Theoretical Model

We present the spatial equilibrium analysis of cotton trade and conduct comparative statics of the exchange rate effects on trade flows and prices.^{Footnote 4} The model consists of the following market-clearing and spatial-arbitrage conditions, which can be derived from the first-order conditions of the net welfare optimization problem of the SEM^{Footnote 5}

(1)$$\sum\limits_{i = 1}^N {X_{ij}} = Q_j^D\left( {P_j^D} \right),{\kern 1pt} j = 1,...,N$$

(2)$$Q_i^S\left( {P_i^S} \right) = \sum\limits_{j = 1}^N {X_{ij}},{\kern 1pt} i = 1,...,N$$

(3)$$P_j^D = \left( {P_i^S - {S_i} + {T_{ij}} + {\tau _{ij}}} \right)*{E_{ij}},{\kern 1pt} i,j = 1,...,N$$

where $Q_i^D\left( {P_i^D} \right)$ is the demand quantity as a function of demand price, $P_i^D,$ in country $i$, $Q_i^S\left( {P_i^S} \right)$ is the supply quantity as a function of supply price $P_i^S$, ${X_{ij}}$ is bilateral trade flows from $i$ to $j,$${S_i}$ is subsidies provided by $i,$${T_{ij}}$ is transport costs from $i$ to $j,$${\tau _{ij}}$ is tariffs imposed on $i$ by $j,$ and ${E_{ij}}$ is the exchange rate from $i$ to $j.$ Equation (1) indicates that all the imports by country $j,$ including from itself, should meet its demand. Equation (2) entails that quantity supplied in country $i$ should be equal to all of its exports, including to itself. Equation (3) denotes the spatial arbitrage, indicating that demand price in country $j$ is equal to price in country $i$, excluding subsidy, but inclusive of all trade costs. To obtain analytical results, we condense the above $N$-region model into a stylized model of four regions with two exporters (the United States $\left( U \right)$ and India $\left( I \right)$) and two importers (China $\left( C \right)$ and Vietnam $\left( V \right)$) in order to concisely present the market-clearing and spatial-arbitrage conditions.^{Footnote 6} Furthermore, for the ease of analytical derivations, we assume that internal transport costs within a country, ${T_{ii}},$ are $0,$ all tariff rates and subsidies are equal to $0$ with the exception of the tariff between the United States and China, ${\tau _{UC}},$ and all exchange rates are equal to $1$ with the exception of the exchange rate between the United States and China, ${E_{UC}}.$ Lastly, we express the supply and demand prices of India, China, and Vietnam as well as the US demand price as functions of US supply price, and the resulting price linkages are substituted into the market-clearing conditions to obtain^{Footnote 7}

$${{X_{UU}} + {X_{IU}} + {X_{CU}} + {X_{VU}} = Q_U^D\left( {P_U^S} \right),}$$

$${X_{UI}} + {X_{II}} + {X_{CI}} + {X_{VI}} = Q_I^D\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}} - {T_{IC}}} \right),$$

$${X_{UC}} + {X_{IC}} + {X_{CC}} + {X_{VC}} = Q_C^D\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}}} \right),$$

$${X_{UV}} + {X_{IV}} + {X_{CV}} + {X_{VV}} = Q_V^D\left( {P_U^S + {T_{UV}}} \right),$$

$$Q_U^S\left( {P_U^S} \right) = {X_{UU}} + {X_{UI}} + {X_{UC}} + {X_{UV}},$$

$$Q_I^S\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}} - {T_{IC}}} \right) = {X_{IU}} + {X_{II}} + {X_{IC}} + {X_{IV}},$$

$$Q_C^S\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}}} \right) = {X_{CU}} + {X_{CI}} + {X_{CC}} + {X_{CV}},$$

$$Q_V^S\left( {P_U^S + {T_{UV}}} \right) = {X_{VU}} + {X_{VI}} + {X_{VC}} + {X_{VV}}.$$

