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25 January, 03:40

Suppose 20 people each have the demand Q=20-P for streetlights, and 5 people have the demand Q=18-2P for streetlights. The cost of building each streetlight is $10. If it is impossible to purchase a fractional number of streetlights, how many streetlights are socially optimal?

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  1. 25 January, 03:54
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    Q = 435/22.5 = 19 streetlights

    Explanation:

    Since the streetlights is apublic good

    Obtaining the market demand curve by adding them vertically

    P = 20*20Q - 20*Q

    P = 5 * ( - 5*Q/2

    hence

    P = 445 - 22.5Q

    Socially optimal number of street lights

    MB20 + MB5 = MC

    400 - 20Q + 45 - 2.5Q = 10

    22.5Q = 435

    Q = 435/22.5 = 19 streetlights
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