## _wp03229

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---

### I. Introduction — objectives and key insights
- Objectives of the paper:
  - Incorporate intermediate inputs into FTA analysis and derive welfare implications in the presence of rules of origin (ROOs).
  - Analyze the impact of ROOs on the political feasibility of FTAs and show that ROOs could make FTAs more feasible.
- Model environment (summary):
  - Conventional general-equilibrium model with three final goods (0, 1, 2) and an intermediate input m used in production of final good 1.
  - One partner imports the input and exports the final good using that input; the other partner exports the input and imports the final good.
  - This structure allows for an exchange of a tariff preference in the final good for a ROO on the input.
- High-level welfare insights:
  - ROO has an ambiguous effect on welfare of union members individually and jointly.
  - If the final-good preference results in trade diversion:
    - ROO diverts trade in the input market by substituting within-union supply for outside-union supply.
    - In the final-good market, ROO can reverse trade diversion by making within-union production more costly relative to no ROO.
    - Net effect is ambiguous; weakly binding ROO can improve joint welfare but excessive tightening can reduce it.
  - If the tariff preference in the final good is purely trade creating, a binding ROO is unambiguously harmful: no final-good trade diversion to reverse, but ROO causes trade diversion in the input market.
- Political-economy approach:
  - Step 1: Use Grossman-Helpman (1994) model to determine initial tariffs (key result: tariff on the input is zero in both partners).
  - Step 2: Study viability of an FTA without ROOs.
  - Step 3: Examine whether FTAs rejected without ROOs could become acceptable when ROOs are introduced.
- Two possible outcomes when ROO makes an FTA feasible:
  - (i) An FTA that previously lowered joint welfare and was rejected can be accepted with ROO.
  - (ii) An FTA that improved joint welfare but was rejected can be accepted with ROO, but the ROO may be so distortionary that the FTA lowers joint welfare relative to the status quo.

### II. The model — structure, preferences, production, and notation
- World and goods:
  - Three countries: home country (HC), foreign country (FC), and the rest of the world (ROW).
  - Four goods: 0, 1, 2 (final) and m (pure intermediate input used in production of good 1).
  - Good 0 is numeraire; world prices P_i^W normalized to 1 (P_i^W = 1 for i = 0,1,2,m).
  - HC and FC are small relative to ROW; perfect competition.
- Preferences and demand:
  - Quasi-linear preferences as in Grossman and Helpman: consumer utility U = c_0 + u(c_1,c_2).
  - Demand functions c_i = d_i(P_i).
  - Expenditure function E(1,P,P;U) = U + e(P).
- Production:
  - Numeraire produced with labor only: X_0 = L_0; wage w = 1.
  - Non-numeraire production functions F_i(L_i,K_i) are CRS, increasing and concave.
  - Good 1 produced by combining value-added V_1 with a_m units of m per unit of final good.
  - Net value-added price for good 1: P_1^v = P_1 - a_m P_m.
- Tariff and price conventions:
  - Initial tariffs are nondiscriminatory; domestic price equals world price plus per-unit tariff.
  - All tariff revenue redistributed lump-sum to consumers.
- Notation highlights:
  - HC variables given without asterisk; FC variables denoted with *.
  - Quantities X_i, demands c_i, labor L_i, specific factors K_i, total labor L.
  - Domestic prices P_i for i = 1,2,m.

### III. Pattern of trade under MFN tariffs and initial tariff results
- Assumed pattern of trade:
  - HC imports input m from FC and exports final good 1 to FC.
  - Both potential union members may also import the good they would otherwise import from ROW.
- Price notation under nondiscriminatory tariffs:
  - Domestic price of m in HC is 1 + t_m.
  - Domestic price of good 1 in FC is 1 + t_1^*.
  - With no intervention in exportable goods, price of good 1 in HC and m in FC is 1.
- Government payoff and tariff determination:
  - Government payoff G = g U + Σ_i (1+g) π_i, g > 0 (aligning with Grossman-Helpman lobbying framework).
  - Initial tariff results (with nonnegative tariff restriction):
    - t_m = 0, t_1 = 0.
    - FC: t_1^* > 0, t_m^* = 0 with t_1^* = (1+tg)^(-1) α_1^*/η_1^* (standard Grossman-Helpman result).
- Implication for FTA incentives:
  - HC (exporter of final good and importer of input) stands to benefit from FTA because it gains access to partner’s protected market while its own input market is tariff-free.
  - FC (exporter of input and importer of final good) has little incentive to endorse FTA absent other gains; ROOs can provide such gains.

