Tax_equivalence

Tax_equivalence - Proof of Tax Equivalence We made the...

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Unformatted text preview: Proof of Tax Equivalence We made the claim in class that the effects of a tax on equilibrium price do not depend on whether you collect the tax from consumers or suppliers. The following is a proof of this claim. 1 Collect from producers D(p(τ )) = S (p(τ ), τ ) dD dS = dτ dτ ∂D ∂p ∂S ∂p ∂S = + ∂p ∂τ ∂p ∂τ ∂τ ∂S ∂τ ∂p = ∂τ ∂D ∂p − ∂S ∂p Because producers remit the tax they care directly only about the after-tax price, p − τ . Therefore, ∂S ∂S ∂τ = − ∂p . In words, the change in quantity supplied from a unit increase in tax τ is the same as the change from a unit decrease in transaction price p. Using this fact, ∂p = ∂τ ∂S ∂p ∂S ∂p − ∂D ∂p = ν ν− What we found above is the change in the transaction price p. To calculate tax incidence, let’s consider what happens to producer price P S and to the consumer price P D : P S = p(τ ) − τ dP S ∂p = −1 dτ ∂τ ν −1 = ν− = ν− <0 The consumer does not remit the tax directly. Therefore, P D = p(τ ) ∂p dP D = dτ ∂τ ν = ν− 1 >0 2 Collect from consumers D(p(τ ), τ ) = S (p(τ )) dD dS = dτ dτ ∂D ∂p ∂D ∂S ∂p + = ∂p ∂τ ∂τ ∂p ∂τ ∂p = ∂τ ∂D ∂τ ∂S ∂p − ∂D ∂p Now consumers remit the tax so they only care about the after-tax price. To them, a unit increase in tax τ is equivalent to a unit increase in transaction price p. Therefore, ∂D = ∂D . Using this ∂τ ∂p fact, ∂p = ∂τ ∂D ∂p ∂S ∂p − ∂D ∂p = ν− Let’s again examine what happens to the producer price P S and consumer price P D now that the consumers remit the tax instead of the producers. For producers: P S = p(τ ) dP S ∂p = dτ ∂τ = ν− <0 For consumers: P D = p(τ ) − τ dP D ∂p = −1 dτ ∂τ = −1 ν− ν = >0 ν− Note that dP S dτ and dP D dτ don’t depend on who remits the tax. This concludes the proof. 2 ...
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This note was uploaded on 12/10/2011 for the course ECON 401 taught by Professor Burbidge,john during the Winter '08 term at Waterloo.

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Tax_equivalence - Proof of Tax Equivalence We made the...

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