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Show that externalities are Pareto inefficient, (in-depth answer would be really appreciated - I'm really stuck)

Show that externalities are Pareto inefficient, (in-depth answer would be really appreciated - I'm really stuck)

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Externalities impacts the allocation of resources because the market failure to fully price the external effects generated by few economic activities. It occurs because market prices tend to reflect the cost sellers charge buyers of a good, the price based on the derived personal utility, and ignoring the benefits/costs imposed on third parties. Therefore the mechanism of pricing fails to reflect the social or true costs of economic activity and consequently the private costs may diverge from true costs. The allocation of resources will be based of private production and/or consumption decisions and not on social welfare maximising ones and for this causes resources will be inefficiently allocated. The failure of all relevant impacts for making their effect on the pricing system will causes in a sub-Pareto optimum resource allocation because the social marginal cost (MSC) of a product or service will not equal to the marginal private cost (MPC) that equals its price.

Thus the existence of externalities will result to sub-optimal allocation as either too much resources will be used in processes conferring uncompensated costs to society or too few are applied in processes conferring uncompensated benefits to society as the profit maximising output will not be more than the socially optimal output

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