### IV. FTAs in the absence of ROOs — three post-FTA final-good market cases
- FTA formation assumptions:
  - Upon FTA formation, countries freeze external tariffs at initial MFN level; intra-union trade is freed; no trade deflection allowed.
- Three analytically distinct cases for good 1 (imported by FC, exported by HC):
  - Case 1 — Purely Trade Diverting FTA:
    - HC’s supply intersects FC’s import demand above point Y (supply curve S1S1); price in FC remains 1 + t_1^*; HC supplies FC entirely; union-wide imports from outside decline (trade diversion).
    - Welfare: HC gains (producers’ surplus rises), FC loses (welfare falls); HC accepts, FC rejects.
  - Case 2 — Purely Trade Creating FTA:
    - HC’s supply intersects I*I* at or below point T (as in S2S2); union-wide price ≤ 1 + t_1^*; imports from ROW into FC eliminated.
    - Welfare: lost tariff revenue in FC partly shifted to tariff revenue gain in HC and partly to consumer/producer surplus in FC; union welfare gain positive; FC rejects absent other sectoral changes, HC weakly endorses.
  - Case 3 — Mixed Case:
    - HC supply crosses I*I* between Y and T; endogenous FC price; excluded from detailed ROO analysis due to complexity.
- Proposition 1:
  - "An FTA in the absence of a ROO that is purely trade diverting or trade creating in good 1 is necessarily rejected by FC."

### V. Rules of Origin (ROO): definition, mechanics, and equilibrium conditions
- ROO definition:
  - θ = (c_m^* + c_m^m + c_m^W) / (c_m + c_m^* + c_m^W) (equation (9) in source): ratio of intermediate input purchased from within the union to total input used by HC producers of good 1.
  - ROO imposes a lower bound θ_R on θ. Producers from HC receive tariff-inclusive price in FC only if θ ≥ θ_R.
  - Price rule (10): P_1^R = (1+t_1^*) if θ ≥ θ_R; = 1 if θ < θ_R.
- If θ_R sufficiently high, premium on within-union supply raises P_m above unity; P_m determined endogenously by regional demand and supply.
- Key comparative static and equilibrium expressions (as given in source; preserve qualitative form and role):
  - If θ_R ≤ θ_1 then ROO non-binding and P_m = 1 (equation (11)).
  - For θ_R > θ_1 regional demand-supply equality determines P_m (equation (12)).
  - Upper limit θ_2 ensures P_1^v not driven below 1 - a_m (equation (13) and equivalent (14)).
  - Comparative statics of P_m w.r.t θ_R given by an expression involving elasticities ε_1, ε_m^D, ε_m^S (equation (15)); sign ambiguous beyond θ_R = θ_1.

### VI. Effects of ROO — positive analysis by case
- Case 1 — Trade Diverting union (key results and behavior):
  - If θ_R ≤ θ_1: non-binding ROO, P_m = 1.
  - If θ_R > θ_1: regional supply of m must rise, P_m rises above 1; regional and imported m are distinct; P_1^v declines as θ_R increases.
  - Proposition 2:
    - "Assuming the union is purely trade diverting in the final good, P_m may rise monotonically, have an inverted-U shape, or exhibit multiple peaks as a function of the ROO."
  - Comparative intuition:
    - Increasing θ_R raises demand for m (scale effect) but reduces value-added price and output of good 1 (substitution effect); net sign depends on elasticities.
- Case 2 — Trade Creating union (key results and behavior):
  - Without ROO, FTA leads to free-trade outcome with P_1^v = 1 - a_m.
  - A binding ROO increases export cost via higher P_m, which raises P_1* in FC while keeping P_1^v = 1 - a_m.
  - Proposition 3:
    - "In the purely trade creating case, starting at θ_R = θ_1, if we increase θ_R, γ_e decreases and P_m and P_1* increase such that the value-added price received on exports, P_1^v, remains constant at 1 - a_m."
  - Note: At an initially strictly binding ROO, further increases in θ_R may be accompanied by a decrease in P_m if demand for m falls sufficiently.

### VII. Welfare effects of ROO (joint welfare and member-specific outcomes)
- Direct and indirect effects:
  - Direct: ROO diverts demand for the intermediate input toward regionally produced (inefficient) source, creating price distortion in m.
  - Indirect: depends on whether final-good trade was initially trade diverting or trade creating.
    - Case 1 (trade diverting): ROO can reverse some trade diversion in final good by raising the cost of within-union production; weakly binding ROO can improve joint welfare; excessive tightening can reduce joint welfare.
    - Case 2 (trade creating): ROO introduces distortion in FC consumer price with no trade diversion to reverse; tightening a binding ROO weakly worsens joint welfare.
- Proposition 4:
  - (a) "When the initial FTA is trade diverting in good 1 (case 1), and the ROO is increased at the weakly binding level, joint welfare of the partners improves, but the ROO is tightened further, joint welfare can eventually fall."
  - (b) "When the initial FTA is trade creating in good 1 (case 2), a tightening of a binding ROO weakly worsens the joint welfare of the union."
- Graphical intuition (as in source):
  - In case 1, small ROO tightening can reallocate production away from inefficient within-union supply of final good 1 (gain area abcd) while imposing small distortion cost in m (area efg); sign depends on magnitudes.
  - In case 2, introduction of ROO has second-order small effect at θ_R = θ_1 but further tightening raises distortions via P_m and P_1* reducing joint welfare.