This system contains 8 equations and 17 endogenous variables. To convert this into a square system and further condense the model, several variables can be logically excluded. For example, importing countries do not export and we can exclude ${X_{CU}},$${X_{CI}},$${X_{CV}},$${X_{VU}},$${X_{VI}},$ and ${X_{VC}}.$ In addition, exporting countries do not trade among themselves, and we can ignore ${X_{IU}}$ and ${X_{UI}}.$ Further, we assume India does not export to Vietnam, ${X_{IV}} = 0.$^{Footnote 8} These simplifications lead to $Q_U^D\left( {P_U^S} \right) = {X_{UU}},$$Q_I^D\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}} - {T_{IC}}} \right) = {X_{II}},$$Q_C^S\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}}} \right) = {X_{CC}},$ and $Q_V^S\left( {P_U^S + {T_{UV}}} \right) = {X_{VV}}.$ That is, for an exporting country, total internal demand is met by exports to itself, and for an importing country, total supply is equal to exports to itself. By plugging these relationships into the remaining equations, the simplified version of the model is

(4)$${X_{UC}} + {X_{IC}} + Q_C^S\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}}} \right) = Q_C^D\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}}} \right),$$

(5)$${X_{UV}} + Q_V^S\left( {P_U^S + {T_{UV}}} \right) = Q_V^D\left( {P_U^S + {T_{UV}}} \right),$$

(6)$$Q_U^S\left( {P_U^S} \right) = Q_U^D\left( {P_U^S} \right) + {X_{UC}} + {X_{UV}},$$

(7)$$Q_I^S\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}} - {T_{IC}}} \right) = Q_I^D\left( {\left[ {P_U^S + {T_{UC}} + {\tau _{UC}}} \right]*{E_{UC}} - {T_{IC}}} \right) + {X_{IC}}.$$

Thus, the system of $2N + {N^2}$ equations depicted in (1)–(3) is condensed into four equations with four endogenous variables. This four-region model is illustrated graphically in Figure 1.

Figure 1. Four-country trade model.

The domestic markets for the United States, India, China, and Vietnam are characterized in the upper left, upper right, bottom left, and bottom right graphs, respectively. The domestic markets in the United States and India present autarky equilibria (the intersection of domestic supply and demand curves) that are below the free trade world price, ${P_W},$ which indicates that the United States and India are exporting countries. The US excess supply curve, $E{S_U},$ is the difference between its domestic supply and demand curves and is drawn in the adjacent graph. Similarly, Indian excess supply, $E{S_I},$ is drawn next to its domestic market. The sum of these two excess supply curves is the total excess supply, $E{S_{U + I}},$ which appears in the upper middle graph and is also translated into the bottom middle graph. These middle graphs represent the world market and are identical to each other. The reason for including a world market graph in both the upper and bottom sections is to transmit the prices that are determined in the world market equilibrium to each of the four countries’ domestic markets. The autarky equilibria in the Chinese and Vietnamese domestic markets are above the free trade world price, implying that China and Vietnam are importing countries. The Chinese excess demand curve, $E{D_C},$ is the difference between domestic demand and supply, which is drawn in the adjacent graph. Similarly, the Vietnamese excess demand curve, $E{D_V},$ is drawn next to its domestic market. The sum of these two excess demand curves is the total excess demand, $E{D_{C + V}},$ which is also included in the world market graphs. The free trade equilibrium is found at the intersection of the total excess supply and total excess demand curves, which determines the world equilibrium quantity traded, ${Q_T},$ and equilibrium price, ${P_W}.$ The effects of the decline in Yuan value are also depicted in Figure 1 and will be explained along with the comparative static results below.

