Trade policy III: Export subsidies

Transcription

1 The Vienna Institute for International Economic Studies - wiiw June 25, 2015

2 Overview Overview 1 1 Under perfect competition lead to welfare loss 2 Effects depending on market structures 1 Subsidies to third market exports improve welfare under Cournot competition 2 Result reversed when considering Bertrand competition 3 Settings 1 Partial equilibrium

3 Welfare gains from exports Graphical exposition: Welfare effects of exports p S p w 0 Exports D q

4 Exports... 1 World price above autarky price 2 Trade opening implies decrease in consumer rent 2... increase in producer rent 3... positive welfare effect

5 Numerical example The demand curve is given by q D = 10 p and the supply curve by q S = 2 + p. Autarky equilibrium is characterised by p a = 6 and q a = 4. The consumer rent is CR a = 8 and the producer rent is PR a = 8. Let the world price be given by p w = 7. Demand is therefore q D = 3 and supply is q S = 5. Therefore exports are x = 2. Consumer rent decreases to CR = 4.5 and producer rent increases to P R = 12.5; thus CR = 3.5 and PR = 4.5. Total welfare increases by W = 1.

6 Assumptions Overview Welfare effects Non-perfect competition frameworks Assumptions and concepts 1 Perfect competition 2 Country size 1 Small country assumption (world price given) 2 Large country (influencing world price) 3 Partial equilibrium setting 4 Considering single export good (ceteris paribus) 5 Applying concepts of consumer and producer rent

7 Welfare effects of export subsidies Overview Welfare effects Non-perfect competition frameworks Graphical exposition: Welfare effects (loss) of export subsidies p S p w 0 + s p w 0 D q Constant world price

8 Overview Welfare effects Non-perfect competition frameworks 1 Exporting firms benefit 2 however imply 1... increase in producer rent 2... decrease in consumer rent 3... revenue cost of subsidies is larger than net change in consumer and producer rent 4... welfare loss 3 For a large country... 1 terms-of-trade improvement 2 lead to even larger welfare loss 4 Conclusion: lead unambiguously to welfare loss

9 Overview Welfare effects Non-perfect competition frameworks Numerical example The demand curve is given by q D = 10 p and the supply curve by q S = 2 + p. Autarky equilibrium is characterised by p a = 6 and q a = 4. The consumer rent is CR a = 8 and the producer rent is PR a = 8. Free Trade: Let the world price be given by p w = 7. Demand is therefore q D = 3 and supply is q S = 5. Therefore exports are x = 2. Consumer rent decreases to CR = 4.5 and producer rent increases to P R = 12.5; thus CR = 3.5 and PR = 4.5. Total welfare increases by W = 1. : Let be s = 1. Then p w + s = 8. Demand is therefore q D = 2 and supply is q S = 6. Therefore exports increase to x = 4. The consumer rent decreases to CR = 2 and the producer rent increases to 18; thus - compared to free trade situation - CR = 2.5 and the producer rent PR = 5.5 which would result in an welfare effect of +3. However subsidy payments are s x = 1 4 = 4; thus there is a welfare loss of W = 1.

10 Overview Welfare effects Non-perfect competition frameworks Non-perfect competition frameworks 1 Single home and single foreign firm sell to third market (duopoly) 2 Cournot competition (Brander and Spencer, 1985) 1 Export subsidy lead to welfare improvement 2 However, retaliation possible (see later) 3 Bertrand competition (Eaton and Grossman, 1986) 1 lead to welfare loss 2 Export tax would be welfare enhancing 4 Further reasons why export subsidies do not lead to welfare improvement: 1 Free entry 2 are considered endogenous in two-stage game 3 Productivity differences across exporting firms 4 Subsidy wars 5 Further reasons why export subsidies are welfare improving 1 R&D subsidies 2 Subsidies to capacities rather than exports 3 Subsidies might enhance learning (by doing)

11 1 Two firms (monopolists) compete in third market 1 Choosing volumes of production of a homogenous good that is entirely exported to third market 2 Cournot competition in third market 2 1 Governments choose level of export subsidies 2 Level depends on other country s subsidies

12 1 Third market (inverse) demand function p(q) = a b Q = a b (q + q ) 1 p... price in third market 2 Q = q + q... output (=exports) of home and foreign firm 2 Home firm s profit function incl. export subsidy π = p q C(q) + s q = [a b (q + q )] q C(q) + s q 1 C(q)... Cost function with constant marginal costs 2 s... (per unit) subsidy 3 Foreign firm s profit function (assuming no subsidies) π = p q C(q ) = [a b (q + q )] q C(q )

13 1 Assume that firms compete in quantities sold to third market 1 Cournot oligpoly 2 Cournot-Nash non-cooperative equilibrium 1 Find profit maximising output given the quantity sold by other firm 2 Home firm takes (per unit) subsidy as given 2 First-order conditions 3 Second-order conditions dπ dq = a 2 b q b q c + s = 0 dπ dq = a 2 b q b q c = 0 d 2 π dq 2 = d2 π = 2 b < 0 dq 2