### VIII. Political viability — ROOs affecting lobbying, government payoffs, and FTA endorsement
- Political mechanism:
  - ROO raises regional price of m, increasing returns to owners of K_m* and K_m; via Grossman-Helpman style lobbying, this can change government payoffs G and political support for the FTA.
- Proposition 5:
  - (a) "An initially infeasible FTA that reduces joint welfare of the union (case 1) can become feasible after the inclusion of a ROO."
  - (b) "An initially infeasible FTA that improves the joint welfare of the union (case 2) can become feasible at the inclusion of the ROO, although the ROO supporting it can be so distortionary that joint welfare of the union could actually fall with the FTA."
- Intuition:
  - Under case 1: HC supports FTA; ROO raises profits in sector m which can reverse FC’s rejection into acceptance because the increased producers’ surplus in m receives a larger weight in FC’s G* than the tariff revenue loss.
  - Under case 2: ROO can convert FC’s vote to positive if increased producer returns to m are sufficient, but the ROO may be distortionary enough to make the FTA joint-welfare reducing.
- Numerical examples (reported simulation highlights):
  - Common simulation parameters: a_m = 0.8, g = 1.
  - Case 1 numerical observations:
    - Two MFN tariff scenarios: t1* = 0.24 and t1* = 0.32.
    - P_m achieves a maximum at a ROO between 0.90 and 0.95 for both t1* values.
    - Value-added export price P_1^v falls monotonically with ROO.
    - G*ROO - G*MFN increases with ROO.
    - FTA weakly endorsed by FC when G*ROO - G*MFN = 0 at:
      - Rθ = 0.92 when t1* = 0.24
      - Rθ = 0.96 when t1* = 0.32
    - At these ROOs, union’s joint welfare change is negative; FTA continues to be welfare reducing after inclusion of ROO.
  - Case 2 numerical observations:
    - With higher α_1 satisfying the trade-creating condition, G*ROO - G*MFN is strictly positive for all ROOs ⇒ FC unambiguously endorses the FTA once ROO binds.
    - Price P_1* in FC increases monotonically with ROO.
    - If θ_R ≤ 0.35, joint welfare improves with the FTA; for θ_R > 0.35, the ROO is so distortionary that joint welfare of the union falls with the FTA.

### IX. Extensions (qualitative implications)
- Extension 1 — Both HC and FC import good 2:
  - If t2 < t2* and ROW continues to export goods 1 and 2 to the union, FTA without ROO can make HC better off and FC worse off (FTA infeasible). A ROO on m can make FC accept if producers’ surplus gains in m compensate tariff-revenue loss on goods 1 and 2.
  - Alternatively, if t2* < t2 and FTA was marginally acceptable without ROO, a binding ROO can reduce HC exporters’ payoff in good 1 and render the FTA infeasible.
- Extension 2 — Endogenous external tariffs post-FTA:
  - If union members set external tariffs endogenously after FTA, the optimal external tariff on good 1 for FC would be lower than pre-FTA; tariff revenue effects depend on how imports from ROW change.
  - With a binding ROO, reduced HC export supply raises FC’s imports from ROW and tariff revenue; an FTA rejected before might be accepted after ROO inclusion, but other outcomes (FTA becoming infeasible) are possible.
- Extension 3 — Exogenously positive tariffs on final good and intermediate input:
  - If MFN tariffs t1 and t_m with t_m > 0 exist, introducing a (non-binding) ROO that tightens can shift HC’s purchases of m from ROW to FC and increase HC’s tariff revenue loss on m, possibly leading HC to oppose the FTA.
  - If ROO is binding (P_m > 1 + t_m), HC may still support the FTA if producers’ surplus gains in m offset tariff revenue losses.

### X. Conclusion — policy-relevant takeaways
- Main results:
  - A ROO may improve or worsen joint welfare of the union; effects are case-specific.
  - The price distortion created by the ROO affects the political economy of FTA endorsement: ROOs increase rents for the intermediate-input–owning interest group and can switch a member’s vote from opposed to supportive.
  - Two policy-relevant outcomes:
    - An initially infeasible but welfare-reducing FTA can become feasible after inclusion of the ROO.
    - An infeasible but joint-welfare-improving FTA can become feasible upon ROO inclusion; caveat that the ROO can be so distortionary that after inclusion the FTA becomes joint-welfare diminishing.
- Empirical/political observations:
  - Product-specific ROOs can be driven by industry lobbying (examples cited in source include auto parts and yarn-forward textile rule under NAFTA).
  - ROOs that protect import-competing industries and intermediate-exporting industries can improve chances of FTA endorsement for input exporters and final-good importers, but stringent ROOs may be undesirable.
- Suggested future extension:
  - Endogenize ROO choice subject to industry-specific lobbying (analogous to exclusion of sensitive sectors in Grossman and Helpman (1995)).

*Source content from _wp03229 (provided PDF content unit).*

### References..............................................................................................................

### _wp03229 - References..............................................................................................................