To obtain comparative static results, we totally differentiate the system of equations in (4)–(7), treating transport costs and tariffs as constants, and place them in matrix form Ax =b (See below equation (4) in the Appendix for these steps):

$$\left[{\matrix{ {\left( {\frac{{\partial Q_C^S}}\over{{\partial P_C^S}}} - {\frac{{\partial Q_C^D}}\over{{\partial P_C^D}}} \right){E_{UC}}} 1 0 1\cr\\{\left( {\frac{{\partial Q_V^S}}\over{{\partial P_V^S}}} - {\frac{{\partial Q_V^D}}\over{{\partial P_V^D}}} \right)} {0} {1} {0}\cr \\{\left( {\frac{{\partial Q_U^S}}\over{{\partial P_U^S}}} - {\frac{{\partial Q_U^D}}\over{{\partial P_U^D}}} \right)} { - 1} { - 1} 0\cr\\{\left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right){E_{UC}}} 0 0 { - 1}}}\right]\left[{\matrix{{{dP_U^S}}\cr \\{d{X_{UC}}}\cr\\{d{X_{UV}}}\cr\\{d{X_{IC}}}}} \right] = \left[{\matrix{{- \left( {\frac{{\partial Q_C^S}}\over{{\partial P_C^S}}} - {\frac{{\partial Q_C^D}}\over{{\partial P_C^D}}} \right)\left( P_U^S + {T_{UC}} + {\tau _{UC}} \right)d{E_{UC}}}\cr {0} \cr 0 \cr\\{ - \left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right)\left( {P_U^S + {T_{UC}} + {\tau _{UC}}} \right)d{E_{UC}}}}}\right]$$

The above system is solved using Cramer’s rule to determine the comparative static effects of a change in the exchange rate, ${E_{UC}},$ on the endogenous variables. The determinant of the coefficient matrix A is

$$\left| {\bi A} \right| = - \left[ {\left( {\frac{{\partial Q_U^S}}\over{{\partial P_U^S}}} - {\frac{{\partial Q_U^D}}\over{{\partial P_U^D}}} \right) + \left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right){E_{UC}} + \left( {\frac{{\partial Q_C^S}}\over{{\partial P_C^S}}} - {\frac{{\partial Q_C^D}}\over{{\partial P_C^D}}} \right){E_{UC}} + \left( {\frac{{\partial Q_V^S}}\over{{\partial P_V^S}}} - {\frac{{\partial Q_V^D}}\over{{\partial P_V^D}}} \right)} \right] \lt 0.$$

The negative sign of the determinant of the coefficient matrix is important in ascertaining the direction of the analytical results. Specifically, the sign of the numerator in the following comparative static analysis is reversed by the negative sign of $\left| {\bi A} \right|$ in the denominator. The magnitude of this determinant hinges upon the supply and demand slopes of each country included in the model. This is because the world price is determined by the interactions of excess supply and excess demand of all countries. Thus, the effects of the decline in Yuan value on the world price reverberates through these slopes (elasticities).

The effect of a fall in Yuan value on US cotton exports to China is

(8)$${\frac{{d{X_{UC}}}}\over{{d{E_{UC}}}}} = {\frac{{\left( {P_U^S + {T_{UC}} + {\tau _{UC}}} \right)\left[ {\left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right) + \left( {\frac{{\partial Q_C^S}}\over{{\partial P_C^S}}} - {\frac{{\partial Q_C^D}}\over{{\partial P_C^D}}} \right)} \right]\left[ {\left( {\frac{{\partial Q_V^S}}\over{{\partial P_V^S}}} - {\frac{{\partial Q_V^D}}\over{{\partial P_V^D}}} \right) + \left( {\frac{{\partial Q_U^S}}\over{{\partial P_U^S}}} -{ \frac{{\partial Q_U^D}}\over{{\partial P_U^D}}} \right)} \right]}}\over{{\left| {\bi A} \right|}}}}}} \lt 0.$$

