## wpiea2020242-print-pdf — Appendix A and policy chapters (summarized)

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---

### A. Calibration (model parameterization)
- Common parameters follow ERT (2020).
- Mortality rate 휋_d = 0.5 percent for both economies.
- Time from infection to recovery or death = 18 days.
- Initial infections: 휖* = 휖 = 0.001 for both countries.
- Contagion probabilities 휋1, 휋2, 휋3 calibrated so that:
  - consumption activities account for 16 percent of contagion,
  - labor interactions account for 17 percent of contagion,
  - random encounters account for the remainder.
- Pre-epidemic targets:
  - agents work 28 hours per week,
  - yearly income = $58.000.
- Other parameter values:
  - 훽 = 0.96^(1/52),
  - 휙 = 0.8 for productivity when infected,
  - Frisch labor supply elasticity 1/휓 = 1.
- Open-economy parameters:
  - home bias 훼 = 0.7 for both countries,
  - elasticity of substitution between home and foreign goods = 1 (unitary).

### B. Baseline model — synchronous vs asynchronous pandemic (qualitative dynamics)
- Synchronous scenario (benchmark):
  - both economies hit simultaneously by the same-intensity virus.
  - Contagion continues until population immunity when some 60 percent of surviving population has been infected.
  - Susceptible agents reduce consumption and hours by about 10 percent relative to pre-pandemic levels.
  - Symmetric decline in exports and imports; relative price of home and foreign goods does not change.
- Asynchronous scenario (foreign first, home delayed by 20 periods = 20 weeks):
  - time paths for infections, recoveries, deaths are delayed for the home economy.
  - Relative price of domestic good initially declines then rises above pre-pandemic level.
  - Mechanism: foreign supply declines when foreign is hit → foreign good relative price rises; when foreign recovers and home is hit, roles reverse.
  - Trade opportunities via expenditure switching: foreign consumers increase imports of home good when foreign infections peak, allowing containment without as large consumption cuts.
- Three contrasting early-phase patterns (asynchronous vs synchronous):
  1. foreign consumption falls less initially and foreign hours worked fall more;
  2. home hours worked rise initially;
  3. home exports rise while home imports decline (early phase); reverses when home becomes infection center.
- Empirical alignment: model implication that more infected economies reduce relative supply and see relative price increase (terms of trade improvement) is consistent with data linking sharper workplace mobility contractions to greater nominal effective exchange rate appreciation.

### C. Sensitivity analysis — key numerical outcomes (selected Table 1 results)
- Table 1 reports largest deviations from steady state in percent and the period at which peak occurs (in parentheses).
- Baseline
  - H infected 5.3 ( 53 ); consumption -8.3 ( 52 ); hours -11.4 ( 53 ); appreciation 11.2 ( 55 )
  - F infected 5.2 ( 34 ); consumption -8.1 ( 35 ); hours -11.5 ( 34 ); appreciation 12.2 ( 32 )
- γ = 0.5 (no home bias)
  - H infected 5.3 ( 53 ); consumption -6.4 ( 50 ); hours -13.7 ( 53 ); appreciation 15.6 ( 55 )
  - F infected 5.2 ( 34 ); consumption -6.5 ( 50 ); hours -14.0 ( 33 ); appreciation 16.9 ( 32 )
- 1/ψ = 0.5
  - H infected 5.4 ( 53 ); consumption -6.2 ( 53 ); hours -8.4 ( 54 ); appreciation 7.9 ( 55 )
  - F infected 5.5 ( 34 ); consumption -6.1 ( 35 ); hours -8.5 ( 34 ); appreciation 8.5 ( 33 )
- 1/ψ = 2
  - H infected 5.1 ( 52 ); consumption -10.2 ( 52 ); hours -14.2 ( 53 ); appreciation 14.6 ( 55 )
  - F infected 5.0 ( 34 ); consumption -9.9 ( 34 ); hours -14.4 ( 33 ); appreciation 16.1 ( 32 )
- φ_i = 0.4
  - H infected 3.7 ( 58 ); consumption -7.1 ( 57 ); hours -9.3 ( 59 ); appreciation 8.3 ( 62 )
  - F infected 3.7 ( 40 ); consumption -6.9 ( 41 ); hours -9.3 ( 39 ); appreciation 8.9 ( 36 )
- AF > AH (home poorer)
  - H infected 4.6 ( 55 ); consumption -7.1 ( 55 ); hours -10.1 ( 55 ); appreciation 10.6 ( 57 )
  - F infected 5.9 ( 32 ); consumption -8.9 ( 32 ); hours -13.1 ( 32 ); appreciation 14.5 ( 31 )
- ω = 5.00
  - H infected 5.3 ( 53 ); consumption -9.6 ( 53 ); hours -9.9 ( 53 ); appreciation 1.3 ( 55 )
  - F infected 5.3 ( 34 ); consumption -9.5 ( 34 ); hours -9.9 ( 34 ); appreciation 1.4 ( 32 )
- ω = 0.10 (near-complements)
  - H infected 5.3 ( 53 ); consumption -11.5 ( 54 ); hours -7.7 ( 52 ); appreciation 14.3 ( 32 )
  - F infected 5.3 ( 34 ); consumption -11.7 ( 34 ); hours -7.5 ( 35 ); appreciation 13.2 ( 55 )
- Main sensitivity findings (qualitative):
  - No home bias (γ = 0.5): stronger relative price change, milder consumption decline, larger reduction in hours worked due to milder trade-off between hours and consumption.
  - Frisch elasticity changes: lower 1/휓 (0.5) → smaller hours response and smaller consumption contraction; higher 1/휓 (2) → larger hours response and larger consumption contraction.
  - Larger productivity loss when infected (φ_i = 0.4): agents flatten infection curve more via earlier larger reductions in consumption and hours; troughs spread over time so smaller trough magnitudes.
  - Asymmetric productivity (AF > AH): richer economy bears larger adjustment (foreign: peak infections rise, larger consumption and labor declines, stronger peak appreciations).
  - Elasticity of substitution ω:
    - Higher ω (>1) → milder hours response and milder appreciation due to more effective expenditure switching.
    - Near-zero ω (ω = 0.1, complements): home and foreign goods consumed in fixed proportions → no expenditure switching; foreign exports greater share of output for home consumption; relative price of foreign good falls rather than home good; home consumption can rise in early phase while home hours decline (risk sharing produces steeper consumption profile and asymmetric welfare effects across phases).
- Conclusion: qualitative baseline results robust except when goods are complements (low ω).

