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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?

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# Tax incidence and Price Elasticity

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