In response to a decrease in Yuan value, US cotton exports to China decline because US cotton, relative to other exporters’ cotton, is more expensive in the Chinese market. The qualitative change in US cotton exports is graphically illustrated in Figure 1, where the drop in Yuan value causes a leftward rotation of the US excess supply curve from $E{S_U}$ to $E{S'_U}.$^{Footnote 9} This is because the value of the Yuan in terms of US dollar is lower and, consequently, the United States will expect to receive more Yuan per unit of exports or, in other words, the United States will export less at any given price, which is reflected by the US excess supply curve rotating upward. This causes the total excess supply curve to rotate, $E{S_{U + I}}$ to $E{S'_{U + I}},$ and the world equilibrium after the fall in Yuan value is at the intersection of the new total excess supply curve, $E{S'_{U + I}},$ and initial total excess demand curve, $E{D_{C + V}}$. Therefore, the equilibrium quantity traded decreases from ${Q_T}$ to ${Q'_T},$ and US exports decline from ${E_U}$ to ${E'_U}$.^{Footnote 10}

The impact of a decline in Yuan value on US producer price is

(9)$${\frac{{dP_U^S}}\over{{d{E_{UC}}}}} = {\left( {P_U^S + {T_{UC}} + {\tau _{UC}}} \right){\frac{{\left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right) + \left( {\frac{{\partial Q_C^S}}\over{{\partial P_C^S}}} - {\frac{{\partial Q_C^D}}\over{{\partial P_C^D}}} \right)}}\over{{\left| {\bi A} \right|}}} \lt 0.}$$

A fall in Yuan value decreases US exports to China and more is sold within the US market, leading to a lower price. This decline in the US price is illustrated in Figure 1, where the US price decreases from ${P_W}$ to ${P'_U}.$ At this new lower US price, domestic cotton supply falls, harming US cotton producers. In contrast, the Chinese price, traced from the intersection of $E{S'_{U + I}}$ and $E{D_{C + V}},$ increases from ${P_W}$ to ${P'_C},$ as less US cotton is imported by China. In response to this higher price, Chinese producers increase their cotton production, and Chinese cotton users decrease their demand. From this graphical analysis, we can observe the price wedge, that is, higher Chinese price and lower US price, caused by the exchange rate change.

The comparative static result of a decline in Yuan value on US exports to Vietnam is

(10)$${\frac{{d{X_{UV}}}}\over{{d{E_{UC}}}}} = {\frac{{ - \left( {P_U^S + {T_{UC}} + {\tau _{UC}}} \right)\left( {\frac{{\partial Q_V^S}}\over{{\partial P_V^S}}} - {\frac{{\partial Q_V^D}}\over{{\partial P_V^D}}} \right)\left[ {\left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right) + \left( {\frac{{\partial Q_C^S}}\over{{\partial P_C^S}}} - {\frac{{\partial Q_C^D}}\over{{\partial P_C^D}}} \right)} \right]}}\over{{\left| {\bi A} \right|}}} \gt 0.$$

As a result of the decline in value of the Yuan, the United States augments its exports to Vietnam because US exporters are seeking to expand their sales to other importers in order to mitigate lost sales to China. Furthermore, the lower US price incentivizes Vietnamese cotton users to import more from the United States. These changes are shown graphically in Figure 1 where the price in Vietnam falls from ${P_W}$ to ${P'_W},$ and Vietnam’s imports increase from ${I_V}$ to ${I'_V}.$

The effect of a fall in Yuan value on Chinese imports from India is

(11)$${\frac{{d{X_{IC}}}}\over{{d{E_{UC}}}}} = {\frac{{ - \left( {P_U^S + {T_{UC}} + {\tau _{UC}}} \right)\left( {\frac{{\partial Q_I^S}}\over{{\partial P_I^S}}} - {\frac{{\partial Q_I^D}}\over{{\partial P_I^D}}} \right)\left[ {\left( {\frac{{\partial Q_V^S}}\over{{\partial P_V^S}}} - {\frac{{\partial Q_V^D}}\over{{\partial P_V^D}}} \right) + \left( {\frac{{\partial Q_U^S}}\over{{\partial P_U^S}}} - {\frac{{\partial Q_U^D}}\over{{\partial P_U^D}}} \right)} \right]}}\over{{\left| {\bi A} \right|}}} \gt 0.$$