### VI. Optimal containment policies — instruments, scenarios, and welfare outcomes
- Policy instrument: time-varying Pigouvian consumption taxes μ_c,t (home) and μ_c,t* (foreign).
- Governments choose tax paths to optimize objective functions; can cooperate or act non-cooperatively.
- Cooperation maximizes global welfare U_world = U* + U; non-cooperation maximizes domestic welfare only.
- Consumption taxes reduce consumption and labor, thereby reducing local aggregate supply and infection risk.
- Terms of trade play a critical role in open-economy policy effects.

A. Cooperation scenario — key outcomes
- Containment policies under cooperation reduce infections and deaths but deepen recessions (employment, consumption, trade fall more).
- Optimal policies exploit relative price adjustments: larger increase in relative price of more infected country induces substitution toward cheaper imports, mitigating consumption drops.
- Welfare effects (Table 2, cooperative "C" cell):
  - Home welfare rises by 0.18 percent above no-policy baseline.
  - Foreign welfare rises by 0.29 percent above no-policy baseline.
- Slight asymmetry favors foreign economy due to initial 19-period window where home is not yet affected enabling expenditure switching and risk sharing to support foreign output.

B. Non-cooperation scenario — key outcomes
- Non-cooperative policies save more lives but cause much larger recessions due to "infect-thy-neighbor" strategic behavior.
- Mechanism: each country hikes consumption tax to raise its good's relative price and reduce domestic hours, but fails to internalize adverse spillovers on the other country; both raise taxes aggressively leading to partial offsetting of terms-of-trade movements and reduced overall volatility of terms of trade relative to cooperation.
- Result: stronger recession and significant welfare reductions in both countries despite lower deaths.
- Quantified welfare changes relative to no-policy baseline:
  - Non-cooperation (international Nash game) leads to welfare declines of 1.01 and 0.87 percent for the home and the foreign countries, respectively.
- Partial cooperation where home government maximizes global welfare while foreign government maximizes own welfare:
  - cooperating (home) country welfare increases by 0.66 percent above the baseline (top right panel of table 2 labeled "C" for home and "NC" for foreign).
  - a benevolent government policy at home (global-welfare-maximizing home government) can reduce home welfare by 1.43 percent relative to the no-policy baseline because it increases employment, reduces consumption, and increases infections and deaths.
- Cooperative scenario raises welfare above the no-policy baseline for both countries and is Pareto-superior to the unique Nash equilibrium (the non-cooperative outcome), but the cooperative solution is not a Nash equilibrium.