### I. INTRODUCTION
- Rules of origin (ROOs) are integral to Free Trade Areas (FTAs): union members confer duty-free status on a product only if a pre-specified proportion of its value added originates within the union.
- There is practically no formal analysis in the political-economy-theoretic literature that incorporates ROOs, because intermediate inputs are rarely included in formal FTA models.
- Paper objectives:
  - Incorporate intermediate inputs into FTA analysis and derive welfare implications in the presence of the ROO.
  - Analyze the impact of ROOs on the political feasibility of FTAs and show that ROOs could make FTAs more feasible.
- Model setting summary:
  - Conventional general-equilibrium model with three final goods and an intermediate input used in the production of one final good.
  - One partner country imports the input and exports the final good using the input; the other partner exports the input and imports the final good.
  - This structure allows for an exchange of a tariff preference in the final good for a ROO.
- Key welfare insights:
  - ROO has an ambiguous effect on welfare of union members individually and jointly.
  - If the final-good preference results in trade diversion:
    - In the input market, the ROO diverts trade by substituting within-union supply for outside-union supply.
    - In the final-good market, ROO can reverse trade diversion by making within-union production more costly relative to no ROO.
    - Net effect is ambiguous.
  - If ROO is weakly binding on the input price, tightening it improves joint welfare because input price distortion is second-order small while the benefit from reversing final-good trade diversion is finite.
  - As ROO is tightened further, input price distortion may offset benefits.
  - If the tariff preference in the final good is purely trade creating (post-FTA price at its free trade level), a binding ROO is unambiguously harmful: no final-good trade diversion to reverse, but ROO causes trade diversion in the input market.
- Political-economy analysis approach:
  - Step 1: Use Grossman-Helpman (1994) model to determine structure of initial tariffs—key result: tariff on the input is zero in both partners.
  - Step 2: Study viability of an FTA without ROOs.
  - Step 3: Examine whether FTAs rejected without ROOs could become acceptable when ROOs are introduced.
- Asymmetric union-membership structure emphasized:
  - One country imports the input, the other imports the final good using that input.
  - Starting from initial tariffs chosen to maximize the final-good-importing country’s government payoff and neutralizing other asymmetries, the final-good importer necessarily rejects the FTA (because it loses tariff revenue without reciprocal gains).
- Effect of introducing a binding ROO:
  - ROO raises the price of the regionally produced intermediate input and effectively provides protection to input producers.
  - An FTA unattractive to the input exporter in absence of ROO can become attractive with ROO.
  - Two possible outcomes when an FTA becomes feasible after inclusion of ROO:
    - (i) An FTA that previously lowered joint welfare and was rejected can be accepted with ROO.
    - (ii) An FTA that improved joint welfare but was rejected can be accepted with ROO, but the ROO may be so distortionary that the FTA lowers joint welfare relative to the status quo.
- Paper organization (sections noted):
  - Section II: general equilibrium model with nondiscriminatory tariff initial equilibrium.
  - Section III: economics and viability of FTA without ROOs.
  - Section IV: introduce ROO and derive price and welfare outcomes.
  - Section V: reassess feasibility and welfare when FTA includes ROO, provide numerical examples and extensions.
  - Section VI: conclusion.

### II. THE MODEL
- World and goods:
  - World comprised of three countries: home country (HC), foreign country (FC) and the rest of the world (ROW).
  - Four goods: 0, 1, 2 and m. Goods 0, 1 and 2 are final; m is a pure intermediate input used in production of good 1.
  - Good 0 is the numeraire; world prices P_i^W are normalized to 1 (P_i^W = 1 for i = 0,1,2,m).
  - HC and FC are small relative to ROW. Markets are perfectly competitive.
- Tariff and price conventions:
  - Initial tariffs are nondiscriminatory; domestic price of each good exceeds its world price by per-unit tariff.
  - All tariff revenue redistributed lump-sum to consumers.
- Notation (HC variables; FC denoted with *):
  - X_i and c_i (i = 0,1,2,m): quantities supplied and demanded.
  - L_i (i = 0,1,2,m) and K_i (i = 1,2,m): quantities of labor and specific factor used in good i.
  - L: total endowment of labor.
  - P_i (i = 1,2,m): domestic price of non-numeraire good i.
- Consumption (quasi-linear preferences as in Grossman and Helpman):
  - Consumer problem: minimize sum_i P_i c_i + c_0 subject to U = c_0 + u(c_1,c_2).
  - Demand functions c_i = d_i(P_i) where d_i(.) is inverse of u_i′(.).
  - Expenditure function: E(1,P,P;U) = U + e(P).
  - Consumer surplus for non-numeraire good i: -e_i(P_i) defined via u_i(d_i(P_i)) - P_i d_i(P_i).
- Production:
  - Numeraire good produced under CRS using labor only: X_0 = L_0; competitive wage w = 1.
  - Non-numeraire production functions F_i(L_i,K_i) are CRS, increasing and concave.
  - Good 1 produced in two stages:
    - Value-added V_1 produced, then a_m units of m combined with 1 unit V_1 to produce one unit of good 1.
  - Producer optimization problems yield rents π_i(P;K) for specific factors K_i.
  - Net value-added price for good 1: P_1^v = P_1 - a_m P_m.
  - Supply X_i = π_i′(.).
- Footnote model clarifications:
  - Production and demand in ROW not modeled as they are irrelevant for analysis.
  - Production specification prevents substitutability between intermediate input and value-added to simplify ROO handling; main results robust if not perfect substitutes.