This result shows that Yuan decline relative to the US dollar causes China to increase its imports from other exporters, such as India. Since US cotton exports to China decrease, the Chinese importers fill some of the void with imports from other exporters and also purchases from domestic producers. These changes are depicted in Figure 1 with the increase in Indian exports from ${E_I}$ to ${E'_I}.$ Because of the higher price in China, overall demand is lower and Chinese imports fall from ${I_C}$ to ${I'_C}.$

Note that the determinant of the coefficient matrix A appears in the denominator of each of the comparative static results. Therefore, the magnitude of each result is dependent on the supply and demand slopes, that is, elasticities, of all countries. The SEM captures the bilateral trade flow changes between any pair of countries which depend on these elasticities. That is why the SEM is highly suitable for analyzing exchange rate changes.

Empirical Model

The four-country theoretical (graphical) model concisely conveys the quantitative (qualitative) impacts of a fall in Yuan value on a pair of exporters and a pair of importers. The comparative statics show the basic trade reallocations that take place as a result of the Yuan–Dollar exchange rate change. These results reflect the expected trade diversions in a world market with only two exporters and two importers; however, the real-world cotton market consists of numerous exporters and importers allowing for many trade reallocations to take place. Consequently, we include 58 regions in the empirical model. The basis of the SEM, from which the market-clearing and spatial-arbitrage conditions of the theoretical model are derived, is an optimization problem. To begin setting up this optimization problem, first consider the following linear supply and demand functions:

(12)$$p_i^D = {a_i} - {b_i}q_i^D,{\kern 1pt} i = 1,...,N$$

(13)$$p_i^S = {c_i} + {d_i}q_i^S,{\kern 1pt} i = 1,...,N$$

where $p_i^D$ is the regional demand price, ${a_i}$ is the demand intercept, ${b_i}$ is the demand slope, $q_i^D$ is the demand quantity, $p_i^S$ is the regional supply price, ${c_i}$ is the supply intercept, ${d_i}$ is the supply slope, and $q_i^S$ is the supply quantity in country $i.$ We utilize these inverse supply and demand functions to set up the SEM optimization problem:

$${L = \sum\nolimits_i^N \left[ {\left( {{a_i} - {b_i}q_i^D} \right)q_i^D - \left( {{c_i} + {d_i}q_i^S} \right)q_i^S} \right] - \sum\nolimits_{i,j}^N {T_{ij}}{X_{ij}} - \sum\nolimits_{i,j}^N {X_{ij}}\left( {\rho _j^D - \rho _i^S} \right) + \sum\nolimits_{i,j}^N {X_{ij}}\left( {\frac{{\rho _j^D}}\over{{\left( {1 + {\tau _{ij}}} \right)*{E_{ij}}}}} - {\rho _i^S} \right)}$$

subject to

(a)$$\sum\nolimits_i^N {X_{ij}} \ge q_j^D,{\kern 1pt} {\kern 1pt} j = 1,...,N,$$

(b)$$q_i^S \ge \sum\nolimits_j^N {X_{ij}},{\kern 1pt} {\kern 1pt} i = 1,...,N,$$

(c)$$\rho _i^D \ge {a_i} - {b_i}q_i^D,{\kern 1pt} {\kern 1pt} i = 1,...,N,$$

(d)$${c_i} + {d_i}q_i^S \ge \rho _i^S,{\kern 1pt} {\kern 1pt} i = 1,...,N,$$

(e)$$\left( {\rho _i^S - {S_i} + {T_{ij}}} \right)\left( {1 + {\tau _{ij}}} \right)*{E_{ij}} \ge \rho _j^D,{\kern 1pt} {\kern 1pt} i,j = 1,...,N,$$

and

(f)$$q_i^D,{\kern 1pt} q_i^S,{\kern 1pt} \rho _i^D,{\kern 1pt} \rho _i^S,{\kern 1pt} {X_{ij}} \ge 0,{\kern 1pt} {\kern 1pt} i,j = 1,...,N,$$

where ${T_{ij}}$ is the per-unit transport cost from $i$ to $j,$${X_{ij}}$ is the quantity traded from $i$ to $j,$$\rho _j^D$ is the market demand price in $j,$$\rho _i^S$ is the market supply price in $i,$${\tau _{ij}}$ is the ad valorem tariff imposed on $i$ by $j,$${S_i}$ is the domestic subsidy in $i,$ and ${E_{ij}}$ is the exchange rate between $i$ and $j.$

