Recently, international trade becomes an important part of the world economy. Every country needs raw materials from other countries to produce intermediate and final goods that are needed. The objectives of dissertation are therefore two-fold. First, the static import demand system is presented and estimated by employing Deaton & Muelbauer's (1980) Almost Ideal Demand System (AIDS). The indirect production function is applied to generate this system. Because of the limitations of static analysis, the second objective is to incorporate intertemporal production behavior as summarized by the Euler equation. The input demand system and the Euler equation constitute a system of recursive equations with cross-equation parameter restrictions, which require the jointly estimation of the input demand system and the Euler equation. More importantly, these systems are estimated by a careful implementation of the orthogonality conditions using generalized method of moments. The input demand systems are illustrated with an application to Australian quarterly data. Results indicate that the proposed methods are operational. The signs and size of the estimated Marshallian, Morishima elasticity of substitution, intertemporal elasticity of substitution and Frisch price elasticities are found to be sensible, and capital and imports are found to be substitution, which is inconsistent with the findings in earlier studies.