### Pattern of Trade under MFN Tariffs
- Assumed pattern of trade (Figure 1 described in text):
  - HC imports input m from FC and exports final good 1 to FC.
  - Each potential union member also imports the good it would import from its potential partner from ROW.
  - Good 2 may also be imported from ROW by both HC and FC, but is dropped from immediate analysis to focus on input-specific ROOs.
- Price notation under nondiscriminatory tariffs:
  - Domestic price of m in HC is 1 + t_m.
  - Domestic price of good 1 in FC is 1 + t_1^*.
  - With no intervention in exportable goods, price of good 1 in HC and m in FC is 1.
  - Numeraire price is 1 everywhere.
- Welfare of HC from income-expenditure equality:
  - Utility expression (equation (5)):
    - U = L + [π_1(1 - a_m(1+t_m)) + π_m(1+t_m)] + [-e_1(1)] + [t_m{a_m π_1′(.) - π_m′(.)}]
  - Interpretation:
    - L: wage income.
    - Bracketed terms: profits, consumer surplus, and tariff revenue respectively.
- Tariff endogenization setup:
  - Government payoff (HC) is G = g U + Σ_i (1+g) π_i, g > 0 (equation (6)), aligning with Grossman-Helpman lobbying framework.
  - First-order conditions from maximizing G with respect to tariffs coincide with Grossman-Helpman (1994, 1995) lobbying game results.
- Initial tariff results (restricting tariffs to be nonnegative):
  - t_m = 0, t_1 = 0 (equation (7)).
  - Intuition:
    - Export subsidies ruled out by assumption (Article XVIII of GATT), so t_1 = 0.
    - For imported intermediate input m: lobbying by owners of factor for good 1 (demanders of m) dominates because HC is a net importer of m, leading to an interior solution of an import subsidy which is ruled out, yielding t_m = 0.
- FC tariffs:
  - t_1^* > 0, t_m^* = 0 with t_1^* = (1+tg)^(-1) α_1^*/η_1^* (equation (8)), where α_1^* is ratio of domestic output of good 1 to its imports and η_1^* is absolute value of price elasticity of import demand for good 1 in FC.
  - Standard Grossman-Helpman result: MFN tariff inversely proportional to elasticity and government weight on social welfare, directly proportional to domestic production/imports ratio.
- Implication for FTA incentives:
  - Country exporting final goods and importing intermediate goods (like HC) stands to benefit from FTA because it gains access to partner’s protected markets while its own input market is tariff-free.
  - Country exporting intermediate inputs (like FC) has little incentive to endorse FTA absent other gains (ROOs can provide such gains).

### III. THE ECONOMICS AND POLITICS OF FTAS IN THE ABSENCE OF ROOS
- FTA formation assumptions:
  - When FTA is formed, countries freeze external tariffs at initial MFN level.
  - Intra-union trade is freed; no trade deflection allowed (goods imported from ROW by one partner cannot be re-exported to the other).
- Method of evaluation:
  - Acceptance or rejection of FTA based on impacts on welfare, total profits, and hence government payoff G in (6).
- Under an FTA:
  - Members remove import duty on partner but retain it on ROW.
  - Depending on demand and supply configurations, three analytically distinct possibilities for each good arise.
- Example: final good 1 (imported by FC, exported by HC)
  - Denote MFN tariffs t_1 and t_1^* with 0 ≤ t_1 ≤ t_1^*.
  - If HC’s total supply intersects FC’s import demand I*I* at point Y or above (supply curve S1S1), price in FC remains 1 + t_1^*, and HC sells all its production in FC; HC satisfies its own demand by imports from ROW.
  - This leads to pure trade diversion / enhanced protection:
    - Union’s total imports from outside decline.
    - FC loses tariff revenue MHRQ; consumers’ and producers’ surpluses in FC remain unchanged.
    - Part of the lost tariff revenue is a net increase in producers’ surplus accruing to HC (area MHJL), and part becomes additional tariff revenue raised by HC since it imports quantity LJ (area LJNQ).

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### Section V discusses the case when external tariffs are endogenously chosen in the post- FTA

### Section V discusses the case when external tariffs are endogenously chosen in the post- FTA

### Post-FTA market outcomes for the final good (three cases)
- Case 1 — Purely Trade Diverting FTA
  - HC’s supply intersects I*I* above point Y (as in S1S1). Union-wide price rises above 1+t1*, imports from ROW into FC are replaced by HC suppliers.
  - Deadweight loss in FC: trapezium JHRN (trade diversion).
  - Welfare: HC gains (profits from good 1 rise), FC loses (welfare falls). HC accepts the FTA; FC rejects it.
- Case 2 — Purely Trade Creating FTA
  - HC’s supply intersects I*I* at or below point T (height 1+t1+), as in S2S2. Union-wide price settles at 1+t1+ or less; imports into FC from ROW eliminated.
  - Lost tariff revenue in FC (area MYSQ) is partly shifted to tariff revenue gain in HC (area LTZQ) and partly to consumers’+producers’ surplus in FC (area MYTL). Overall union welfare gain = area YTZS.
  - Outcome on parties: FC’s price for good 1 drops to world price in FC; HC’s price remains at world price of 1. Based purely on sector 1, HC weakly endorses the welfare-increasing FTA; FC rejects it absent other sectoral changes.
- Case 3 — Mixed Case
  - HC supply crosses I*I* between Y and T. Price in FC is endogenous; HC producers sell their entire quantity in FC and imports in FC entirely supplied by HC.
  - Mixed case is dropped from detailed analysis due to complication with ROOs.

