Assignment:
Invariance. With zero transaction costs, the farmer fences the cornfield rather than the rancher fencing the ranch-regardless of the rule of law. Notice that in this example, the use of the fields for cattle-ranching and corn growing is the same, regardless of the initial assignment of property rights. This version of the Coase Theorem is called the invariance version (because the use of resources is invariant to the assignment of property rights). This version turns out to be a special case. The more general case is one in which the resource allocation will be efficient (but not necessarily identical), regardless of the assignment of property rights. There will be a Pareto-efficient allocation of goods and services, but it may be different from the Pareto-efficient allocation that would have resulted from assigning that same entitlement to someone else.
To illustrate, assume that farmers like to eat more corn and less beef, whereas ranchers like to eat more beef and less corn. Assume that farmers and ranchers own their own land, that transaction costs are zero, and that fence is costly relative to their incomes. The change from "ranchers' rights" to "farmers' rights" will increase the income of farmers and decrease the income of ranchers.
Consequently, the demand for corn will increase, and the demand for beef will decrease. Greater demand for corn requires the planting and fencing of more cornfields. Thus, the change in law causes the building of more fences. Remember the distinction between "price effects" and "income effects" in demand theory? Can you use these concepts to explain this example?