## wpiea2020257-print-pdf

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---

### Overview and central result
- Paper analyzes strategic import and export bans on a “digital” input characterized by a natural monopoly and examines welfare, security, and technological diffusion implications of such trade restrictions.
- Novel result: it may be optimal for an exporter (the technological leader) to impose an export ban to limit international technology diffusion and delay a challenger’s eventual overtaking.

### Model structure (concise)
- Two countries i ∈ {a, b} with constant populations (labor supplies) L_i; time is infinite and discrete.
- Final good:
  - Utility U_{i,t} = Σ_{s=t}^∞ ln(c_{i,s}) β^{(s−t)} with β ∈ (0,1).
  - Production: y_{i,t} = l_{i,t}^{1−α} (B + n_{i,t}^α), α ∈ (0,1), B>0.
  - No savings; consumption equals income C_{i,t}.
- Digital good:
  - Natural monopoly with fixed cost K (incurred every period) and marginal cost 1/A_{i,t}.
  - At most one firm supplies a market (domestic monopolist or global monopolist).
  - Cyberattack loss: fraction ρ ∈ [0,1] of foreign-provided digital good lost each period; each unit supplied to a foreign country requires producing 1/(1−ρ) units.
  - Subsidy to fixed cost τ_{i,t} ≥ 0 paid conditional on firm being active; financed lump-sum by consumers T_{t,i}=τ_{i,t} if domestic producer active.
- Technology and diffusion:
  - Leader at frontier A_F; frontier grows exogenously at rate g_i ≥ 1.
  - Laggard diffusion: A_{i,t} = A_{i,t−1} * g_i + σ_i * (A_{F,t−1} − A_{i,t−1}) * I(n_{−i,t}^i + n_{i,t}^{−i} > 0), σ_i ≥ 0.
- Government policy tools: unilateral import bans b_{i,t}^i = 1, unilateral export bans b_{i,t}^{−i} = 1, and subsidies τ_{i,t}; government maximizes domestic lifetime utility U_{i,t}.

### Static equilibrium: firms, prices, and market structure
- Factor prices:
  - w_{i,t} = (1−α) l_{i,t}^{−α} (B + n_{i,t}^α)
  - p_{n,t}^i = α l_{i,t}^{1−α} n_{i,t}^{α−1}
- Digital-good inverse demand: n(p,l) = (α/p)^{1/(1−α)} l.
- Digital producer supply (if active) to market j:
  - n_{i,t}^j = [ (1 − ρ * I(i ≠ j)) α^2 / A_{i,t} ]^{1/(1−α)} l_{j,t}.
- Entry and profitability:
  - Global producer break-even price p̂_{n,t}^{−i} satisfies: π_{i,t}^i + (p̂_{n,t}^{−i} − 1/((1−ρ) A_{i,t})) n(p̂_{n,t}^{−i}, l_{−i,t}) − K + τ_{i,t} = 0.
  - Minimum credible global price p̃_{n,t}^{−i} = max{ 1/((1−ρ) A_{i,t}), p̂_{n,t}^{−i} }.
  - Domestic entry deterred when: (p̃_{n,t}^{−i} − 1/A_{−i,t}) n(p̃_{n,t}^{−i}, l_{−i,t}) − K + τ_{−i,t} ≤ 0.  (Equation 3)
- Market clearing:
  - n_{i,t} = Σ_{j∈{a,b}} n_{j,t}^i; l_{i,t} = L_i.

### Key theoretical findings
- Import bans:
  - Can be optimal to repatriate monopoly rents even if domestic production is less efficient.
  - Create strategic interactions and potential retaliation; may yield inefficient symmetric autarky outcomes.
- Export bans:
  - A technological leader may optimally ban exports to slow diffusion and delay a challenger becoming global producer.
  - Do not induce strategic interaction in the two-country model because only the leader would impose them; harder to deter via reciprocity.
- Cybersecurity (ρ>0) and monopoly rents jointly create incentives for both import and export bans.
- Choice between export vs import ban depends on expected productivity growth of the challenger:
  - If challenger expected to surpass leader, leader may prefer export bans to delay leapfrogging.
  - If frontier growth rates are the same, import bans may suffice.
- Trade bans promote technological and economic decoupling, slow diffusion, and harm global welfare.

### Policy implications and international cooperation dimensions
- Technological diffusion is a global public good; sharing fosters convergence and global growth.
- Minimum objective: international cooperation to reduce cyber security vulnerabilities.
- Even with improved cybersecurity, sizeable monopoly rents remain; incentives to ban exports or imports persist.
- Additional cooperation avenues:
  - Strengthen protection of intellectual property.
  - Facilitate broad cross-border ownership of suppliers to align incentives.
- Political economy:
  - Concentrated monopoly rents in digital sector help explain trade conflicts centered on digital/technology sectors.
  - Trade restrictions in one monopolistic sector can cascade to broader decoupling of supply chains.
- Suggested international instruments: cross-ownership, IP protection, cybersecurity standards, and coordinated regulation of large firms.

