unit tax,

the bigger that interval.

Now some textbooks

will try to model the effect of this tax

by shifting curves.

They'll say

that if the government charges

consumers a $4 tax

on every left-handed coffee mug

they buy,

it will show up

by shifting the demand curve

downwards by $4.

Likewise, they'll say that

if instead the government

charges the producers $4

for every left-handed coffee mug

they produce,

that shows up

by shifting the supply curve

upwards by $4.

Those are pretty confusing ways to do it.

So here's a simpler method.

If the government

is putting a $4 tax

on every left-handed coffee mug,

simply find the place

where demand is $4 above supply.

Remember that demand indicates

how much value consumers place

on a specific unit of output

and supply indicates

how much it costs producers

to produce that unit.

So you're looking for the unit,

the specific quantity

where the value to consumers

is $4 greater

than the production cost

for the producers.

You sort of take

a Goldilocks approach.

At this quantity the vertical gap

between demand and supply is $9

so that can't be it.

At this quantity the vertical gap

between demand and supply is only $2

so that can't be it either.

But at an output of 800

left-handed coffee mugs

the demand or the value to consumers

is exactly $4 greater than supply,

the cost of producers.

So that's where we draw the line

for our $4 per unit tax.

So we have our new quantity.

Notice that is less than

the original equilibrium quantity

before the tax,

but where's the price?

Well there are

essentially two new prices.

There's a new price

that consumers have to pay

which is higher than before,

and there's a new price

that producers receive

when they sell an item

which is lower than before,

and it turns out it doesn't matter

whether the government taxes

consumers $4 on every item they buy

or taxes producers $4

on every item they produce.

Either way the market ends up

with the same higher consumer price

and the same lower price

that producers receive.

So what do we have so far?

We find the quantity

where the vertical distance

between demand and supply

is equal to the per unit tax.

That new quantity is lower than

the original equilibrium.

There are now effectively two prices.

A higher one that consumers pay

and a lower one

that producers receive.

Finally, what's happening

in the middle here?

That's the tax revenue

going to the government

which after all

is the whole point of imposing a tax.

The total tax revenue is the tax per unit

times the number of units

produced and consumed

and hey what do you know

here is our tax per unit

and here is our number of units.

So the area of this rectangle

gives us the tax revenue.