lecture19

# lecture19 - Externalities An externality occurs whenever...

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1 Externalities • An externality occurs whenever the activities of one economic agent affect the activities of another agent in ways that are not taken into account by the operation of the market. •E x am p l e s : – One firm produces down river from another firm. The first firm pollutes the river and prevents the second from producing. – Doctor works next door to a noisy factory. – I care what my daughter eats. A Downriver Externality • Consider the firms on the river example. Both firms use only labor as an input. – The upriver firm produces Y with a production function of Y = g ( L Y ). – The downriver firm produces X. Its production is affected by the upriver firm’s production: X = f ( L X ; Y ), where: 0 < Y X The Social Optimum • Suppose there is a fixed amount of labor L in the economy. • Suppose prices for X and Y are P x and P y . • The total value of output is P x X + P y Y . • At the social optimum, labor is allocated to the two firms such that the total value of output in the economy is maximized: () () L L L t s L Y P Y L X P L L y x y y x x y x = + + . . ; , max First Order Condition at the Social Optimum • The first order conditions are: 0 = ÷ ÷ ø ö ç ç è æ = λ y x x x L Y Y X L X P L V 0 = = λ y y y L Y P L V y y y x x L Y P L Y Y X L X P = ÷ ÷ ø ö ç ç è æ 0 = = y L L L V λ This “extra” term arises because of the externality. The Market Will Not Lead to the Social Optimum • In a competitive market, price taking maximize profits: π x = P x X - wL x and π y = P y Y wL y • The first order conditions in a competitive market are: 0 = = w L X P L x x x x π 0 = = w L Y P y y y y π x x y y L X P L Y P = This is not the same f.o.c. as the social optimum. Firm Y ignores the externality it imposesonXandproduces too much. Can the Market be Fixed? • Pigouvian taxes – Impose a tax ( t ) on the production of Y such that it chooses to cut back production to the socially optimal level. – Y’s profits after the tax are π y =( P y -t ) Y wL y – Y’s new f.o.c. is: – For the socially optimal amount: () 0 = = w L Y t P L y y y π Y X P t x

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2 Can the Market be Fixed? (II) • The firms can merge. – If X and Y merge, the new super firm will maximize
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## This note was uploaded on 02/11/2012 for the course ECON 51 at Stanford.

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lecture19 - Externalities An externality occurs whenever...

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