Klaus Conrad: Taxes and Subsidies for Pollution-Intensive Industries as Trade Policy, Journal of Environmental Economics and Management, 1993:

Size: px

Start display at page:

Download "Klaus Conrad: Taxes and Subsidies for Pollution-Intensive Industries as Trade Policy, Journal of Environmental Economics and Management, 1993:"

Chrystal Clarke
6 years ago
Views:

1 Klaus Conrad: Taes and Subsidies for Pollution-Intensive Industries as Trade Policy, Journal of Environmental Economics and Management, 1993: AED 7210, Applied Microeconomics

2 Motivation Rules on tariffs and eport subsidies have resulted in governments seeking other instruments to shift rents To maintain competitiveness and reduce leakage, environmental policy instruments may be substitutes for both industrial and trade policy In an oligopolistic setting, Conrad (1993) models a dirty industry in two countries competing in a thirdcountry market If government taes SO 2 or CO 2 emissions, affects its firm (s) competitiveness as a consequence, may adopt abatement and input subsidies Essentially an application of strategic trade theory as originally applied by Brander and Spencer (1985)

3 Model Motivation for government policy: seek to target negative eternalities without reducing share of eport market captured by domestic firm Two-stage game, played by two competing firms, located in two different countries, with two rentseeking governments: (1) governments pre-commit to environmental policies (2) firms determine level of abatement, and choose output to maimize profits Equilibrium in (2) is Nash given policy choices in (1) Nash game between countries determined by Nash game between firms, resulting in sub-game perfect equilibrium of two-stage game

4 Stage 2 Production and Abatement Costs: Domestic firm produces at cost c(,q(t)), where q(t) is price of polluting input, other input prices being constant, and thereby omitted from cost function Price of polluting input is: q( t) = q0 + ca. a. e + t(1- a) e where q 0 is basic input price, ca=ca(a) is unit abatement cost, which depends on level of abatement a (0<a<1), e is emissions coefficient (CO 2 per ton of input), and t is emissions ta; ca a >0, and ca aa >0, i.e, unit abatement costs are increasing and conve in degree of abated emissions (1)

5 Stage 2 Firm Behavior: Profit for a domestic firm is: π(, X, t) = r (, X )- c(, q( t)) where r is revenue, and π is profit of domestic firm, (upper-case letters refer to foreign firm) Profit for foreign firm is: Π(, X, T ) = R(, X )- C( X, Q( T )) where foreign firm s cost function is: (2) (3) Q(T) = Q (4) 0 + CA. A. e + T (1- A) e e being assumed to be the same in both countries

6 Stage 2 and X are substitutes, and marginal revenue of firms declining in output of other firm: rx < 0; rx < 0; R < 0; RX < 0 First-order conditions are: π = r (, X )- c (, q( t)) = 0 (5) (6) ΠX = RX (, X )- CX ( X, Q( T )) = 0 with second-order conditions: (7) Also assume: π < 0; Π < 0 XX (8) Ω = π ΠXX - π XΠX > 0 (9)

7 Stage 2 Solutions to (6) and (7) depend on domestic and foreign emissions taes, t and T: = f ( t, T ); X = F( t, T ) (10) Degree of abatement a(a) is function of t(t), level of a(a) being chosen prior to production; firm acts to minimize unit cost of q (Q), such that: q = ca. a + ca - t = 0 Similarly for foreign firm: a a Q = CA. A + CA - T = 0 A A i.e., marginal abatement costs equal ta rate a and A then treated as eogenous in output game (11) (12)

8 Stage 2 Totally differentiating (6) and (7) with respect to, X, t and T, using (5), (8) and (9), and also Shepard s lemma, v=c q (,q) and V=C Q (X,Q), v(v) being input quantity: ΠXX d / dt = f t = v (1- a). e. < 0 Ω r d dt f = V A e Ω π dx dt F = V A e Ω X / = T - X(1- ).. > 0 / = T X(1- ).. < 0 (13) RX dx / dt = F t = - v X(1- a). e. > 0 Ω Domestic (foreign) firm s output decreasing in domestic (foreign) ta and increasing in foreign (domestic) ta

9 Non-Cooperative Behavior: Taes Pollutant is global public bad, i.e., d(p) is a conve domestic damage function, P = (1- a) e. v +(1- A) e. V Governments maimize relevant objective functions: ma w = r (, X )- c (, q ( t t )) + t.(1- a ). e. v - d ( P ) ma W = R (, X )- C ( X, Q ( T T )) + T.(1- A ). e. V - D ( P ) (14) (15) First-order condition from (14) is: rxft +((1- a) e. v ft )( t - md ) = 0 where md is marginal damage in domestic country (16)

10 Non-Cooperative Behavior: Taes Re-writing (16) gives optimal domestic ta foreign ta T: ˆ RX t = g md + rx md A e VX (1- a) e. v. Π [ -.(1- ). ] XX tˆg, given (17) Optimal ta set lower than Pigouvian ta of - second term in (17) is negative (see (5) and (8)), and v >0, i.e., prevents loss of market share by domestic firm - need to account for increased marginal damage from emissions leakage, md.(1- A) e. V X Optimal environmental policy incorporates both industrial and trade policy tˆg = md

11 Cooperative Behavior: Taes If governments cooperate over environmental taes t and T, maimize objective function: ma TW = (, )- (, ( )) + (, )- (, ( )) r X c q t R X C X Q T tt, + t.(1- a). e. v +T.(1- A). e. V - d( P)- D( P) (18) where D(P) is foreign damage function; solving δtw/δt = 0 and δtw/δt = 0 simultaneously for t and T: ˆ R t = md + MD - (1- a ) e. v ˆ r T = md + MD - (1- A ) e. V X (19)