C. Strategic interactions and welfare implications
- Policy choices form a prisoners’ dilemma: non-cooperation reduces deaths but at large welfare costs; cooperation raises global welfare but requires coordinated containment paths that internalize cross-country infection externalities.
- Policy relevance:
  - coordinated containment that leverages terms-of-trade adjustments can mitigate consumption losses while reducing infections;
  - unilateral aggressive containment taxes can be self-defeating economically.
- Observed trade-policy behavior during pandemic consistent with "infect-thy-neighbor" incentives: as of May 2020, 120 new export restrictions were counted for 2020 on a net basis so far; the most affected sectors comprise roughly 1.01 percent of global trade.
- Governments can achieve desired terms-of-trade effects via Pigouvian consumption taxes in the model; in practice, import tariffs and export subsidies could produce similar effects but risk overuse by selfish governments.

### Mechanisms — how trade and policy interact with the epidemic
- Asynchronous pandemic timing creates opportunities to shift production toward less-affected countries, expanding consumption possibilities via terms-of-trade changes.
- Terms-of-trade appreciation when countries approach relative infection peaks allows substitution from local production to imports, enabling reductions in hours worked and infections.
- Non-cooperative use of trade-policy channels leads to overuse of relative-price manipulation, ignoring external infection effects and producing suboptimal global outcomes.

### Model structure and supporting analysis (appendices summary)
- Epidemiological block: SIR-type distributional laws of motion for susceptible (S), newly infected (T), overall infected (I), recovered (R), and dead (D) agents in home and foreign countries; parameters and transition rates (휋1, 휋2, 휋3, 휋r, 휋d) specify infection, recovery, and death flows.
- Macroeconomic block:
  - Heterogeneous agent types (recovered, infected, susceptible) with first-order conditions for labor and composite consumption choices; Lagrange multipliers on budget and infection-rate constraints (e.g., 휆b,tj, 휆휏,t s).
  - Composite consumption baskets with CES aggregation between home and foreign goods parameterized by elasticity of substitution 휔 and share parameter 훾; relative price normalization differs by country.
  - Resource constraints and governments’ budget constraints incorporate Pigouvian consumption taxes (휇c,t and 휇c,t*).
  - Trade balance identities derive from Walras’ law.
- Sensitivity analysis (Appendix B):
  - Role of elasticity of substitution 휔: when goods are complements (휔 close to 0), trade-channel dynamics differ from baseline substitutes case; for 휔 between 0 and 0.49 Home consumption rises and employment falls when foreign pandemic occurs, while for 휔 between 0.51 and infinity Home consumption falls and employment rises; at 휔 = 0.5 there is no solution.
- Counterfactual without pandemic (Appendix C):
  - In non-cooperative environment without epidemic, each country exploits relative price channel to reduce labor and consumption, inducing higher relative prices and substitution toward imports; simultaneous adoption cancels relative-price effects but produces permanent consumption and labor allocation changes that reduce global welfare.

*Source: wpiea2020242-print-pdf — Appendix A presents the first order conditions, the household’s and the government’s budget constraints, and the SIR block for each economy.*

### Appendix A presents the first order conditions, the household’s and the government’s budget

### Appendix A presents the first order conditions, the household’s and the government’s budget constraints, and the SIR block for each economy.

### A. Calibration
- Common parameters follow ERT (2020).
- Mortality rate 휋_d = 0.5 percent for both economies.
- Time from infection to recovery or death = 18 days.
- Initial infections: 휖* = 휖 = 0.001 for both countries.
- Contagion probabilities 휋1, 휋2, 휋3 calibrated so that:
  - consumption activities account for 16 percent of contagion,
  - labor interactions account for 17 percent of contagion,
  - random encounters account for the remainder.
- Pre-epidemic targets:
  - agents work 28 hours per week,
  - yearly income = $58.000.
- Other parameter values:
  - 훽 = 0.96^(1/52),
  - 휙 = 0.8 for productivity when infected,
  - Frisch labor supply elasticity 1/휓 = 1.
- Open-economy parameters:
  - home bias 훼 = 0.7 for both countries,
  - elasticity of substitution between home and foreign goods = 1 (unitary).