The Lagrangian above maximizes the net social monetary gain function of the world cotton market. The interpretation of each term in the Lagrangian is as follows. The SEM maximizes the sum of all countries’ sales revenues, $\sum\nolimits_i^N \left( {{a_i} - {b_i}q_i^D} \right)q_i^D,$ minus producers’ revenues, $\sum\nolimits_i^N \left( {{c_i} + {d_i}q_i^S} \right)q_i^S,$ minus transport costs, $\sum\nolimits_{i,j}^N {T_{ij}}{X_{ij}},$ minus the loss resulting from the price wedge created by a change in the currency value, $ {- \left[ {\sum\nolimits_{i,j}^N {X_{ij}}\left( {\rho _j^D - \rho _i^S} \right)} - {\sum\nolimits_{i,j}^N {X_{ij}}\left( {\frac{{\rho _j^D}}\over{{\left( {1 + {\tau _{ij}}} \right)*{E_{ij}}}}} - {\rho _i^S} \right)} \right].}$ Constraints a) and b) are the market-clearing constraints, similar to those of the theoretical model. The first ensures that the total quantity imported by $j,$ including from itself, is greater than or equal to the total demand in $j.$ The second states that the total quantity exported by $i,$ including to itself is less than or equal to the total supply in $i.$ Constraint c) requires that the market demand price is greater than or equal to the regional demand price. Constraint d) entails the regional supply price is greater than or equal to the market supply price. Note, the market demand (supply) price will be exactly equal to the regional demand (supply) price when there is an interior solution, but greater (less) than the regional demand (supply) price when there is a corner solution. Constraint e) restricts the market demand price in the importing region to be less than or equal to the market supply price minus the domestic subsidy plus transport, tariff, and exchange rate costs. Lastly, constraint f) states that all endogenous variables are nonnegative.

The above maximization problem yields first-order conditions consisting of $3,596$ equations ($58$ demand constraints, $58$ supply constraints, $58$ market versus regional demand price constraints, $58$ market versus regional supply price constraints, and $58 \times 58$ price linkage equations) and $3,596$ endogenous variables ($58$ demand quantities, $58$ supply quantities, $58$ market demand prices, $58$ market supply prices, and $58 \times 58$ bilateral trade flows). This square system of equations is solved simultaneously, and any trade reallocations among countries in response to a change in currency value are determined.

Data and Empirical Analysis

The $58$ regions in the empirical model consist of $57$ major cotton producing, consuming, and trading regions plus an aggregate ROW region. These $58$ regions account for all cotton production, consumption, and trade in the world. Solving the empirical model requires the construction of supply and demand functions, and values for exogenous variables ($T,{\kern 1pt} {\kern 1pt} \tau ,$ and $E$). To construct the supply and demand functions, we compute the intercept and slope parameters using production, consumption, price, and elasticity data for each region. Production, consumption, and price data were gathered from U.S. Department of Agriculture (2018, 2019) and are average values over a 3-year period prior to the trade dispute (2015 to 2017). The production and consumption values for the ROW region are calculated by subtracting the total production and consumption of the 57 regions from the total world production and consumption values. For ROW price, we use the world price in 2017, which was obtained from Statista (2019).

