Lectures in Macroeconomics- Charles W. Upton Taxes and Efficiency Losses- A Proof

Two Propositions

Taxes and Efficiency Losses- A Proof Two Propositions

Taxes and Efficiency Losses- A Proof The General Efficiency Loss S D PoPo QoQo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss Now suppose we impose a tax on the product, so the quantity sold drops. The efficiency loss is, of course, the shaded area. S D PoPo QoQo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss The EL is ½BH S D PoPo QoQo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss The EL is ½BH B = τP o H= µB = µ τP o EL = (½) µ τ 2 P o 2 S D PoPo QoQo τPoτPo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss The EL is ½BH B = τP o H= µB = µ τP o S D PoPo QoQo τPoτPo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss The EL is ½BH B = τP o H= µB = µ τP o EL = (½) µ τ 2 P o 2 S D PoPo QoQo τPoτPo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss The EL is ½BH B = τP o H= µB = µ τP o EL = (½) µ τ 2 P o 2 S D PoPo QoQo τPoτPo

Taxes and Efficiency Losses- A Proof The General Efficiency Loss The EL is ½BH B = τP o H= µB = µ τP o EL = (½) µ τ 2 P o 2 S D PoPo QoQo τPoτPo R τ = τ R 1

Taxes and Efficiency Losses- A Proof The Second Proposition

Taxes and Efficiency Losses- A Proof The Second Proposition

Taxes and Efficiency Losses- A Proof The Second Proposition

Taxes and Efficiency Losses- A Proof The Algebra

Taxes and Efficiency Losses- A Proof The Algebra

Taxes and Efficiency Losses- A Proof Optimization

Taxes and Efficiency Losses- A Proof Optimization

Taxes and Efficiency Losses- A Proof Optimization

Taxes and Efficiency Losses- A Proof Optimization

Taxes and Efficiency Losses- A Proof Optimization

Taxes and Efficiency Losses- A Proof Optimization

Taxes and Efficiency Losses- A Proof End ©2004 Charles W. Upton. All rights reserved