### B. Baseline Model — synchronous vs asynchronous pandemic
- Synchronous scenario:
  - both economies hit simultaneously by the same-intensity virus (benchmark).
  - Contagion continues until population immunity when some 60 percent of surviving population has been infected.
  - Susceptible agents reduce consumption and hours by about 10 percent relative to pre-pandemic levels.
  - Symmetric decline in exports and imports; relative price of home and foreign goods does not change.
- Asynchronous scenario (foreign first, home delayed by 20 periods = 20 weeks):
  - time paths for infections, recoveries, deaths are delayed for the home economy.
  - Relative price of domestic good initially declines then rises above pre-pandemic level.
  - Mechanism: when foreign is hit, foreign supply declines → foreign good relative price rises; when foreign recovers and home is hit, roles reverse.
  - Trade opportunities emerge via expenditure switching:
    - foreign consumers increase imports of home good when foreign infections peak, allowing containment without as large consumption cuts.
- Three contrasting patterns in early asynchronous phase vs synchronous:
  1. foreign consumption falls less initially and foreign hours worked fall more;
  2. home hours worked rise initially;
  3. home exports rise while home imports decline (early phase); reverses when home becomes infection center.
- Empirical alignment:
  - Model implication that the more infected economy reduces relative supply and sees relative price increase (terms of trade improvement) is consistent with data showing economies with sharper workplace mobility contractions experienced greater nominal effective exchange rate appreciation.

### C. Sensitivity Analysis — key numerical outcomes (Table 1 highlights)
- Table 1 reports largest deviations from steady state in percent and the period at which peak occurs (in parentheses). Selected rows:
  - Baseline
    - H infected 5.3 ( 53 ); consumption -8.3 ( 52 ); hours -11.4 ( 53 ); appreciation 11.2 ( 55 )
    - F infected 5.2 ( 34 ); consumption -8.1 ( 35 ); hours -11.5 ( 34 ); appreciation 12.2 ( 32 )
  - γ = 0.5 (no home bias)
    - H infected 5.3 ( 53 ); consumption -6.4 ( 50 ); hours -13.7 ( 53 ); appreciation 15.6 ( 55 )
    - F infected 5.2 ( 34 ); consumption -6.5 ( 50 ); hours -14.0 ( 33 ); appreciation 16.9 ( 32 )
  - 1/ψ = 0.5
    - H infected 5.4 ( 53 ); consumption -6.2 ( 53 ); hours -8.4 ( 54 ); appreciation 7.9 ( 55 )
    - F infected 5.5 ( 34 ); consumption -6.1 ( 35 ); hours -8.5 ( 34 ); appreciation 8.5 ( 33 )
  - 1/ψ = 2
    - H infected 5.1 ( 52 ); consumption -10.2 ( 52 ); hours -14.2 ( 53 ); appreciation 14.6 ( 55 )
    - F infected 5.0 ( 34 ); consumption -9.9 ( 34 ); hours -14.4 ( 33 ); appreciation 16.1 ( 32 )
  - φ_i = 0.4
    - H infected 3.7 ( 58 ); consumption -7.1 ( 57 ); hours -9.3 ( 59 ); appreciation 8.3 ( 62 )
    - F infected 3.7 ( 40 ); consumption -6.9 ( 41 ); hours -9.3 ( 39 ); appreciation 8.9 ( 36 )
  - AF > AH (home poorer)
    - H infected 4.6 ( 55 ); consumption -7.1 ( 55 ); hours -10.1 ( 55 ); appreciation 10.6 ( 57 )
    - F infected 5.9 ( 32 ); consumption -8.9 ( 32 ); hours -13.1 ( 32 ); appreciation 14.5 ( 31 )
  - ω = 5.00
    - H infected 5.3 ( 53 ); consumption -9.6 ( 53 ); hours -9.9 ( 53 ); appreciation 1.3 ( 55 )
    - F infected 5.3 ( 34 ); consumption -9.5 ( 34 ); hours -9.9 ( 34 ); appreciation 1.4 ( 32 )
  - ω = 0.10 (near-complements)
    - H infected 5.3 ( 53 ); consumption -11.5 ( 54 ); hours -7.7 ( 52 ); appreciation 14.3 ( 32 )
    - F infected 5.3 ( 34 ); consumption -11.7 ( 34 ); hours -7.5 ( 35 ); appreciation 13.2 ( 55 )
- Main sensitivity findings:
  - No home bias (γ = 0.5): stronger relative price change, milder consumption decline, larger reduction in hours worked due to milder trade-off between hours and consumption.
  - Frisch elasticity changes: lower 1/휓 (0.5) → smaller hours response and smaller consumption contraction; higher 1/휓 (2) → larger hours response and larger consumption contraction.
  - Larger productivity loss when infected (φ_i = 0.4): agents flatten infection curve more via earlier larger reductions in consumption and hours; troughs spread over time so smaller trough magnitudes.
  - Asymmetric productivity (AF > AH): richer economy bears larger adjustment (foreign: peak infections rise, larger consumption and labor declines, stronger peak appreciations).
  - Elasticity of substitution ω:
    - Higher ω (>1) → milder hours response and milder appreciation due to more effective expenditure switching.
    - Near-zero ω (ω = 0.1, complements): home and foreign goods consumed in fixed proportions → no expenditure switching; foreign exports greater share of output for home consumption; relative price of foreign good falls rather than home good; home consumption can rise in early phase while home hours decline (risk sharing produces steeper consumption profile and asymmetric welfare effects across phases).
- Conclusion: qualitative baseline results robust except when goods are complements (low ω).