### Dynamic equilibrium and numerical solution (Appendix I)
- Dynamic equilibrium converges to a balanced growth path only as time tends to infinity given B>0 and K>0.
- Intertemporal optimization solved numerically; planner weighs trade benefits (lower fixed costs, faster diffusion) versus costs (trade frictions, cyberattacks).
- First-best (global planner) eliminates monopoly markup; planner more likely to sustain trade than decentralized equilibrium.

### Import bans — incentives, channels, and static equilibria (Appendix I & main text)
- Five possible static Nash equilibrium types (parameters and technology dependent):
  1. Defensive ban — country b bans imports; both countries produce domestically.
  2. Offensive ban — country b bans imports to become sole global producer.
  3. Coordination game — either global producer feasible; two equilibria where either country prevails.
  4. Full trade war — both impose bans, preferring autarky.
  5. Free trade — b is not feasible as global producer and importing preferable.
- Import bans have a forward-looking component by stopping technology diffusion, but decision is partly static.

### Export bans — leader incentives and intertemporal trade-offs (Appendix I)
- Banning exports reduces current consumption but can increase medium-run utility by preventing/delaying rival entry as global producer.
- Net impact depends on discount factor β and diffusion rate σ.
- Export bans are unilateral (leader-only) and unaffected by rival trade policies; tit-for-tat strategies ineffective.
- In two-country model, export ban optimal only if import ban not possible; result may change with larger world.

### Subsidies to fixed costs — effects and limitations
- Fixed-cost subsidy lowers domestic producer’s break-even price p̂_{n,t}^{−i}, helping deter foreign entry.
- For a given trade pattern, subsidy amount irrelevant for production quantities because financed lump-sum.
- Fixed-cost subsidy can mimic import ban effects in some cases but cannot affect intensive margin; limited against lower marginal cost foreign entrants.

### Production subsidies and intensive margin (Appendix III)
- Production subsidies can facilitate foreign market capture but may cause excessive production and transfer rents to foreign consumers.
- Domestic production subsidy that induces marginal-cost pricing: τ_{i,t}^* = (1−α)/α, replicating first best in static domestic market.
- Fixed-cost subsidy is least costly way to change trade patterns compared to deviating from τ_{i,t}^*.

### Rest of the world (third economy c) and implications
- Country c cannot produce digital good (A_{c,t}=0); including RoW increases leader’s incentive to ban exports because lost current market share is smaller while future protection is larger.
- If laggard can surpass leader (g_a < g_b), export ban can be optimal even when import bans available.
- Entry deterrence conditions extend to entrants targeting domestic market and RoW; incumbent may set domestic price = marginal cost 1/(1−ρ) A_{i,t} when deterring RoW entry.

### International financial integration (cross-ownership)
- Consumer budget with cross-ownership φ_i ≤ 1/2: C_{i,t} = w_{i,t} l_{i,t} + π_{i,t}^f + (1−φ_{−i}) Π_{i,t} + φ_i Π_{−i,t}.
- Cross-ownership compresses utility gaps across trade patterns and reduces states where trade bans are optimal.
- Broad sharing of gains mitigates trade tensions; cross-shareholdings of 15 percent substantially align utilities; full alignment at 50 percent.

### Illustrative calibration scenarios and exact parameter values
- Calibration parameters (values preserved exactly):
  - L_i: US 1, EU 1.1, China 1.5, RoW 4
  - A_{i,0}: US 1, EU 0.9, China 0.2, RoW -
  - σ_i: US 0.05, EU 0.02, China 0.05, RoW -
  - B: 1
  - α: 0.3
  - K: 0.8
  - ρ: 0.02
  - β: 0.99
  - g: 1.067
- Notes:
  - g implies GDP per capita growth of 2 percent (α*(g−1)) as time tends to infinity.
  - ρ=0.02 implies a cost of cybercrime at 0.4 percent of US GDP.
  - σ_US only applies in case where China assumed to have higher frontier growth rate.

### Scenario: US vs EU (calibration)
- US small tech advantage; EU larger population; EU diffusion from US small.
- Under free trade: US becomes global supplier; EU never becomes global producer.
- Policy findings:
  - EU may optimally ban US imports after domestic producer profitable; optimal timing is a few periods after profitability.
  - US would not optimally ban exports to EU.
  - Reciprocal bans lower US flow utility relative to free trade.

