# Trade - C3IAM

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Taking foreign trade into account, we adopts Armington assumption, which assumes there is imperfect substitutability between imports and domestic output sold domestically. The degree to which domestic and imported goods differ is reflected by the elasticity of substitution between them. Changes in the relative shares of foreign and domestic goods in the composite are determined by changes in the relative prices of these goods at home and abroad, given the Armington substitution elasticity and the initial shares of these goods in the benchmark SAM (Social Accounting Matrix). The commodity that supplied domestically is composed of domestic and imported commodities following a CES function. Furthermore, domestic commodity is used to meet domestic demands and for exports. In C3IAM, we use a constant elasticity transformation (CET) function to allocate total domestic output between exports and domestic sales, shown in Equations. (1) and (2).

${\displaystyle X_{i,r}=A_{Ex,i,r}\centerdot [\alpha _{Ex,i,r}\centerdot E_{i}^{\rho _{Ex,i,r}}+(1-\alpha _{Ex,i,r})\centerdot D_{i}^{\rho _{Ex,i,r}}]{\frac {1}{\rho _{Ex,i,r}}}}$(1)

${\displaystyle {\frac {E_{i},t,r}{D_{i},t,r}}=[{\frac {1-\alpha _{E}X,i,r}{\alpha _{E}X,i,r}}\centerdot {\frac {PE_{i},t,r}{PD_{i},t,r}}]_{E}^{\alpha }X,i}$(2)

Where ${\displaystyle E_{i,r}}$and${\displaystyle D_{i,r}}$respectively represent exports and domestic sales of domestically produced good ${\displaystyle i}$in region ${\displaystyle r}$; ${\displaystyle PE_{i,r}}$and ${\displaystyle PD_{i,r}}$respectively represent export price and domestic sale price of domestically produced good ${\displaystyle i}$in region ${\displaystyle r}$;  and

${\displaystyle \alpha _{Ex,i}}$respectively represent the shift parameter and share parameter in transformation function;

${\displaystyle \rho _{Ex,i}}$and ${\displaystyle \sigma _{Ex,i}}$respectively represent the substitution parameter and substitution elasticity in CET function between export and domestic sales.