14 1 Let c = c 2 Reaction function 1 Expresses each firm s output as a function of the other firm s output (and parameters) q = a b q c + s 2 b q = a b q c 2 b 3 Properties 1 Exports are a decreasing function of other firm s exports 2 Exports raise with subsidies in home

15 q q R R q R R s R q No subsidies Effects of (unilateral) subsidy

16 1 Solving for export levels 2 After subsidy profits 3 Home subsidies q = a + c 2 c + 2 s 3 b q = a + c 2 c s 3 b π = (a + c 2 c + 2 s) 2 9 b π = (a + c 2 c s) 2 9 b 1 Raise home firm s output and profits 2 Decrease foreign firm s output and profits

17 Welfare effects 1 Profit-shifting effect versus subsidy costs 2 Assumption that subsidies are financed by non-distorting lump-sum taxes; redistribution policy is welfare neutral 1 Local consumers pay taxes s q 2 Given to domestic firms as export subsidies 3 Definition of welfare W = π s q = (a + c 2 c + 2 s) (a + c 2 c s) 9 b 1 s = 0 W = (a + c 2 c) 2 9 b

18 Numerical example Let the inverse demand function be p = 20 2 Q. Marginal costs in both countries are c = 4. Free trade Subsidy s s q q π π W W Q p CR

19 1 Government sets subsidies to maximise welfare 2 First-order condition dw ds = 2 (a + c 2 c s)) (a + c 2 c + 2 s) 9 b = a + c 2 c 4 s = 0 9 b 3 Solving for optimal subsidy level 4 Interpretation s U = a + c 2 c 4 > 0 1 Subsidy increases with rival s marginal costs 2 Subsidies decrease with domestic marginal costs 1 More cost-competitivenss firm should receive larger subsidies

20 Numerical example Let the inverse demand function be p = 20 2 Q. Marginal costs in both countries are c = 4. Optimal Free Unilateral unilateral trade Subsidy subsidy s s q q π π W W Q p CR

21 1 Profits 2 First-order conditions... 3 Reaction functions π = [a b (q + q )] q C(q) + s q π = [a b (q + q )] q C(q ) + s q q = a b q c + s 2 b q = a b q c + s 2 b

22 1 Output levels 2 Profit levels q = a 2 c + c + 2 s s 3 b q = a + c 2 c + 2 s s 3 b 3 Aggregate output π = (a 2 c + c + 2 s s ) 2 9 b π = (a 2 c + c + 2 s s) 2 9 b Q = q + q = 2 a (c + c ) + (s + s ) 3 b

23 q q s R R R q R R s R q No subsidies Effects of (bilateral) subsidies

24 Numerical example Let the inverse demand function be p = 20 2 Q. Marginal costs in both countries are c = 4. Optimal Free Unilateral unilateral Bilateral trade Subsidy subsidy subsidy s s q q π π W W Q p CR

25 Welfare 1 Welfare W = π s q = (a + c 2 c + 2 s s )(a + c 2 c (s + s )) 9 b W = π s q = (a + c 2 c + 2 s s)(a + c 2 c (s + s)) 9 b 2 Both governments choose non-cooperatively welfare maximising subsidy level s B = a 3 c + 2 c 5 s B = a 3 c + 2 c 5 3 Inserting back above yields the equilibrium welfare levels W B = 2 (a 3 c + 2 c ) 2 25 b W B = 2 (a 3 c + 2 c) 2 25 b

26 q q R R q RRR b s s R b R q No subsidies Effects of subsidy game

27 1 Consider symmetric case c = c 2 Subsidy levels 0 < s B = s B = a c 5 < s U = a c 4 3 Firm s profits with subsidies are larger than under free trade π = π = (a c + s)2 9 b > (a c)2 9 b 4 Welfare levels with subsides are lower than under free trade W B = W B = 2 (a c) 2 < W Free trade = 1 (a c) 2 25 b 9 b 5 Third country is better off with subsidies

28 1 Output levels Note that: q B = q B = 2 a c 5 b q U = 1 a c > q B = 2 a c > q Free trade = 1 a c 2 b 5 b 3 b 2 Note: When considering output, employment and income effect of subsidies welfare effects might differ!

29 Numerical example Let the inverse demand function be p = 20 2 Q. Marginal costs in both countries are c = 4. Optimal Optimal Free Unilateral unilateral Bilateral bilateral trade Subsidy subsidy subsidy subsidy s s q q π π W W Q p CR

30 Summary 1 Bilateral subsidy is smaller than unilateral subsidy 2 Welfare is smaller than under free trade 1 Prisoner s dilemma 2 Welfare losses compared to free trade 3 In bilateral case output lower than in unilateral case, but higher than production level under free trade 4 Aggregate output is higher than under free trade and unilateral subsidies 5 Welfare gains in third market 6 Brander and Spencer (1985) results are not robust to these alternative frameworks 1 Bertrand competition 2 General equilibrium effects 3 Subsidising R&D 4 Free entry and increasing costs