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An externality occurs when a third party is affected by an economic activity but does not have control over the actions that led to that impact. These can be either positive, like beekeepers providing pollination benefits to nearby crops, or negative, such as pollution from a factory affecting residents' health.

Consider a factory emitting smoke and soot, impacting the health of nearby residents. This negative externality creates an additional cost for the community, which the factory does not account for when considering its production expenses. In a world with no externalities, the costs and benefits of all transactions would be fully reflected in market prices. However, in reality, externalities are common and can disrupt the balance, leading to inefficient market outcomes unless corrected through negotiation or policy intervention.

Property rights are the legal provisions that determine the ownership and use of resources. They are fundamental for efficient market operations as they assign accountability and allow for the exchange of goods and services.

For example, if a landowner has clear rights to their property, they can negotiate with parties that may cause negative externalities, such as a polluting factory. With these rights established, the landowner can assert their position and seek reparations or solutions to mitigate the negative effects. Well-defined property rights thus help in establishing a platform for negotiation, enabling parties to work towards a mutually beneficial solution.

Transaction costs include any expenses incurred during the process of exchange or negotiation between parties. These can be monetary, such as legal fees, but can also include time, effort, and even psychological burdens.

High transaction costs can hinder negotiations and prevent parties from reaching an agreement. If, for instance, the cost of negotiating with a polluting factory exceeds the benefits of reduced pollution, the affected resident may decide it's not worth pursuing a resolution. This is where the Coase theorem suggests that with zero transaction costs, negotiations will lead to an efficient outcome, as parties can easily reach agreements that improve overall welfare.

An efficient market outcome is one in which resources are allocated in the most beneficial way for all parties involved, taking into account all costs and benefits. The Coase theorem posits that with zero transaction costs and well-established property rights, parties will naturally negotiate to correct any externalities and reach an efficient outcome.

Continuing with the previous example, if the resident and factory can bargain without costs or barriers, they can achieve a solution beneficial to both. The resident's well-being is improved with reduced pollution, and the factory may benefit from community support or subsidies to implement clean technologies. This is the ideal scenario envisioned by the Coase theorem, where the market corrects itself through private negotiation.