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

2. Two Propositions

3. Taxes and Efficiency Losses- A Proof Two Propositions

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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Taxes and Efficiency Losses- A Proof The Second Proposition

13. Taxes and Efficiency Losses- A Proof The Second Proposition

14. Taxes and Efficiency Losses- A Proof The Second Proposition

15. Taxes and Efficiency Losses- A Proof The Algebra

16. Taxes and Efficiency Losses- A Proof The Algebra

17. Taxes and Efficiency Losses- A Proof Optimization

18. Taxes and Efficiency Losses- A Proof Optimization

19. Taxes and Efficiency Losses- A Proof Optimization

20. Taxes and Efficiency Losses- A Proof Optimization

21. Taxes and Efficiency Losses- A Proof Optimization

22. Taxes and Efficiency Losses- A Proof Optimization

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