Fixing the Trade Deficit with China—One Equation at a Time

A Phased Mathematical Model to Balance U.S.-China Trade

In recent years, the persistent trade imbalance between the United States and China has become a pressing economic issue. China’s global trade surplus reached $992 billion in 2024—with $49 billion attributed to its trade with the U.S. in early 2025—highlighting the need for strategic, data-driven solutions.

A phased mathematical model offers a powerful way to simulate, analyze, and guide policy interventions. By integrating trade data, economic theory, and optimization techniques, we can create a roadmap for reducing the U.S. trade deficit with China over time—while minimizing economic shocks.

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1. Defining the Problem

The model’s core objective is to reduce the U.S. trade deficit with China in a gradual, structured manner. It should:

• Address the underlying causes of China’s persistent trade surplus

• Include key policy levers such as tariffs, exchange rates, and domestic subsidies

• Minimize disruptions to industries and consumers

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2. Choosing the Right Modeling Framework

A variety of quantitative tools can support the development of a phased trade strategy:

• Linear Programming (LP) – Optimize trade flows within policy constraints

• Nonlinear Autoregressive Distributed Lag (NARDL) – Capture asymmetric effects of exchange rate changes

• Game Theory Models – Simulate strategic interactions in tariff negotiations

• Dynamic General Equilibrium Models – Analyze long-term structural adjustments

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3. Key Variables and Parameters

To build an effective model, we must incorporate the following elements:

• Trade Flows – U.S. exports ($X$) and imports ($M$) with China, adjusted for re-exports (e.g., via Hong Kong)

• Tariffs and Subsidies – Initial rates ($T_0$), policy adjustments ($T_t$), and export incentives

• Exchange Rates – Impact of currency valuation on trade volumes, including J-curve effects

• Elasticities – Price responsiveness of imports and exports

• Domestic Capacity – Limits to how much domestic production can replace imports

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4. Model Structure

🎯 Objective Function

Minimize the U.S.-China trade deficit over time ($D_t$):

$$\text{Minimize } D_t = M_t - X_t$$

Where $M_t$ and $X_t$ are functions of tariffs, exchange rates, and subsidies.

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✅ Constraints

1. Phased Reduction Target

$$D_{t+1} \leq D_t \cdot (1 - r)$$

Where $r$ is the annual reduction rate

2. Elasticity-Based Trade Response

$$X_t = f(E_t, T_t), \quad M_t = g(E_t, T_t)$$

3. Production Capacity Constraint

$$X_t \leq P_{\text{max}}$$

4. Tariff Boundaries

$$T_{\text{max}} \geq T_t \geq T_{\text{min}}$$

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5. Phased Implementation Strategy

Phase 1: Short-Term (Years 1–3)

• Raise tariffs on non-essential imports with domestic substitutes

• Offer subsidies to boost exports in high-potential sectors (e.g., tech, agriculture)

Phase 2: Medium-Term (Years 4–7)

• Encourage domestic manufacturing via tax incentives

• Pursue bilateral agreements to reduce export barriers

Phase 3: Long-Term (Years 8–10)

• Restructure supply chains to diversify sourcing

• Invest in innovation to improve global export competitiveness

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6. Data Requirements

Accurate modeling requires high-quality data sources, including:

• Sector-level import/export data between the U.S. and China

• Tariff schedules and historical changes

• Exchange rates and trade elasticity estimates

• Domestic industry production capacities

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7. Tools for Implementation

A range of modeling platforms can be used depending on the framework:

• Optimization Software – GAMS, MATLAB, Python

• Econometric Packages – R, Stata (for NARDL or elasticity modeling)

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📊 Example Model Output

Year	Trade Deficit ($B)	Tariff Rate (%)	Export Growth (%)	Import Reduction (%)
2025	350	10	5	2
2026	300	12	7	4
2027	250	15	10	6

This projection illustrates how a measured policy approach can reduce the trade deficit while sustaining economic stability.

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Conclusion

Balancing trade with China won’t happen overnight—but with a structured, data-driven model, policymakers can design targeted, phased strategies that address the root causes of the deficit. By combining mathematical modeling with pragmatic economics, we can move toward a more sustainable and mutually beneficial trade relationship.

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Sources

[1] China Balance of Trade – Trading Economics
[2] Mathematical Programming Model – GTAP
[3] China Trade Surplus Hits New Record – CPA
[4] Modeling Trade Wars – ScienceDirect
[5] Exchange Rate Impact on Trade – Taylor & Francis
[6] J-Curve in Trade Services – ScienceDirect
[7] Shock Propagation in Trade – MDPI
[8] China-LAC Trade Scenarios – Atlantic Council

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