# Tax incidence and Price Elasticity

1. Jan 23, 2014

### Zalajbeg

Hello everyone,

I see that economists define a formula to calculate how the tax is shared between consumers and suppliers.

They call it "Pass-thorugh" fraction:

Customers share = (-PED)/(PES-PED)
Suppliers share = PES/(PES-PED)

However I see this doesn't work when I use it with arc-elasticity.

Let us assume we have a very little supply and demand schedule

Price ---------$1------$2-------$3 Supply--------10------20-------30 Demand-------30------20-------10 Let us say we have got a specific tax of$2 per unit. Then our new schedule will be:

4. Oct 8, 2014

### Staff: Mentor

Depends on the type of tax. Some product-specific taxes are per unit, not %. Gas tax and cigarette tax are key examples. According to wiki, most excise taxes are per unit.

5. Oct 22, 2014

### MrAnchovy

Yes you are missing the fact that arc elasticity cannot in general be used in place of point elasticity!

6. Oct 22, 2014

### Zalajbeg

Thanks for your reply but I am not sure if it is the thing I am missing. The example I made up above has the supply and demand functions which are linear. Therefore the arc elasticity shoudn't give different results from the point elasticity. Also we may need to clarify that, if I use the point elasticity which point shoul I use, the old price or the new price?

7. Oct 22, 2014

### MrAnchovy

Your demand function is non-linear (calculate PED at £1, £2 and £3)

The price before tax. Note that the pass-through percentage itself is not constant, it is a funciton of PES, PED and the amount of tax.

Last edited: Oct 22, 2014
8. Oct 23, 2014

### Zalajbeg

Actually I am quite sure the demand function is linear and it is $P=-0.1Q+4$ but I see your point, PED is not the same for every point although the demand function is linear, I agree.

It was the thing I was missing, If the equilibrum point before the tax is used the pas through formulas works properly. Thanks for your answer.