A closed electricity network with three markets is modeled to illustrate the impacts of transmission constraints and market power on prices and economic welfare. Four scenarios are presented, the first two assume perfect competition with and without transmission constraints, while the second two model market power with and without transmission constraints. The results show that transmission constraints reduce total surplus relative to the unconstrained case. When firms exercise market power their profits increase, while consumer surplus and total surplus decrease. Some results are counter intuitive, such as price exceeding the marginal cost of the most inefficient generator in a market with perfect competition, caused by transmission constraints and Kirchoff’s voltage law governing power flows. The GAMS code used to solve the models is included in the appendix. Next steps for research involve building the model to replicate a real-world market, to simulate impacts of proposed market restructuring or to identify areas of deregulated markets at high-risk of market power abuse.