Traders may not always find what they want due to search frictions, leading to market rationing. A new model incorporates this uncertainty into commodity definitions, affecting prices. The traditional idea of market equilibrium is expanded to include a matching condition reflecting the trading process's friction. This model, using linear programming, shows that when search frictions disappear, it aligns with a known competitive assignment model. The approach used allows for broader application of efficiency and existence results in economies with search frictions. Linear programming can be used to compute equilibria in this framework.