### Scenario: US vs China (calibration and quantitative results)
- US begins with significant technology advantage; China can adopt US technology when connected.
- Under free trade: US global supplier initially; diffusion to China can make China more competitive later and may cause discontinuous US utility fall when provision shifts.
- US may optimally delay China’s global provision by banning exports to China.
- Table 3 (percentage deviation in NPV of per capita utility relative to free trade) — values preserved exactly:
  - Intrinsic growth same for US & China:
    - Export ban: US utility 0.6, China utility -6.1, World utility -1.3
    - Import ban: US utility 3.2, China utility -2.8, World utility -0.1
  - +0.5% for China:
    - Export ban: US utility 4.5, China utility -16.0, World utility -4.4
    - Import ban: US utility 3.8, China utility -3.3, World utility -0.3
- Table 4 (comparison with subsidy) — values preserved exactly:
  - Export ban: US utility 0.6, China utility -6.1, World utility -1.3
  - Subsidy to fixed cost: US utility 3.2, China utility -2.8, World utility -0.1
- Subsidy timing optimized by US in simulations (example: subsidy starting in period 150 in one figure).

### Sensitivity: financial integration, cybersecurity, and discounting (Table 5 summary)
- Percentage deviation of NPV per capita utility relative to free trade (Table 5 entries preserved exactly):
  - Baseline: - 0.58
  - Financial integration φ=0.2: -0.28
  - Lower tech theft σ=0.04: -2.00
  - Less cyberattacks ρ=0.005: 0.24
  - More intertemp. discount β=0.98: -1.79
- Lowering cyberattack rate reduces incentives for bans but does not eliminate them; heavier discounting of future (lower β) makes export bans less attractive.

### Global welfare, mitigants, and institutional proposals
- Export bans harm global welfare by blocking access or creating duplicated fixed costs.
- Import bans can also be harmful, especially if reciprocal.
- Mitigants:
  - Financial integration and cross-ownership to share rents.
  - Rules preventing technological theft and cyberattacks.
  - Cross-border regulatory coordination, IP protection, cybersecurity standards, and open capital accounts.
  - Coordinated regulation of large domestic firms.
- Longer-term remedy: reduce natural monopoly properties (reduce fixed cost relative to economy size), though network externalities may persist.
- Institutional proposals: international cooperation on cybersecurity and standards, potentially via strengthened roles for global institutions.

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020257-print-pdf.pdf*

### Chapter 11), the novel result here is that it may also be optimal for an exporter to do so.

### wpiea2020257-print-pdf - Chapter 11), the novel result here is that it may also be optimal for an exporter to do so.

### Overview and central result
- The paper analyzes strategic import and export bans on a “digital” input characterized by a natural monopoly and the welfare, security, and technological diffusion implications of such trade restrictions.
- Novel result: it may be optimal for an exporter (the technological leader) to impose an export ban to limit international technology diffusion and delay a challenger’s eventual overtaking.

### Model structure (concise)
- Two countries i ∈ {a, b} with constant populations (labor supplies) L_i; time is infinite and discrete.
- Final good:
  - Produced in perfect competition; consumption c_{i,s}; utility U_{i,t} = Σ_{s=t}^∞ ln(c_{i,s}) β^{(s−t)} with β ∈ (0,1).
  - Production function: y_{i,t} = l_{i,t}^{1−α} (B + n_{i,t}^α), α ∈ (0,1), B>0.
  - No savings; consumption equals income C_{i,t}.
- Digital good:
  - Natural monopoly with fixed cost K (incurred every period) and marginal cost 1/A_{i,t}.
  - Producers choose prices after entry; if two producers sell to same market they compete on prices; at most one firm supplies a market (domestic monopolist or global monopolist).
  - A fraction ρ ∈ [0,1] of foreign-provided digital good is lost each period in a cyberattack; each unit supplied to a foreign country requires producing 1/(1−ρ) units.
  - Subsidy to fixed cost τ_{i,t} ≥ 0 paid conditional on firm being active; subsidies financed lump-sum by consumers T_{t,i}=τ_{i,t} if domestic producer active.
- Technology and diffusion:
  - Leader at frontier A_F; frontier grows exogenously at rate g_i ≥ 1.
  - Laggard bridges a fraction of the distance to the frontier when connected (trading digital good): A_{i,t} = A_{i,t−1} * g_i + σ_i * (A_{F,t−1} − A_{i,t−1}) * I(n_{−i,t}^i + n_{i,t}^{−i} > 0), where σ_i ≥ 0.
  - σ captures speed of technology diffusion; higher σ may proxy theft/transfer of IP.
- Government policy tools: unilateral import bans b_{i,t}^i = 1, unilateral export bans b_{i,t}^{−i} = 1, and subsidies τ_{i,t}; government maximizes domestic lifetime utility U_{i,t}.

