a. The Coase theorem requires that: government is active and markets are competitive. government is active and transaction costs are low property rights are well defined and markets are competitive. Oproperty rights are well defined and transaction costs are low. b. Under the Coase theorem, resources will allocate toward their highest-valued use: based on who has the most resources if the households (or others affected) own the property rights. if the polluter owns the property rights regardless of who owns the property rights.