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Andre45
6 days ago
12

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?
Business
1 answer:
arsen [3.2K]6 days ago
8 0

Response:

Q = 435/22.5 = 19 streetlights

Clarification:

Given that the streetlights represent a public good

To derive the market demand curve, we sum them in a vertical manner

P = 20*20Q - 20*Q

P = 5*( - 5*Q/2

thus

P = 445 - 22.5Q

The social optimum quantity of streetlights

MB20 + MB5 = MC

400 - 20Q + 45 - 2.5Q = 10

22.5Q = 435

Q = 435/22.5 = 19 streetlights

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