- Proposition 1 (summary from cases above):
  - "An FTA in the absence of a ROO that is purely trade diverting or trade creating in good 1 is necessarily rejected by FC."

### Role of the intermediate input m before ROO
- In the initial MFN equilibrium, t1 = 0 for the particular good considered, so horizontal lines at 1+t1 and 1 coincide.
- For input m: no tariff in MFN equilibrium in either HC or FC within the model; hence no scope for trade creation or diversion in m until a ROO is introduced.
- Given separability across goods and fixity of input price, profits in m are unchanged and changes in m make no contribution to changes in G until ROO is introduced.

### Rules of Origin (ROO): definition and mechanics
- ROO defined via θ, the ratio of intermediate input purchased from within the union to total input used by HC producers of good 1:
  - Equation (9): θ = (c_m^* + c_m^m + c_m^W) / (c_m + c_m^* + c_m^W) — as given in the source.
  - ROO imposes a lower bound θ_R on θ. Producers from HC receive the tariff-inclusive price in FC only if θ ≥ θ_R.
  - Price rule (10): P_1^R = (1+t_1^*) if θ ≥ θ_R; = 1 if θ < θ_R.
- If θ_R set sufficiently high, it creates a premium on within-union supply of m and raises P_m above unity; P_m then determined endogenously by regional demand and supply.

### Effects of the ROO: Positive analysis (Case 1 — Trade diverting union)
- Pre-ROO under FTA (no ROO):
  - Price received for V1 (value-added) = 1+t1* - a_m; quantity supplied OX_F; total within-union supply of m at P_m = 1 equals OM_F.
  - Define θ_1 ≡ OM_F / OM_T.
- If θ_R ≤ θ_1:
  - ROO non-binding; P_m = 1. (Equation (11): P_m^R = 1 for θ_R ≤ θ_1)
- If θ_R > θ_1:
  - Regional supply of m must rise → P_m rises above 1. Regionally supplied m becomes distinct from imported m.
  - Price determination via regional demand = regional supply:
    - Equation (12): θ a_m π_v*'(P_1^v) = π_m'(P_m) + π_m*'(P_m); θ such that θ_1 ≤ θ ≤ θ_2 (as in source).
  - Value-added price received on exports: P_1^v = 1 + t_1* - a_m {θ P_m + (1-θ)}.
  - Effective unit price of m used by HC producers: θ_R P_m + (1-θ_R).
- Upper limit θ_2 ensures ROO not so restrictive as to lower P_1^v below 1 - a_m:
  - Equation (13): P_1^v + t_1* - a_m{θ P_m + (1-θ)} = 1 - a_m.
  - Equivalent (14): θ = θ_2* = [t_1* a_m (P_m - 1)] / (...) — as in source (preserve expression form).
- Comparative statics of P_m with respect to θ_R (equation (15)):
  - dP_m/dθ_R = [mR1.... expression as in source], where ε_1 is elasticity of supply of good 1 in HC, ε_m^D absolute elasticity of demand for within-union m, ε_m^S elasticity of total supply of m.
  - At θ_R = θ_1 (P_m = 1) the RHS is unambiguously positive; but for P_m > 1 the numerator can turn negative.
- Intuition:
  - Increasing θ_R raises demand for m (scale effect) but reduces v1 P and thus output of good 1 (substitution effect). The net sign depends on elasticities.
- Proposition 2:
  - "Assuming the union is purely trade diverting in the final good, P_m may rise monotonically, have an inverted-U shape, or exhibit multiple peaks as a function of the ROO."

### Effects of the ROO: Positive analysis (Case 2 — Trade creating union)
- Without ROO, FTA leads to free-trade outcome; HC producers sold at world price 1 in both home and FC.
- Binding ROO increases export cost via higher P_m, which can only be sustained by increasing the consumer price P_1* in FC (given fixed tariff on imports from outside).
- At binding ROO, exporters in HC require P_1^v = 1 - a_m; P_1* > 1 is endogenously determined by θ_R and P_m.
- A larger θ_R (and hence larger P_m) reduces export proportion e_γ and increases P_1*.
- Key equilibrium conditions (binding ROO):
  - (15) γ_e θ_R a_m π_1'(1 - a_m) = π_m'(P_m) + π_m*'(P_m) ; for θ_R ≥ θ_1
  - (16) P_1* = 1 + a_m θ(P_m - 1)
  - (17) e'1(P_1*) - π_1'(P_1* - a_m) = γ π_m(1 - a_m)  — as in source
- Proposition 3:
  - "In the purely trade creating case, starting at θ_R = θ_1, if we increase θ_R, γ_e decreases and P_m and P_1* increase such that the value-added price received on exports, P_1^v, remains constant at 1 - a_m."
  - Note: at an initially strictly binding ROO, further increases in θ_R may be accompanied by a decrease in P_m (due to lower demand for intermediate input), analogous to the trade-diverting case.

