This thesis investigates questions of international trade, multinational firm production and economic growth. Firstly, Chapter 2 quantifies the total gains from openness such that firms can either export to their foreign markets or carry out horizontal FDI characterised by intra firm exports of intermediate inputs from parent firms to their subsidiaries. This is motivated by the fact that despite empirical evidence on the rising importance of intermediate good inputs in trade shares, literature on gains from trade has not adequately accounted for intermediate input share in calculating total trade gains. Intermediate input shares play an important role as they affect the trade elasticity hence welfare changes, we find that gains from trade and FDI derived in this model are higher than the current documented gains in trade literature. Chapter 3 presents a dynamic general equilibrium model of corporate taxation of heterogeneous productivity firms that enter foreign markets via exports or setting up a multinational firm subsidiary. This model is at the nexus of international trade models of firm heterogeneity and endogenous growth model without scale effects. Chapter 4 investigates international trade of exhaustible resources in a differential game over a continuous time. When exhaustible resources are concerned in questions of economics, inter-temporal trade offs between generations cannot be ignored as resources are depleting. Standard static models of international trade that argue that countries trade because of different factor endowments are not enough because resource prices change over time, and the exhaustible resource endowment is also declining over time. It is therefore natural to consider dynamic tools such as differential games to address economic questions of trade of exhaustible resources. Central to our study is the result that Hartwick's rule is broken, i.e. not all resource rents are reinvested into capital.