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23 February, 04:44

Suppose that demand for a product is Q = 1200 - 4P and supply is Q = - 240 + 2P. Furthermore, suppose that the marginal external damage of this product is $12 per unit. How many more units of this product will the free market produce than is socially optimal? Calculate the deadweight loss associated with the externality.

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  1. 23 February, 05:14
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    Answer: 16 units more than social optimum.

    DWL = dead weight loss = (1/2) * (Q * - Q°) 12 = 96

    Explanation:

    Q=1200 - 4P and Q=-240 + 2P

    In a free market quantity demand = quantity supplied

    1200 - 4P = - 240 + 2P

    P = 240

    Sub P

    Q * = 240

    Socially optimal quantity is

    Marginal social benefit (MSC) = marginal social cost (MSC), including external damage = MEC

    MPC = marginal private cost = inverse of supply function

    MPC = (1/2) * Q + 120

    MEC=12

    MSC = (MPC + MEC) = (1/2) Q + 120 + 12

    MSC = MPB where MPB is marginal private benefit = inverse of demand functn

    MPB = 300 - (1/4) Q

    (1/2) Q + 132 = 300 - (1/4) Q

    Q° = 224

    Difference btw Q * & Q° = 16 units more than social optimum.

    DWL = dead weight loss = (1/2) * (Q * - Q°) 12 = 96
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