### Static equilibrium: firms, prices, and market structure
- Factor prices (marginal products):
  - w_{i,t} = (1−α) l_{i,t}^{−α} (B + n_{i,t}^α)
  - p_{n,t}^i = α l_{i,t}^{1−α} n_{i,t}^{α−1}
- Digital-good demand inverse form: n(p,l) = (α/p)^{1/(1−α)} l.
- Final-good producer profits: π_{i,t}^f = α l_{i,t}^{1−α} B.
- Digital producer supply (if active) to market j:
  - n_{i,t}^j = [ (1 − ρ * I(i ≠ j)) α^2 / A_{i,t} ]^{1/(1−α)} l_{j,t}.
- Entry and profitability conditions:
  - A producer produces only if total net profits Π_{i,t} ≥ 0 and no foreign producer can profitably enter the markets it serves.
  - Global producer’s break-even price p̂_{n,t}^{−i} satisfies π_{i,t}^i + (p̂_{n,t}^{−i} − 1/((1−ρ) A_{i,t})) n(p̂_{n,t}^{−i}, l_{−i,t}) − K + τ_{i,t} = 0.
  - Minimum credible global price p̃_{n,t}^{−i} = max{ 1/((1−ρ) A_{i,t}), p̂_{n,t}^{−i} }.
  - Domestic producer is deterred from entry when the potential domestic producer −i makes negative profits facing the global producer’s minimum price:
    (p̃_{n,t}^{−i} − 1/A_{−i,t}) n(p̃_{n,t}^{−i}, l_{−i,t}) − K + τ_{−i,t} ≤ 0.  (Equation 3)
- Market clearing:
  - Digital goods: n_{i,t} = Σ_{j∈{a,b}} n_{j,t}^i.
  - Labor: l_{i,t} = L_i.
  - Final goods: global final production minus marginal and fixed costs must equal global consumption; equations solvable analytically except for (2) which needs numerical solution.

### Key theoretical findings
- Import bans can be optimal for a country to capture monopoly rents by repatriating rents to domestic shareholders even if domestic production is less efficient; import bans create strategic interactions (retaliation potential).
- Export bans can be optimal for a technological leader to slow diffusion and delay a challenger from becoming the global producer; export bans do not induce strategic interaction in the two-country model because only the leader would impose them.
- Cybersecurity vulnerability (ρ>0) and monopoly rents create incentives for both import and export bans.
- The expected productivity growth rate in the digital input determines whether the leader prefers an export ban or an import ban:
  - If the challenger is expected to eventually surpass the leader, the leader may impose export bans to delay leapfrogging.
  - If frontier growth rates are the same, import bans may suffice because the leader can limit scale economies needed by the challenger.
- Import bans lead to strategic interaction: best responses depend on the rival’s policy; banning imports could provoke symmetric retaliation, possibly yielding inefficient outcomes with domestic producers in each country.
- Export bans do not lead to strategic interaction and are therefore harder to deter through retaliation, even in repeated games.
- Trade bans promote technological and economic decoupling, slow technological diffusion, and are deleterious for global welfare.

### Policy implications and international cooperation dimensions
- Technological diffusion is a global public good (Romer 1986, 1990); sharing ideas and technology fosters convergence and global growth.
- Minimum policy objective: international cooperation to reduce cyber security vulnerabilities.
- Even with improved cyber security, sizeable monopoly rents remain; incentives to ban exports or imports persist.
- Two additional international-cooperation avenues:
  - Strengthening protection of intellectual property.
  - Facilitating broad cross-border ownership of suppliers to align incentives.
- Political economy considerations:
  - Monopoly rents concentrated in the digital sector (relative to large tradeable sectors like car manufacturing) help explain recent trade conflicts centered on digital/technology sectors.
  - The monopolistic sector need not be an input to all sectors for main results to hold; if at least one sector has suppliers with significant rents, trade restrictions there can trigger broader trade partnership risks.
  - Conflict in a monopolistic digital sector could cascade to other sectors, causing cascading decoupling of supply chains.
  - Multi-sector extensions could feature different leaders across sectors (e.g., China in 5G).
  - Rents of digital suppliers could reflect market power and also political and military benefits of global dominance.

### Strategic interaction and dynamic considerations
- Import bans generate a game-theoretic interaction: best responses depend on rival actions; repeated-game credible threats could potentially sustain free trade policies.
- Export bans are a privilege of the technological leader and do not create symmetric strategic interaction, making them more persistent absent international agreements.
- Subsidies (τ) can be used to support domestic producers; appendix analyzes production-proportional subsidies as alternative instruments.
- Cybersecurity can be modeled both as direct losses in foreign-supplied inputs (ρ>0) and as a higher diffusion parameter σ reflecting IP theft; policy must address both dimensions.