### Welfare effects of ROO
- Direct effect: ROO diverts demand for intermediate input toward regionally produced (inefficient) source, distorting its price.
- Indirect effect: depends on whether post-FTA final-good market was trade diverting or trade creating.
  - Case 1 (initially trade diverting): ROO raises cost of exporting good 1 from HC, reduces HC→FC export supply and can reverse initial trade diversion.
  - Case 2 (initially trade creating): ROO introduces distortion in FC consumer price; no trade diversion to reverse.
- Proposition 4:
  - (a) "When the initial FTA is trade diverting in good 1 (case 1), and the ROO is increased at the weakly binding level, joint welfare of the partners improves, but the ROO is tightened further, joint welfare can eventually fall."
  - (b) "When the initial FTA is trade creating in good 1 (case 2), a tightening of a binding ROO weakly worsens the joint welfare of the union."
- Intuition and graphical interpretation (Figures 3a, 3b):
  - In case 1, initial tightening of ROO reduces inefficient production in HC (area abcd gain) but raises distortion cost in regional m market (area efg). Small ROO increases can yield net joint-welfare gains; excessive tightening can cause net losses.
  - In case 2, introduction of a just-binding ROO has second-order small welfare effect at θ_R = θ_1; further tightening reduces welfare due to increasing distortions transmitted through P_m and P_1*.

### Political viability: ROOs, FTA viability, and welfare (link to lobbying/returns)
- Key mechanism: ROO increases regional price of m, raising returns to owners of K_m* and K_m; this can alter political support (Grossman-Helpman style lobbying).
- Proposition 5:
  - (a) "An initially infeasible FTA that reduces joint welfare of the union (case 1) can become feasible after the inclusion of a ROO."
  - (b) "An initially infeasible FTA that improves the joint welfare of the union (case 2) can become feasible at the inclusion of the ROO, although the ROO supporting it can be so distortionary that joint welfare of the union could actually fall with the FTA."
- Intuition:
  - Under case 1: HC continues to support FTA; ROO raises profits in sector m which get a larger weight in G* than tariff revenue loss, potentially reversing FC’s rejection into acceptance.
  - Under case 2: ROO benefits owners of m K and can convert FC’s vote to positive (for sufficiently high g*), but ROO may be so distortionary that union joint welfare falls despite political feasibility.
- Numerical examples are used in the source to substantiate Proposition 5; the model setup for numerical analysis begins with linear demand and supply functions:
  - Demand in HC: D_1^1 = D - c P_1, with c > 0.
  - Supply: X_1^v = α_1 P_1^v and M_m = α_m P_m with α_k > 0 for k = 1, m.
  - Governments assign identical weights g to social welfare.
  - (The source continues derivations for MFN tariffs and subsequent comparisons.)

*Source: _wp03229 - Section V discusses the case when external tariffs are endogenously chosen in the post- FTA*

### Section II) are given by:

### _wp03229 - Section II) are given by:

### Case 1 — Purely Trade Diverting Case
- Defining condition (total within-union supply < total demand of the FC) implied by equation:
  - (19) ****1111m D - (1+t  )c > (α+α) (1+t  -a   ) .
- From Proposition 1(a), FC rejects this welfare reducing FTA in the absence of the ROO.
- Endogenous price of regional intermediate input m for this case:
  - (20) 22 * mR1 mm R m 22 mmR aθ(1+t  -a   )+aθ P=, β+aθ where * mm m 1 α+α β= α .
- For the above price of regional m, change in FC’s value of G between the FTA with ROO and MFN tariffs:
  - (21) * ****2 m ROOMFN1 11mm Rmm Tariff revenue loss from good 1 Increase in rents of m α G-G=- g{tα(1 + t  -a   - aθ(P  - 1)) + (1+g){(P  ) - 1}. 2 1444442444443 1442443
- Numerical simulation setup and results (parameters satisfy initial MFN pattern and equation (19); slope parameter *1 α varied so t1* ranges from 0.2 to 0.4; g = 1):
  - Two particular equilibrium MFN tariffs considered: t1* = 0.24 and t1* = 0.32.
  - Upper-left panel: Pm moves with ROO and achieves a maximum at a ROO between 0.90 and 0.95 for both t1* = 0.24 and t1* = 0.32.
  - Lower-left panel: value-added export price Pv*1 falls monotonically with increases in the ROO.
  - Lower-right panel: G*ROO - G*MFN increases with ROO.
  - FTA weakly endorsed by FC when G*ROO - G*MFN = 0:
    - Rθ = 0.92 when t1* = 0.24
    - Rθ = 0.96 when t1* = 0.32
  - At these ROOs, union’s joint welfare change (upper-right panel) is negative; the FTA continues to be welfare reducing after inclusion of the ROO.
- Simulation parameter snapshot shown in figure caption:
  - CASE 1: am = 0.8, g = 1
  - **1 0.05, 0.1, 1.1, 1, 0.2 mm Dcααα=====; t1* = 0.32 , --- t1* = 0.24

