Tax incidence and Price Elasticity

[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:

Price ---------$1------$2-------$3
Supply---------0-------0-------10
Demand-------30------20-------10

The new equilibrium price is $3 instead of $2 and quantity is 10. Therefore I can say half of the tax is paid by customers and the other half is by suppliers.

However when I use the equations above with arc-elasticity I don't get the values 0.5 and 0.5 because the P in the formula (ΔP/P) is not the same for both supply and demand. If I use the beginning value of the P instead of the middle point of new P and old P it is OK. However this is not specified in any lecture not.

Am I missing something?

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[Kerrie]

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:

Price ---------$1------$2-------$3
Supply---------0-------0-------10
Demand-------30------20-------10

The new equilibrium price is $3 instead of $2 and quantity is 10. Therefore I can say half of the tax is paid by customers and the other half is by suppliers.

However when I use the equations above with arc-elasticity I don't get the values 0.5 and 0.5 because the P in the formula (ΔP/P) is not the same for both supply and demand. If I use the beginning value of the P instead of the middle point of new P and old P it is OK. However this is not specified in any lecture not.

Am I missing something?

I know this is an old post, but my question is, why is the tax a flat $2? Typically tax is a rate of the product price set by a governing agency (in the US anyway).

 

[russ_watters]

I know this is an old post, but my question is, why is the tax a flat $2? Typically tax is a rate of the product price set by a governing agency (in the US anyway).

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.

 

[pbuk]

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

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

 

[Zalajbeg]

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

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?

 

[pbuk]

The example I made up above has the supply and demand functions which are linear.

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

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?

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.

 

[Zalajbeg]

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

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.

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.

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.