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020257-print-pdf.pdf*

### Appendix I characterizes the first best equilibrium from a global perspective.

### Appendix I characterizes the first best equilibrium from a global perspective

### Dynamic equilibrium and numerical solution
- The dynamic equilibrium only converges to a balanced growth path when time tends to infinity, given the presence of 퐵퐵>0 and 퐾퐾>0.
- Intertemporal optimization must be solved numerically.
- The appendix provides a characterization of the main forces driving optimal policy choices.

### Import bans — incentives, channels, and static equilibria
- Rationale for import bans:
  - A country may ban imports of the digital good to repatriate monopoly rents even if domestic production would be less efficient than perfect competition.
  - Sourcing the digital good from abroad exposes the country to cyberattacks 휌휌>0, which act like a trade friction not fully absorbed in the foreign monopolist’s price and increase the relative cost of imports.
- Forward-looking component:
  - Import bans stop technology diffusion and may affect future consumption paths, including for the technological leader.
  - Apart from the technology-diffusion channel, the import-ban decision is static.
- Static game between two countries (a and b):
  - Payoffs assume, without loss of generality, that country 푎푎 is the global producer under free trade; payoffs use uppercase letters for domestic production (A, B) and lowercase for markets supplied by foreign producers (a, b); A+b denotes supplying both domestic and foreign markets.
  - Five possible types of static Nash equilibria (depend on parameters and technology stocks):
    1. Defensive ban — country 푏푏 bans imports to avoid paying monopoly rents; both countries produce domestically.
    2. Offensive ban — country 푏푏 bans imports to become sole global producer.
    3. Coordination game — either global producer is feasible; two equilibria exist where either country prevails.
    4. Full trade war — both countries impose bans, preferring autarky to importing.
    5. Free trade — country 푏푏 is not feasible as a global producer and importing is preferable to not using digital goods.
  - Coordination game caveat:
    - The coordination case (type 3) could be prevented with tit-for-tat strategies mirroring import bans, though making good on such threats incurs a utility cost; if credible, country 푎푎 would be the global producer in equilibrium.
  - If there is no global producer under free trade, import bans are irrelevant.

### Export bans — leader incentives and intertemporal trade-offs
- Novel result: banning exports may be optimal for a technological leader once technology diffusion is considered.
- Mechanism:
  - Exporting to a technologically inferior country increases that country’s ability to become the global producer.
  - Technological growth in country −푖푖 always reduces import prices and benefits country 푖푖, but when country −푖푖 can switch to production, country 푖푖 may lose future monopoly rents and face increased security vulnerabilities (exposure to 휌휌>0).
- Trade-offs and timing:
  - Banning exports reduces current consumption (export profits vanish) but can increase consumption in the medium run by preventing or delaying the rival’s entry as global producer.
  - In the long run, once the trade pattern stabilizes, diffusion is never detrimental to any country.
  - The net impact of an export ban on utility depends on multiple factors, including the intertemporal discount rate 훽훽 and the rate of technology diffusion 휎휎.
- Strategic implications:
  - The export-ban decision is unilateral and does not depend on the other country’s trade policies because only a technological leader would ban exports and banning exports is inconsequential if the other country bans imports.
  - Unlike import bans, export bans do not create strategic interaction (in the game-theoretic sense), making tit-for-tat strategies ineffective against unilateral export bans.
  - Thus, export bans are harder to defuse using trade-policy reciprocity and may require broader policy instruments (e.g., ownership of foreign producers, reducing cybersecurity risks or costs).
- Two-country specificity:
  - In a two-country set-up, banning exports is only optimal if banning imports is not possible; otherwise the leader prefers to keep exporting until the rival becomes competitive and then ban imports.
  - This conclusion may change when the rest of the world beyond countries 푎푎 and 푏푏 is considered.

### Subsidies to fixed costs — effects and limitations
- Rationale and effect:
  - A subsidy to the fixed cost can help the domestic producer become active or become the global producer by lowering the domestic producer’s break-even price 푝푝̂
푛푛,푡푡
−푖푖, enabling a monopolist to threaten lower prices in a potential price war.
  - For a given international trade pattern, the subsidy amount is irrelevant for production quantities because it is financed with lump-sum taxes.
- Comparisons with import bans:
  - A fixed-cost subsidy can have similar implications to an import ban in certain cases but is a more limited tool.
  - A subsidy may fail to deter entry by a foreign producer with lower marginal costs because it does not affect the intensive margin.

