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Tax_equivalence

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

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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 ∂D ∂p ∂p ∂τ = ∂S ∂p ∂p ∂τ + ∂S ∂τ ∂p ∂τ = ∂S ∂τ ∂D ∂p - ∂S ∂p Because producers remit the tax they care directly only about the after-tax price, p - τ . Therefore, ∂S ∂τ = - ∂S ∂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 ∂τ - 1 = ν ν - - 1 = ν - < 0 The consumer does not remit the tax directly. Therefore, P D = p ( τ ) dP D = ∂p ∂τ = ν

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

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