12 Cooperative Behavior: Taes Comparing (17) with (19), ta higher with cooperation: - reflects marginal damage in both countries, md(md) - taes also eceed marginal damage, R < 0 and r X < 0, i.e., neither country has to worry about loss of competitiveness/leakage - each country takes into account negative effects of their contribution to global public bad, so there is cooperation over ta rates - importing country s damage function is ignored though, plus their consumers face potential deadweight loss

13 Non-Cooperative Behavior: Abatement Subsidies (1) can be modified to include an abatement subsidy s: q( s, t) = q0 +( ca - s). a. e + t(1- a) e (20) Totally differentiating (6) and (7) with respect to, X, t, s, T and S: Π d ds f = v a e Ω XX / = s -... > 0 r d ds f = V A e Ω π dx ds F = V A e Ω X / = S X... < 0 / = S - X... > 0 (21) R dx ds F = v a e Ω X / = s X... < 0

14 Non-Cooperative Behavior: Taes and Subsidies Domestic government maimizes: ma = (, )- (, (, )) +.(1- ).. w r X c q s t t a e v st, - s. a. e. v - d( P) (22) where = f ( t, T, s, S); X = F( t, T, s, S), and the new cost minimizing condition for domestic firm is: caa. a + ca = s + t Optimal ta and subsidy rates are: ˆ RX t = md + rx md A e VX ev.. Π [ -.(1- ). ] XX (23) (24) ˆ RX s = - [ rx - md.(1- A) e. VX] > 0 ev. Π X XX (25)

15 Non-Cooperative Behavior: Taes and Subsidies Comparing (24) and (17), tˆ ˆ, due to (1-a)<1 not being G > t in denominator of (24), i.e., abatement plays no role in ta, abatement being directly rewarded through s Also, as tˆ + s ˆ = md, given (23), firm equates marginal abatement cost to marginal damage, determining, â and with tˆ+ s ˆ > tˆ G, then a ˆ> aˆ Size of s depends on impact of gain in foreign firm s market share and resulting emissions leakage Higher welfare compared to ta-only case highlights importance of using two policy instruments to target two eternalities - pollution and imperfect competition

16 Cooperative Behavior: Taes and Subsidies If governments cooperate over taes and subsidies t, T, s and S, they maimize objective function: ma TW = (, )- (, (, )) r X c q s t t, T, s, S + R(, X )- C( X, Q( S, T )) + ( t.(1- a)- s. a). e. v + ( T.(1- A)- S. A). e. V - d( P)- D( P) Solving simultaneously for t,t,s and S: R R e. v e. v t = md + MD -, s = < 0 T = md + MD -, S = < 0 r r e. V e. V X X (26) (27)

17 Cooperative Behavior: Taes and Subsidies Compared to (19), ta rate on emissions is still greater than total marginal damage, (md+md), but taes no longer dependent on abatement Effects of environmental damage and abatement efforts are disentangled Differences in abatement associated with differences in abatement cost function, taing abatement offsets a country s advantage at abatement efforts Marginal abatement costs equal to t + s ; T + S, and also know from (28) that t + s = md + MD ; T + S = md + MD, i.e., marginal abatement costs equalized across countries

18 Non-Cooperative Behavior: Input Subsidies (1) can also be modified to include an input subsidy z: q( z, t) = q0(1+ z) + ca. a. e + t(1- a) e (28) Totally differentiating (6) and (7) with respect to, X, t, z, T and Z: ΠXX d / dz = f z = v q0. < 0 Ω rx d / dz = f Z = - VX. Q0. > 0 Ω (29) π dx / dz = F Z = VX. Q0. < 0 Ω R dx dz F = v q Ω X / = z - X. 0 > 0

19 Non-Cooperative Behavior: Taes/Input Subsidies Domestic government maimizes: ma = (, )- (, (, )) +.(1- ).. w r X c q z t t a e v zt, + z. q. v - d( P) 0 (31) z does not affect degree of abatement, marginal abatement costs being equal to ta rate as in (11) Optimal ta and input subsidy rates are: t* = md R = [ -.(1- ). ] < 0 X z* rx md A e VX q0. vxπxx (32) Ta is targeted at eternality, while input subsidy is targeted at raising domestic firm s eports

20 Cooperative Behavior: Taes/Input Subsidies If governments cooperate over taes and input subsidies t, T, z and Z, they maimize: ma TW = (, )- (, (, )) r X c q z t t, T, z, Z + R(, X )- C( X, Q( Z, T )) + t.(1- a). e. v + z. q. v Solving simultaneously for t,t, z and Z: 0 +T.(1- A). e. V + Z. Q. V - d( P)- D( P) t * * md MD z = + ; * * = > 0 0 -R q. v = + ; = -r Q 0. V > 0 X T * * md MD Z * * 0 (33) (34)

21 Cooperative Behavior: Taes/Input Subsidies Globally uniform emissions ta takes care of global public bad efficiently marginal abatement costs same across countries Ta on polluting input internalizes effect of own eports on other firm s market share Essentially cooperative policy with taes/input subsidies resolves eternality problem, but also facilitates collusion among firms i.e., deadweight losses imposed on importing country

AED 7210, Applied Microeconomics

Steve McCorriston and Ian Sheldon: Market Access and WTO Border Tax Adjustments for Environmental Taxes under Imperfect Competition, Journal of Public Economic Theory, 2005: 579-592 AED 7210, Applied Microeconomics