Demand elasticities were obtained from Poonyth et al. (Reference Poonyth, Sarris, Sharma and Shui2004) for 28 of the countries included. Of these 28 countries, 23 of them have demand elasticities of −0.60. The elasticities of the remaining five countries are: China and Pakistan −1.00, Columbia and Mexico −1.30, and India −0.8. For the remaining 29 countries, we considered demand elasticities of −0.6, consistent with the estimates for most of the countries in Poonyth et al. (Reference Poonyth, Sarris, Sharma and Shui2004). Thus, the demand elasticities range in absolute values from a low of −0.6 to a high of −1.3, with a mean elasticity of −0.642. The supply elasticities for 28 countries (reported in Poonyth et al. (Reference Poonyth, Sarris, Sharma and Shui2004)) are the average between the supply elasticities found in Poonyth et al. (Reference Poonyth, Sarris, Sharma and Shui2004) and Shepherd (Reference Shepherd2006). Shepherd (Reference Shepherd2006) has elasticities for eight additional countries that were not covered by Poonyth et al. (Reference Poonyth, Sarris, Sharma and Shui2004), and we used the supply elasticities for these eight countries from Shepherd. For the remaining 21 countries, we utilized supply elasticities of 0.8, which is the supply elasticity for the majority of the 28 countries in Poonyth et al. (Reference Poonyth, Sarris, Sharma and Shui2004). Countries with small supply elasticities are Nigeria (0.251), Cote d’Ivoire (0.339), and Cameroon (0.386), and countries with large supply elasticities are Argentina (1.044), and Bangladesh and Turkmenistan (1.2). The supply elasticities range from a low of 0.251 to a high of 1.2, with a mean elasticity of 0.719. Using the elasticity formula, ${\varepsilon _i} = {\frac{dq_i^S}\over{dp_i^S}}{\frac{p_i^S}\over{q_i^S}}$, and the obtained price and production values, the supply slope is calculated as

$${\frac{{dq_i^S}}\over{{dp_i^S}}} = {\varepsilon _i}{\frac{{q_i^S}}\over{{p_i^S}}} = {D_i}.$$

Using this slope parameter, the supply intercept is computed as

$${C_i} = q_i^S - {D_i}p_i^S.$$

The resulting supply function is $q_i^S = {C_i} + {D_i}p_i^S$, which is then converted into inverse supply equation (13) with intercept ${c_i}$ and slope ${d_i}.$ We construct the inverse demand equation in a similar fashion.

With the computed inverse demand and supply functions, we can run the baseline. However, the baseline solutions for the endogenous variables may not replicate the actual data for these variables because the constructed demand and supply functions are based on elasticities which came from several studies. These studies used different periods and functional forms to estimate these elasticities. To match the baseline solutions to actual data, we calibrate the model by matching the solved values of production, consumption, and trade flows to actual data. For this calibration, we employ the calibration procedure developed by Paris et al. (Reference Paris, Drogué and Anania2009), which adjusts the supply and demand parameters and transport costs such that the model’s baseline results replicate the actual values of the endogenous variables.^{Footnote 11} The data sources for these variables are given above, with the exception of bilateral trade flow data, which came from Simoes and Hidalgo (Reference Simoes and Hidalgo2019). Tariff data for each region were found at World Trade Organization (2019) and Government of Canada (2017). The ROW region, being a conglomerate of several regions, does not have bilateral tariff data of its own. However, any tariffs imposed by or on the ROW region are accounted for in the transportation cost via the calibration process. Furthermore, subsidy data was taken from Hudson (Reference Hudson2018) and EWG (2019), and the Yuan–Dollar exchange rate was collected from International Monetary Fund (2019). Transport costs were obtained using the World Freight Rates (2019) online freight calculator for an average cotton price of $1816.95/metric ton with a 10,000 metric ton (MT) break bulk load. For regions with multiple ports, calculations were made based on the shortest port-to-port distance. For landlocked countries, we included additional transportation costs based on the distance from the nearest port at a price of 0.09$/ton/mile (Qiao and Paggi, Reference Qiao and Paggi2019).

After the model is calibrated, we run two scenarios: a baseline and an alternate. The baseline maintains the Yuan–Dollar exchange rate before the US–China trade war. In the alternate scenario, we increase the Yuan–Dollar exchange rate by 12.6% which implies the Yuan fell relative to the US dollar by 12.6%. The results of the alternate scenario are compared to the baseline scenario to determine the effects of this decline in Yuan value on endogenous variables.