*Source: Appendix I, wpiea2020257-print-pdf*

### Appendix III describes the implications of production subsidies, which do affect the

### wpiea2020257-print-pdf - Appendix III describes the implications of production subsidies, which do affect the

### Production subsidies and intensive margin
- Subsidizing exports can facilitate the capture of foreign markets, but can lead to excessive production from the point of view of the exporter country, which would be transferring part of its rents to foreign consumers.
- Production subsidies affect the intensive margin but can lead to other inefficiencies.

### Rest of the world (third economy c)
- Country c cannot produce the digital good (A_{c,t}=0) but is otherwise symmetric to countries a and b.
- Modeling the rest of the world:
  - Increases incentives for the leader to ban exports to the challenger because the cost in lost current market share is smaller and the benefit in protecting future market share is higher.
  - If the growth rate at the frontier is not higher for the laggard (g_a ≥ g_b), the technological leader prefers an import ban to an export ban, as in the two-country case.
  - If the laggard can eventually surpass the leader (g_a < g_b), an export ban can be optimal even when import bans are available, because the export ban can delay technological leapfrogging earlier by shutting off technology flows to the challenger.

### International financial integration (cross-ownership)
- Assumption: in period t=0 country i’s representative consumer owns a claim to a fraction φ_i ≤ 1/2 of the profits from the supplier in country −i, and vice versa.
- Consumer budget constraint for country i becomes:
  - C_{i,t} = w_{i,t} l_{i,t} + π_{i,t}^f + (1−φ_{−i}) Π_{i,t} + φ_i Π_{−i,t}
- Implications:
  - Ownership of the foreign monopoly (φ_i >0 and φ_{−i} >0) compresses the consumption (and utility) gap between different trade patterns associated with varying relative profits at home Π_{i,t} and abroad Π_{−i,t}.
  - Financial integration reduces the state space where it is optimal to ban trade; broad sharing of gains from technological progress can mitigate trade tensions.

### Illustrative calibration scenarios (US, EU, China, RoW)
- Calibration table parameters (values preserved exactly):
  - Market size (= population) L_i: US 1, EU 1.1, China 1.5, RoW 4
  - Initial technology A_{i,0}: US 1, EU 0.9, China 0.2, RoW -
  - Technological diffusion rate σ_i: US 0.05, EU 0.02, China 0.05, RoW -
  - No-digital technology B: 1
  - Digital good share α: 0.3
  - Fixed cost K: 0.8
  - Cyberattack rate ρ: 0.02
  - Intertemporal discount factor β: 0.99
  - Frontier growth rate g: 1.067
- Notes from calibration:
  - The value of g implies GDP per capita growth of 2 percent (α*(g−1)) as time tends to infinity.
  - ρ=0.02 implies a cost of cybercrime at 0.4 percent of US GDP.
  - The technological diffusion rate to the US σ_US only applies to the case where China is assumed to have a higher frontier growth rate.

### Scenario: US vs EU
- Setup:
  - US starts with a small technological advantage; EU diffusion from US is small.
  - EU population slightly larger.
- Dynamics under free trade:
  - Initially neither country pays fixed cost of the digital good; eventually US supplies globally; later both countries become domestic producers as fixed costs shrink relative to output.
  - EU never becomes global producer or challenger.
- Policy findings:
  - EU may optimally ban US imports after a domestic producer becomes profitable to stop paying monopoly rents to the US.
  - Optimal EU ban timing is a few periods after domestic profitability, since early benefits from technology inflows dominate.
  - US would not optimally ban exports to the EU (EU cannot threaten global producer status).
  - Reciprocal EU and US bans lower US flow utility relative to free trade.

### Scenario: US vs China
- Setup:
  - US begins with significant technology advantage but smaller population; China adopts US technology when connected to global digital goods.
- Dynamics under free trade:
  - US becomes global supplier; technological diffusion to China can make China a more competitive global provider later, even if China never reaches US productivity, because supplying the largest market domestically can minimize total costs given trade friction ρ.
  - When provision shifts from US to China, US suffers a discontinuous fall in flow utility due to loss of monopoly rents and exposure to cyberattacks (ρ>0).
- Policy trade-offs:
  - It may be optimal for the US to delay China becoming global supplier by banning exports to China, renouncing earlier monopoly rents to postpone leapfrogging.
  - Export bans reduce global welfare because China either loses access to the digital input or fixed cost is incurred twice if China produces domestically.