### Case 2 — Purely Trade Creating Case
- Defining condition (total within-union supply = total demand of the FC) implied by equation:
  - (22) **e 1m1m D- c = α(1- a   ) + γα(1- a   ) ,
  - where γe is as defined in Section IV.
- Properties without ROO:
  - This FTA is welfare improving for FC and has no effect on the welfare of HC.
  - Being purely trade creating without ROO, the FTA necessarily improves joint welfare.
  - In HC, value of G unchanged so HC weakly accepts the FTA.
  - In FC, reduction in price of good 1 can lower G* by lowering return on *1 K.
- With a binding ROO:
  - A binding ROO increases input price, raising the price of good 1 faced by consumers in FC.
  - Parameter values same as case 1 except 1 α assigned higher value to satisfy (22).
  - Verified: G* under FTA without ROO is less than under MFN tariffs for assumed parameters.
- Equations determining equilibrium with ROO:
  - (23) e 1 mRmm * mm α P = θγa(1- a) α+α ,
  - (24) * 1mRm P = 1 + aθ(P  - 1) ,
  - (25) ** ** e 111m 1m (D  - cP  ) - α(P  - a   ) γ = α(1- a   ) .
- Numerical simulation results (Figure 4(b)):
  - G*ROO - G*MFN is strictly positive for all ROOs ⇒ FTA unambiguously endorsed by FC.
  - Price of good 1 in FC, P1*, increases monotonically with stringency of ROO.
  - If the ROO is such that R θ≤ 0.35, then joint welfare improves with the FTA.
  - However, for R θ0.35>, the ROO is so distortionary that joint welfare of the union actually falls with the FTA.
- Simulation parameter snapshot shown in figure caption:
  - CASE 2, am = 0.8, g =1
  - **1 0.05, 0.1, 3.5, 1, 0.2 mm Dcααα=====, t1* = 0.24 , --- t1* = 0.32

### C. Extensions (qualitative implications; no new equations solved)
- Extension 1 — Both HC and FC import good 2
  - If t2 < t2* and ROW continues to export goods 1 and 2 to the union, then under FTA without ROO HC exports all good 2 to FC and HC consumption of good 2 is satisfied by imports; HC benefits and FC is worse off ⇒ FTA infeasible without ROO.
  - With ROO on input m, FC may accept if the tariff revenue loss from goods 1 and 2 is more than compensated by gain from increased producers’ surplus in good m; ROO can increase FTA viability.
  - If t2* < t2 and both governments marginally accepted the FTA without ROO, a binding ROO reduces exporters’ payoff in HC (reducing HC→FC exports) and alters the distribution of tariff revenue and producers’ surplus; the FTA can become infeasible after inclusion of ROO if HC’s losses exceed gains.
- Extension 2 — Endogenous determination of external tariffs post-FTA
  - If union members set external tariffs endogenously after FTA and ROW continues to export good 1 to FC, the “optimal” external tariff on good 1 for FC would be lower than prior to pre-FTA equilibrium.
  - FTA lowers price of good 1 in FC: increases consumer surplus, lowers producer surplus; tariff revenue may increase if import volume rises sufficiently.
  - With a binding ROO, export supply from HC decreases, increasing FC’s imports and tariff revenue from ROW; an FTA rejected before might be accepted after ROO inclusion.
  - Other outcomes possible: a previously feasible FTA could become infeasible with ROO (e.g., if shortfall in HC producer’s surplus in good 1 exceeds producer’s surplus gain in input m).
- Extension 3 — Exogenously given positive tariffs on final good and intermediate input
  - Suppose MFN tariffs t1 and tm with tm > 0. In absence of ROOs, FTA feasibility depends on offsetting of tariff revenue losses by producers’ surplus gains in input m and good 1.
  - If FTA without ROO is weakly feasible, introducing a (non-binding) ROO that tightens shifts HC’s purchases of m from ROW to FC and increases HC’s tariff revenue loss on m ⇒ HC may oppose the FTA.
  - If ROO is binding (Pm > 1+ tm), even though HC loses tariff revenue on m, it may gain greater producers’ surplus in input m; HC may continue to support the FTA if gains outweigh losses.

### VI. Conclusion — Main results and policy implications
- First: Contrary to general policy literature impression, a ROO may improve or worsen the joint welfare of the union.
- Second: The price distortion created by the ROO affects the political economy of FTA endorsement; ROOs increase rents for the intermediate-input–owning interest group and can switch a member’s vote from opposed to supportive.
- Third (policy-relevant): Two notable results on social desirability of FTAs that become feasible after ROO inclusion:
  - An initially infeasible but welfare-reducing FTA can become feasible after inclusion of the ROO.
  - An infeasible but joint welfare improving FTA can become feasible upon ROO inclusion.
  - Caveat: ROO can be so distortionary that after inclusion the FTA becomes joint welfare diminishing.
- Empirical/political observations:
  - Product-specific ROOs can be driven by industry lobbying (examples cited for auto parts and yarn-forward textile rule under NAFTA).
  - ROOs that protect import-competing industries and intermediate-exporting industries can improve chances of FTA endorsement for input exporters and final-good importers, but stringent ROOs may be undesirable.
- Suggested extension left for future work: endogenize ROO choice subject to industry-specific lobbying (analogous to exclusion of sensitive sectors in Grossman and Helpman (1995)).

*Italic: Source content from _wp03229 - Section II) are given by: (PDF chapter/section).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2003/_wp03229.pdf_