Part 6A. 4. Tax and Monopoly Taxes in Monopoly vs Taxes

Transcription

1 Part 6A. Monooly 4. Tax and Monooly 租稅與獨佔 Taxes in Monooly vs. Cometitive Markets Lum-Sum Tax Secific Taxes Ad Valorem Taxes Proortional Profit Taxes

2 Taxes in Monooly vs. Cometitive Markets Taxes (ad valorem and secific) affect monooly differently than a cometitive industry: Tax incidence on consumers (the change in the consumers rice divided by the change in the tax) can exceed 100% in a monooly market but not a cometitive market. If tax rates t Q and t are set so that t the after-tax t outut is the same with either tye of tax, the government raises the same amount of tax revenue in a cometitive market using either tye of tax, but raises more revenue using an ad valorem tax than a secific tax under monooly. 2

3 Lum-Sum Tax 定額稅 Basic Idea: Lum-sum tax is viewed as a Fixed Cost. AC curve shifts u, MC curve doesn t affected. Max ( Q) ( Q) Q VC( Q) FC T { Q} F.O.C.: S.O.C.: d MR MC dq 0 2 d dmr dmc 0 2 dq dq dq MR = MC 3

4 The Effect of Lum-Sum Tax dq M /dt = 0, Q T = Q M. d M /dt =0 0, T = M. SW = 0 ( 租稅中立性 ) Tax burden is totally on monooly. i.e., = T M = T (lum-sum tax revenue) T > 0, Q T = Q M T <0 (a). T < FC, Q T = Q M (stay in the Market in the SR) (b). T >FC FC, Q T = 0 (exit from the market) 4

5 Figure: Lum-Sum Tax & Monooly Price MC AC The monoolist will maximize rofits where MR = MC M C T Q M MR AC D The firm will charge a rice of M. Profits is the shaded rectangle minus lum-sum tax, T. Quantity 5

6 Secific Tax 從量稅 Basic Idea: secific taxisanunittax an tax, t Q, er unit of outut MC curve shifts u. Max ( Q) ( Q) Q VC( Q) FC tq Q { Q} F.O.C.: S.O.C.: d MR MC t Q dq 0 2 d dmr dmc 0 2 dq dq dq MR = MC + t Q 6

7 Let Q = Q() and = (t Q ) Totally differentiating the F.O.C. w.r.t. t Q, we have dmr dq d dmc dq d 10 dq d dt dq d dt Q d 1 00 dtq dmr dmc dq dq dq d Q Q () dq dq d dt d dt Q () () 0 () 7

8 The Effect of Secific Tax dq M /dt Q < 0, Q tq < Q M. d M /dt Q >0 0, tq > M. SW < 0 CS < 0: Tax burden is artially on consumers. However, rofit may not decreased in the secial case where e D, < 1 and is a constant. d FOC F.O.C.: MR MC t Q 0 dq 1 MR MC t e D, 1 Q 8

9 d 1 ed, dt Q e D, 1 ed, Thus, the incidence of the tax that fall on consumers exceed 100%. However, for other tyes of demand curves, the tax on consumers may be less than 100%. 9

10 Figure: Secific Tax & Monooly Price MC MC The monoolist will maximize rofits where tq M C tq C AC MR = MC + t Q The firm will charge a rice of tq > M. Profits can be found in the new shaded rectangle. Q tq Q M MR D Quantity 10

11 Sale (ad valorem) Taxes 從價稅 Basic Idea: sale tax is a tax on rice, t, er unit of outut MR curve shifts inward. Max ( Q) ( Q) Q VC( Q) FC t ( Q) Q { Q} F.O.C.: d (1 t ) MR MC 0 dq d S.O.C.: 2 dmr dmc (1 t ) 0 or 2 dq dq dq (1 t )MR = MC MR MC (1 t ) 11

12 Let Q = Q() and = (t ) Totally differentiating the F.O.C. w.r.t. t, we have dmr dq d dmc dq d (1 t ) MR 0 dq d dt dq d dt d MR dt dmr dmc dq (1 t ) dq dq d () 0 () dq dq d dt d dt () () 0 () 12

13 The Effect of Sale Tax dq M /dt < 0, Q t < Q M. d M /dt >0 0, t > M. SW < 0 CS < 0: Tax burden is artially on consumers. However, firm s rofit will decrease in the case. 13

14 Figure: Sales Tax & Monooly (MR shifts downward) Price t M C t C MC AC The monoolist will maximize rofits where (1 t ) MR = MC The firm will charge a rice of t > M. Profits can be found in the new shaded rectangle. MR Q t Q Q M MR D Quantity 14

15 Figure: Sales Tax & Monooly (MC shifts uward) Price t M C t C MC MC AC The monoolist will maximize rofits where MR = MC/(1 t ) The firm will charge a rice of t > M. Profits can be found in the new shaded rectangle. Q t Q Q M MR D Quantity 15

16 Figure: Ad Valorem vs. Secific Tax Governments tyically use an ad valorem tax rather than a secific tax because the tax revenue is greater. secific tax revenue = A ad valorem tax revenue = A +B Perloff (2014, 3e, GE), Figure 11.6,

17 Proortional Profit Taxes 比例利潤稅 Basic Idea: a a roortional tax on rofit, t. Both MR & MC curves shift inward. Max ( Q) (1 t ) ( Q) Q VC( Q) FC { Q} d F.O.C.: (1 t )( MR MC) 0 MR = MC dq 2 d S.O.C.: dmr dmc (1 t ) 0 2 dq dq dq 17

18 Let Q = Q() and = (t ) Totally differentiating the F.O.C. w.r.t. t, we have dmr dq d dmc dq d (1 t ) ( MRMC) 0 dq d dt dq d dt d MR MC dt dmr dmc dq (1 t ) dq dq d () 0 () dq dq d dt d dt () () 0 () 18

19 The Effect of Proortional Profit Tax dq M /dt = 0, Q T = Q M. d M /dt =0 0, T = M. SW = CS + PS + Tax Revenue = 0 CS = 0 PS < 0: PS = Tax Revenue Tax burden is totally on monooly as long as t 100%. 19

20 Figure: Sales Tax & Monooly (MR shifts downward) Price MC The monoolist will maximize rofits where (1 t ) MR = (1 t ) MC t M C t C (1 t ) AC The firm will charge a rice of t = M. Profits can be found in the new shaded rectangle. MR Q Q M MR D Quantity Q t 20