### Role of intrinsic growth rates and policy comparisons
- If US and China have the same intrinsic growth rate:
  - Appropriately timed US import ban could be better for US than export ban because China never fully catches up and US can deter Chinese entry in third markets.
- If China’s intrinsic growth exceeds US by 0.5 percentage points:
  - Export ban becomes better for the US than an import ban because it keeps China out of the rest of the world market for more periods.
- Table 3 results (percentage deviation in NPV of per capita utility relative to free trade) — values preserved exactly:
  - Intrinsic growth same for US & China:
    - Export ban: US utility 0.6, China utility -6.1, World utility -1.3
    - Import ban: US utility 3.2, China utility -2.8, World utility -0.1
  - +0.5% for China:
    - Export ban: US utility 4.5, China utility -16.0, World utility -4.4
    - Import ban: US utility 3.8, China utility -3.3, World utility -0.3
- Note: assumes China does not impose trade restrictions; US optimizes timing of bans; higher intrinsic growth case assumes g_c = g_u + 0.005.

### Subsidies vs bans
- A subsidy to the fixed cost of the US producer has similar implications as an import ban and can yield higher discounted utility than an export ban in some calibrations.
- Subsidy vulnerability: foreign monopolists could respond with their own subsidies, undoing gains.
- Table 4 (percentage deviation in NPV of per capita utility relative to free trade):
  - Export ban: US utility 0.6, China utility -6.1, World utility -1.3
  - Subsidy to fixed cost: US utility 3.2, China utility -2.8, World utility -0.1
- Timing of subsidies is optimized by the US in simulations (example: subsidy starting in period 150 in one figure).

### Financial integration, cyberattacks, and discounting impacts
- Cross-ownership alignment:
  - Cross-shareholdings of 15 percent substantially align utilities and make export bans undesirable; full alignment at 50 percent.
- Changing parameters and impact on export ban (Table 5 — percentage deviation of NPV per capita utility relative to free trade):
  - Baseline: - 0.58
  - Financial integration φ=0.2: -0.28
  - Lower tech theft σ=0.04: -2.00
  - Less cyberattacks ρ=0.005: 0.24
  - More intertemp. discount β=0.98: -1.79
- Lowering cyberattack rate reduces incentives for import and export bans but does not necessarily eliminate them because monopoly rents remain.
- Heavier discounting of the future (lower β) makes export bans less attractive.

### Policy implications and discussion
- Two main mechanisms justify trade restrictions:
  - Import bans: repatriate monopoly profits when a country has a profitable domestic producer; attractive when cybersecurity vulnerabilities raise cost of foreign sourcing.
  - Export bans: technology leaders may ban exports to delay challengers’ leapfrogging and protect future monopoly rents, especially if challengers have higher expected technological growth.
- Global welfare effects:
  - Export bans harm global welfare by blocking technology access or creating duplication of fixed costs.
  - Import bans can also be harmful, especially if reciprocal.
- Mitigants via international cooperation:
  - Financial integration and cross-ownership to align incentives and share rents.
  - Rules preventing technological theft and cyberattacks to reduce diffusion-driven incentives for export bans.
  - Cross-border regulatory coordination, protection of intellectual property rights, cybersecurity standards, and open capital accounts to facilitate foreign ownership.
  - Coordinated regulation of large domestic firms would be preferable across nations to avoid unilateral disadvantage.
- Longer-term structural remedy:
  - Reducing natural monopoly properties (reducing fixed cost relative to economy size) would weaken incentives for beggar-thy-neighbor policies, though network externalities may persist.
- Institutional proposals:
  - International cooperation on cybersecurity, standards, and enforcement, possibly through institutions akin to a new Bretton Woods moment or strengthened roles for bodies such as the International Telecommunications Union, UN Commission on International Trade Law, G7, OECD, and IMF.
- Extensions suggested:
  - Study how export/import bans in new general-purpose technologies affect other trade areas, potentially causing broader decoupling.
  - Examine substitutability between competitors’ technologies and rest of world choices.
  - Assess feedback loops where trade restrictions alter incentives to invest in technological growth.

*Source: wpiea2020257-print-pdf (Appendix III and Sections III–V excerpts).*

### REFERENCES

### wpiea2020257-print-pdf - REFERENCES

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### Appendix I: First-best allocation — key results
- Social planner maximizes net present value of world utility: max_{c_i,y_i,n_i,l_i} U_{w,t} = Σ U_{i,t}.
- Static equilibrium: optimal quantity of the digital good produced in country i sets prices equal to marginal cost, eliminating monopoly markup:
  - n_{i,t}^j = [ (1−ρ)*I(i ≠ j) * α A_{i,t} ]^{1/(1−α)} l_{j,t}
  - Production occurs as long as incremental cost of supplying country i is smaller than the surplus; otherwise n_{i,t}^j = 0.
- Dynamic equilibrium (solved numerically): planner weighs benefits of trade (lower fixed costs, higher technology diffusion) versus costs (trade frictions, cyberattacks).
  - Compared to decentralized equilibrium, trade is unambiguously more likely under the social planner because two motives for trade restrictions disappear: monopoly rents and preventing technological flows to a laggard.
- Figure 8 comparison (US vs China calibration from Section III) — planner attains higher world utility path because:
  - Corrects static monopoly markup distortion.
  - Starts producing the digital good from period one (total surplus > monopolist surplus, easing fixed cost compensation).
  - US remains a global producer for longer than in decentralized equilibrium (absence of motive to capture rents by China).
  - It takes a few more periods for the US to return as a domestic producer in parallel to China.

