International Trade

International Trade#

The standard model distinguishes imported, domestically sold and exported goods.

Domestic and imported varieties are imperfect substitutes:

\[Q_i = \gamma_i \left[ \delta_i^m M_i^{\eta_i} + \delta_i^d D_i^{\eta_i} \right]^{1/\eta_i}.\]

The relative prices of imports and domestic goods therefore influence how composite demand is divided between \(M_i\) and \(D_i\).

The import first-order condition is:

\[M_i = \left[ \frac{ \gamma_i^{\eta_i}\delta_i^m p_i^q }{ (1+\tau_i^m)p_i^m } \right]^{1/(1-\eta_i)} Q_i.\]

Import tariffs therefore enter through the tariff-inclusive import-price wedge.

Domestic output can be allocated between exports and domestic sales using a constant-elasticity-of-transformation relationship:

\[Z_i = \theta_i \left[ \xi_i^e E_i^{\phi_i} + \xi_i^d D_i^{\phi_i} \right]^{1/\phi_i}.\]

The corresponding export-supply condition is:

\[E_i = \left[ \frac{ \theta_i^{\phi_i}\xi_i^e(1+\tau_i^z)p_i^z }{ p_i^e } \right]^{1/(1-\phi_i)} Z_i.\]

Relative export and domestic prices influence the allocation of output between export and domestic markets.

World prices are converted into local-currency prices by the exchange rate:

\[p_i^e = \varepsilon p_i^{We}, \qquad p_i^m = \varepsilon p_i^{Wm}.\]

The balance-of-payments condition is:

\[\sum_i p_i^{We}E_i + S^f = \sum_i p_i^{Wm}M_i.\]

Together, these equations allow a tariff, world-price or external-balance shock to propagate through domestic production and demand.