Tax incidence and Price Elasticity

• Zalajbeg
In summary, economists define a formula to calculate how the tax is shared between consumers and suppliers, but this formula does not work when used with arc-elasticity. Half of the tax is paid by customers and the other half is paid by suppliers. When using the equation with arc elasticity, the values 0.5 and 0.5 do not appear because the P in the formula (ΔP/P) is not the same for both supply and demand.
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? I'm sorry you are not finding help at the moment. Is there any additional information you can share with us? Zalajbeg said: 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). Kerrie said: 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.

Zalajbeg said:
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!

MrAnchovy said:
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?

Zalajbeg said:
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)

Zalajbeg said:
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.

Last edited:
MrAnchovy said:
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.

MrAnchovy said:
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.

1. What is tax incidence?

Tax incidence is the division of the burden of a tax between buyers and sellers in a market. It refers to who ultimately bears the economic cost of a tax, either through a decrease in consumer spending or a decrease in producer profits.

2. How is tax incidence determined?

Tax incidence is determined by the price elasticity of demand and supply in a market. If the demand for a good or service is relatively inelastic, the tax burden falls more on consumers. If the supply is relatively inelastic, the tax burden falls more on producers.

3. What is price elasticity of demand?

Price elasticity of demand is a measure of the responsiveness of the quantity demanded of a good or service to a change in its price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price. A higher price elasticity means that a small change in price leads to a larger change in quantity demanded.

4. How does price elasticity affect tax incidence?

The more elastic the demand for a good or service, the more the tax burden falls on producers. This is because when demand is elastic, consumers are more sensitive to price changes and will decrease their demand more in response to a price increase, leaving producers with less ability to pass on the tax to consumers.

5. What are the implications of tax incidence?

Tax incidence can have significant impacts on market outcomes, such as the quantity of the good traded, the price of the good, and the welfare of buyers and sellers. It can also have distributional effects, as the burden of the tax may fall more on certain groups (such as low-income consumers) than others.

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