### VI. Optimal Containment Policies — instruments and scenarios
- Policy instrument: time-varying Pigouvian consumption taxes μ_c,t (home) and μ_c,t* (foreign).
- Governments choose tax paths to optimize objective functions; can cooperate or act non-cooperatively.
- Cooperation maximizes global welfare U_world = U* + U; non-cooperation maximizes domestic welfare only.
- Consumption taxes reduce consumption and labor, thereby reducing local aggregate supply and infection risk.
- Terms of trade play a critical role in the open-economy policy effects.

A. Cooperation scenario — key outcomes
- Containment policies under cooperation reduce infections and deaths but deepen recessions (employment, consumption, trade fall more).
- Optimal policies exploit relative price adjustments: larger increase in relative price of more infected country induces substitution toward cheaper imports, mitigating consumption drops.
- Welfare effects (Table 2, cooperative "C" cell):
  - Home welfare rises by 0.18 percent above no-policy baseline.
  - Foreign welfare rises by 0.29 percent above no-policy baseline.
- Slight asymmetry favors foreign economy due to initial 19-period window where home is not yet affected enabling expenditure switching and risk sharing to support foreign output.

B. Non-cooperation scenario — key outcomes
- Each country chooses its consumption tax path to maximize its own welfare, taking other country’s policy as given; solved iteratively to fixed point.
- Non-cooperative policies save more lives but cause much larger recessions due to "infect-thy-neighbor" strategic behavior.
- Mechanism: each country hikes consumption tax to raise its good's relative price and reduce domestic hours, but fails to internalize adverse spillovers on the other country; both raise taxes aggressively leading to partial offsetting of terms-of-trade movements and reduced overall volatility of terms of trade relative to cooperation.
- Result: stronger recession and significant welfare reductions in both countries despite lower deaths.

C. Strategic interactions and welfare implications
- The model yields a prisoners’ dilemma in policy choices: non-cooperation reduces deaths but at large welfare costs; cooperation raises global welfare but requires coordinated containment paths that internalize cross-country infection externalities.
- Policy relevance: coordinated containment that leverages terms-of-trade adjustments can mitigate consumption losses while reducing infections; unilateral aggressive containment taxes can be self-defeating economically.

*Source: wpiea2020242-print-pdf - Appendix A presents the first order conditions, the household’s and the government’s budget constraints, and the SIR block for each economy.*

### 1.01 and 0.87 percent  below  the  no-policy  baseline  scenario,  for  the home  and  the  foreign

### wpiea2020242-print-pdf - 1.01 and 0.87 percent below the no-policy baseline scenario, for the home and the foreign

### Key findings
- Non-cooperation (international Nash game) leads to large welfare losses: welfare would decline by 1.01 and 0.87 percent for the home and the foreign countries, respectively, relative to the no-policy baseline scenario.
- Partial cooperation where the home government maximizes global welfare while the foreign government maximizes own welfare yields a welfare increase of 0.66 percent above the baseline for the cooperating (home) country (top right panel of table 2 labeled "C" for home and "NC" for foreign).
- A benevolent government policy at home (global-welfare-maximizing home government) can reduce home welfare by 1.43 percent relative to the no-policy baseline because it increases employment, reduces consumption, and increases infections and deaths.
- The cooperative scenario raises welfare above the no-policy baseline for both countries and is Pareto-superior to the unique Nash equilibrium (the non-cooperative outcome), but the cooperative solution is not a Nash equilibrium.
- Trade-policy actions observed during the pandemic are consistent with "infect-thy-neighbor" behavior: as of May 2020, 120 new export restrictions were counted for 2020 on a net basis so far; the most affected sectors comprise roughly 1.01 percent of global trade.

