Conditions for Efficiency in Resource Allocation in a Perfectly Competitive Market

To achieve efficiency in resource allocation under a perfectly competitive market, the following conditions must exist:

1. Perfect information -  All households and firms have perfect information on everything they have to know about the goods - prices, quality, future prices, prices of inputs, quality of those inputs, productivity of these inputs, etc.
2. No Joint Consumption - No two persons can consume the same commodity simultaneously.  Only the individual consuming that good gets satisfaction from it.
3. No Externalities - When a person produces or consumes a good or service, the costs and benefits of consuming or producing that good accrue to him alone. That is, all the costs are borne by him and all the benefits go to him. There are no costs and benefits to others as a result of that consumption or production - no external effects.
4. No Economies of Scale in Production - The term economies of scale implies that the more one produces, the larger is his volume, the lower is the unit cost, or the so-called "cheaper by the dozen". In a perfectly competitive market, we assume that it is not cheaper by the dozen but there is a constant return to scale for each additional output; that is, each additional output  will cost as much as or even more than the previous one.
5. Consumers Maximize Utility while Producers Maximize Profits - In a free market system, it is assumed that consumers and producers maximize their own self interest. However, this might not be true in real life. Producers might have other motives besides profits.  On the other hand, consumers might not always maximize utility in the usual sense but might blindly follow fashion.
6. Competition - The market has a large number of buyers and sellers, such that no single buyer or seller can manipulate the price.  
7. Freedom of Entry and Exit - There are many buyers and sellers, and each one can enter and leave the market.

The seven characteristics above are assumptions of a perfectly competitive market system whose operation alone will lead to efficient resource allocation. Since these assumptions do not exist in the real world, we might then deduce that operations of markets and prices do not lead to efficient resource allocation.  Thus, we might say that there is market failure.