Micro-Chapter11 - 11 Externalities and Public Goods 1 A...

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11 Externalities and Public Goods 1 11 Externalities and Public Goods 1. A simple Bilateral Externality 2. Solutions to the Externality Problem 3. Public Goods 4. Multilateral Externalities, Private Information and Second Best Solutions Exercises 11.B.3, D.5, E.5 11 Externalities and Public Goods 2 1. A simple bilateral externality Consider two consumers i = 1,2 whose utility functions depend not only on the own consumption but also on some action h taken by consumer 1. Taking prices as given and to be unaffected, we may simplify the derived utility function as the concave function Suppose we are at a competitive equilibrium so that consumer 1 chooses his optimal level of h to maximize . Hence the equilibrium h* satisfies the first-order condition . In contrast, for any Pareto optimal allocation, the optimal level of h , h o must maximize the joint surplus of the two consumers and thus in optimum. ) ( h i φ ) ( 1 h φ 0 ) ( ´ 1 = h φ ) ( ´ ) ( ´ yields which ) ( ) ( max 2 1 2 1 o o h h h h h φ φ φ φ = +
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11 Externalities and Public Goods 3 1. A simple bilateral externality h * h ) ( ´ 1 h φ o h * 2 1 0 ) ( ´ ) ( ´ h h and thus h h ty gives externali A negative o o o < > = φ φ ) ( ´ 2 h φ 11 Externalities and Public Goods 4 2. Solutions to the externality problem Suppose that consumer 1 is made to pay a tax t h per unit of h . This implies that the optimal tax to implement the optimal level is Consumer 1 chooses the level of h solving which is, indeed, the optimal level . Results : Optimality can be achieved either by (directly) taxing the externality or by subsidizing its reduction (in case of a positive externality). ) ( ´ 2 ° = h t h φ h h h t h h t h = ) ( ´ yields which ) ( max 1 1 φ φ
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11 Externalities and Public Goods 5 h ) ( ´ 1 h φ o h ) ( ´ 2 h φ 2. Solutions to the externality problem ) ( ´ 2 ° = h t h φ 11 Externalities and Public Goods 6 Second approach: assign the enforceable property right to an „externality-free“ environment to consumer 2, so that consumer 1 is unable to engage in his externality-generating activity without consumer 2´s permission. Assume consumer 2 demands a payment of T in return for permission to generate externality level h . Then consumer 2 will solve
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