Competitive Equilibrium in a Radial Network

We examine a competitive market in which producers and consumers are scattered around the economy, linked by a network with finite capacity, along which the good has to be delivered for consumption. A most prominent example would be the deregulated electric power market. Because of the complexity of transaction across the network, the equilibrium allocation is generally complicated. However, we can focus without loss of generality on a class of allocations, called simple allocations, in which the net transaction over a link is equal to the gross transaction over the same link. If a simple allocation can be sustained by an equilibrium, then the allocation must be efficient. If an equilibrium induces a simple allocation that is no longer sustained by an equilibrium, the original equilibrium allocation is not efficient. For any efficient allocation, we can find a simple allocation that can be sustained by a competitive equilibrium, which reveals the structure of the competitive equilibrium allocations and the equilibrium prices.