3. Externalities. Consider a firm that causes pollution in a lake affectinga group of individuals. The production cost of the firm is c(q) = cq²/2,where c> 0 and q is the quantity produced by the firm, and the total costimposed on the individuals (adding the costs suffered by each of them) is(q) = pq²/2, where > 0.(a) Suppose initially that the firm cannot bargain, trade, or otherwisecompensate the individuals. Calculate the profit maximizing choiceof output by the firm, the revenue of the firm, the private cost of thefirm, the externality that the firm imposes over the individuals, andthe total social cost.(b) Suppose now that the individuals affected by pollution in the lakeown the lake, and that they organize to sell pollution permits, witha price of p, so that the firm must pay p per unit of output. Findthe competitive price of pollution permits, as well as the profit max-imizing choice of output by the firm if the firm must buy pollutionpermits and buys them at the competitive price.

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Answered: 3. Externalities. Consider a firm that…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Externalities. Consider a firm that causes pollution in a lake affecting
a group of individuals. The production cost of the firm is c(q) = cq²/2,
where c> 0 and q is the quantity produced by the firm, and the total cost
imposed on the individuals (adding the costs suffered by each of them) is
(q) = pq²/2, where > 0.
(a) Suppose initially that the firm cannot bargain, trade, or otherwise
compensate the individuals. Calculate the profit maximizing choice
of output by the firm, the revenue of the firm, the private cost of the
firm, the externality that the firm imposes over the individuals, and
the total social cost.
(b) Suppose now that the individuals affected by pollution in the lake
own the lake, and that they organize to sell pollution permits, with
a price of p, so that the firm must pay p per unit of output. Find
the competitive price of pollution permits, as well as the profit max-
imizing choice of output by the firm if the firm must buy pollution
permits and buys them at the competitive price.

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I'm unsure about the two Ps in the final part of the answer. Are those both the same variable? It seemed unclear to me how and why that happened. Can you help with that really quickly?

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