### Appendix II: Model with a Rest of the World — set-up and equilibrium conditions
- World consists of three countries: i = {a, b, c}.
  - Country c cannot produce the digital good: A_{c,t} = 0, hence n_{c,t}^j = π_{c,t}^j = Π_{c,t} = 0.
  - Otherwise country c is symmetric to a and b; all Section II.A equations apply with i = {a, b, c}.
- Static equilibrium outcomes (absent trade bans): three possible digital-good production patterns:
  - No production.
  - One producer is the global producer.
  - One producer is domestic and the other serves its domestic market plus the rest of the world.
- Entry deterrence condition (Condition b from Section II.B) extends: if country i = {a,b} is global producer, potential producer from −i must be deterred from entering its domestic market and from entering both its domestic market and the rest of the world.
- Minimum possible price for global producer remains:
  - \tilde p_{n,t}^j = max[ 1/(1−ρ) A_{i,t}, \hat p_{n,t}^j ], where j ≠ i.
  - Break-even price \hat p_{n,t}^j and entrant profits depend on number of markets entrant targets.
- Entrant targets only domestic market:
  - Break-even condition:
    - π_{i,t}^i + π_{c,t}^i + [ \hat p_{n,t}^{−i} − 1/(1−ρ) A_{i,t} ] n( \hat p_{n,t}^{−i}, l_{−i,t} ) − K + τ_{i,t} = 0.
  - Non-positive entrant profits if:
    - [ \tilde p_{n,t}^{−i} − 1/A_{−i,t} ] n( \tilde p_{n,t}^{−i}, l_{−i,t} ) − K + τ_{i,t} ≤ 0.
- Entrant targets domestic market plus rest of the world:
  - Incumbent sets domestic price = marginal cost 1/(1−ρ) A_{i,t}, making zero profits domestically.
  - Break-even price in rest of world \hat p_{n,t}^c satisfies:
    - π_{i,t}^i + [ \hat p_{n,t}^c − 1/(1−ρ) A_{i,t} ] n( \hat p_{n,t}^c, l_{−i,t} ) − K = 0.
  - Associated non-positive entrant profits condition:
    - [ 1/(1−ρ) A_{i,t} − 1/A_{−i,t} ] n[ 1/(1−ρ) A_{i,t}, l_{−i,t} ] + [ \tilde p_{n,t}^c − 1/(1−ρ) A_{−i,t} ] n( \tilde p_{n,t}^c, l_{c,t} ) ≤ K.
- Note 26: Entry cannot occur in the rest of the world only because a viable entrant in the rest of the world would also be more competitive as a domestic producer (it would avoid trade cost ρ in its domestic market).
- If both countries have potentially profitable global producers and neither can be challenged by non-global producers, the producer with higher potential expected profits Π_{i,t} prevails.
- If no global producer is sustainable and both domestic producers are profitable, the producer with the lowest potential price in the rest of the world captures that market; the other produces domestically.
  - Lowest potential rest-of-world price is max between marginal cost in that market and the breakeven price when serving RoW and domestic markets.

### Appendix III: Production subsidies — domestic and foreign market effects
- Focus: subsidy proportional to quantity produced in a market (contrast with fixed-cost subsidy discussed in Section II).
- Domestic market subsidy:
  - Producer receives (1 + τ_{i,t}) p_{n,t}^i per unit sold.
  - Static and domestic optimal production subsidy induces marginal-cost pricing:
    - τ_{i,t}^* = (1−α)/α, replicating the first best.
  - Caveat: production subsidies may affect trade patterns and technology diffusion; the static optimal domestic subsidy could deter entry — welfare effect ambiguous depending on balance between monopoly rents and technology inflows.
  - Subsidy to fixed cost is always a least costly way to alter trade patterns compared to setting a production subsidy different from τ_{i,t}^*.
- Foreign market (export) subsidy:
  - Producer receives (1 + τ_{i,t}) p_{n,t}^j per unit sold in foreign market j ∈ {−i, c}.
  - Export subsidies transfer wealth to foreigners; they can only be optimal if:
    1) they open access to additional foreign markets (by lowering sales price enough to drive out competitors), and
    2) the same outcome cannot be achieved with a fixed-cost subsidy (which is entirely recouped by domestic shareholders).

*Content derived from wpiea2020257-print-pdf - REFERENCES*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020257-print-pdf.pdf_