In this paper we present a modeling framework for analyzing natural gas markets, taking into account the specific technological issues of gas transportation. We model the optimal dispatch of supply and demand in natural gas networks, with different objective functions, i.e., maximization of flow, and different economic surpluses. The models take into account the physical structure of the transportation networks, and examine the implications it has for economic analysis. More specifically, pressure constraints create system effects, and thus, changes in one part of the system may require significant changes elsewhere. The proposed network flow model for natural gas takes into account pressure drops and system effects when representing network flows. Pressure drops and pipeline flows are modeled by the Weymouth equation. A linearization of the Weymouth equation makes economic analyses computationally feasible even for large networks. However, in this paper, the importance of combining economics with a model for pressure drops and system effects is illustrated by small numerical examples.