### Scenario outcomes and strategic interaction
- No-policy baseline: baseline against which welfare changes are measured.
- Non-cooperation (Nash equilibrium):
  - Both countries choose selfish containment policies.
  - Policies neutralize terms-of-trade effects when both act non-cooperatively.
  - Result: too high Pigouvian consumption taxes and the reported welfare declines of 1.01 percent (home) and 0.87 percent (foreign) relative to the no-policy baseline.
- Partial cooperation:
  - Case A: Home maximizes global welfare; foreign maximizes own welfare.
    - Foreign government sharply raises its consumption tax to contain the pandemic and benefits from an improved terms of trade.
    - Home government enforces milder containment; foreign terms of trade appreciate; foreign hours fall more than consumption, reducing infections and deaths.
    - Home welfare rises by 0.66 percent above baseline (table 2, top right panel, "C"/"NC").
    - Nevertheless, relative to no-policy baseline, benevolent home policy reduces home welfare by 1.43 percent because of increased employment, reduced consumption, and increased infections and deaths.
  - Case B: Reverse roles (home maximizes own welfare; foreign maximizes global welfare) produces the opposite pattern (bottom left panel of table 2).
- Prisoners’ dilemma characterization:
  - Each country would gain from exploiting the terms-of-trade channel if the other cooperates.
  - If both act selfishly, they neutralize each other’s terms-of-trade impacts and both suffer welfare losses.
  - Cooperative outcome is globally optimal but not sustained as a Nash equilibrium.

### Mechanisms (how trade and policy interact with the epidemic)
- Asynchronous pandemic timing across countries creates opportunities to shift production toward less-affected countries, expanding consumption possibilities via terms-of-trade changes.
- Terms of trade appreciation when countries approach relative infection peaks allows substitution from local production to imports, enabling reductions in hours worked and infections.
- Governments use Pigouvian consumption taxes in the model as the policy instrument; desired terms-of-trade changes could also be achieved through import tariffs and export subsidies in practice.
- The model predicts overuse of trade-policy channels by selfish governments, ignoring external infection effects, producing infect-thy-neighbor trade measures.

### Policy implications and recommendations
- Global cooperation in containment policies is welfare-improving because it internalizes cross-border infection externalities and preserves gains from trade-induced adjustments.
- The country least affected by the pandemic must be willing to allow its trade balance to improve and its terms of trade to deteriorate to share the burden of more-affected partners.
- Reciprocity and coordinated restraint in trade measures (avoiding unilateral export restrictions and import liberalizations aimed at improving domestic terms of trade) are critical to realizing the global welfare gains.
- Reliance on trade-policy instruments (export restrictions, import reductions) without coordination risks locking countries into a prisoners’ dilemma with suboptimal global outcomes.

### Model structure and supporting analysis (appendices summary)
- Epidemiological block: SIR-type distributional laws of motion for susceptible (S), newly infected (T), overall infected (I), recovered (R), and dead (D) agents in home and foreign countries; parameters and transition rates (휋1, 휋2, 휋3, 휋r, 휋d) specify infection, recovery, and death flows.
- Macroeconomic block:
  - Heterogeneous agent types (recovered, infected, susceptible) with first-order conditions for labor and composite consumption choices; Lagrange multipliers on budget and infection-rate constraints (e.g., 휆b,tj, 휆휏,t s).
  - Composite consumption baskets with CES aggregation between home and foreign goods parameterized by elasticity of substitution 휔 and share parameter 훾; relative price normalization differs by country.
  - Resource constraints and governments’ budget constraints incorporate Pigouvian consumption taxes (휇c,t and 휇c,t*).
  - Trade balance identities derive from Walras’ law.
- Sensitivity analysis (Appendix B):
  - Role of elasticity of substitution 휔: when goods are complements (휔 close to 0), trade-channel dynamics differ from baseline substitutes case; for 휔 between 0 and 0.49 Home consumption rises and employment falls when foreign pandemic occurs, while for 휔 between 0.51 and infinity Home consumption falls and employment rises; at 휔 = 0.5 there is no solution.
- Counterfactual without pandemic (Appendix C):
  - In non-cooperative environment without epidemic, each country exploits relative price channel to reduce labor and consumption, inducing higher relative prices and substitution toward imports; simultaneous adoption cancels relative-price effects but produces permanent consumption and labor allocation changes that reduce global welfare.

*Italic: Source—wpiea2020242-print-pdf (excerpts provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020242-print-pdf.pdf_