<Dd> ∑ j ≠ i v j (θ j, κ i ~ (θ − i)) − ∑ j ≠ i v j (θ j, κ ∗ (θ)) (\ displaystyle \ sum _ (j \ neq i) v_ (j) (\ theta _ (j), (\ tilde (\ kappa _ (i))) (\ theta _ (- i))) - \ sum _ (j \ neq i) v_ (j) (\ theta _ (j), \ kappa ^ (*) (\ theta))), </Dd> <P> where θ − i (\ displaystyle \ theta _ (- i)) is the type vector θ (\ displaystyle \ theta) without its i (\ displaystyle i) - th component . Intuitively, the first term is the hypothetical total payoff for all agents j ≠ i (\ displaystyle j \ neq i) given that agent i (\ displaystyle i) does not exist, and the second (subtracted) term is the actual total payoff for all agents j ≠ i (\ displaystyle j \ neq i) given that agent i (\ displaystyle i) does exist . </P> <P> Voluntary exchange is by definition mutually beneficial to both business parties involved, because the parties would not agree to undertake it if either thought it detrimental to their interests . However, a transaction can cause effects on third parties without their knowledge or consent . From the perspective of those affected, these effects may be negative (pollution from a nearby factory), or positive (honey bees kept for honey that also pollinate neighboring crops). Neoclassical welfare economics asserts that, under plausible conditions, the existence of externalities will result in outcomes that are not socially optimal . Those who suffer from external costs do so involuntarily, whereas those who enjoy external benefits do so at no cost . </P> <P> A voluntary exchange may reduce societal welfare if external costs exist . The person who is affected by the negative externalities in the case of air pollution will see it as lowered utility: either subjective displeasure or potentially explicit costs, such as higher medical expenses . The externality may even be seen as a trespass on their lungs, violating their property rights . Thus, an external cost may pose an ethical or political problem . Alternatively, it might be seen as a case of poorly defined property rights, as with, for example, pollution of bodies of water that may belong to no one (either figuratively, in the case of publicly owned, or literally, in some countries and / or legal traditions). </P>

What is the difference between negative and positive externalities
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