Question

Ketmoree, G St Wunderbar and Red 88 Noodle bar, all located within a short distance on G Street are the three players in this problem, and we will call them A, B and C respectively. Suppose that they would benefit from security lights in the parking lot according to the following demand functions: PA = 65 - Q, PB = 45 – 3Q, Pc = 20 – 20 for A, B, and C, respectively. If security lights cost $60 each, in other words market supply is p = 60, what is the socially efficient quantity of lights? How many security lights will be purchased if each store buys its own lights?

Answer 1

Street light is a public good, so market Demand curve for public good is Vertical Summation of individual demand Curves.

So market demand Curve

P = PA + PB + PC, if Q <= 10

P = 65-Q + 45-3Q + 20-2Q

P = 130 - 6Q

If , 10<Q<=15

P = PA+PB

P = 110-4Q

If Q> 15

P= PA = 65-Q

P = 65-Q

So at eqm, P = 60, so it cuts the demand curve

If P = 60, so,

60 = 110-4Q

Q = (50)/4 = 12.5

If 60= 130-6Q

Q = 70/6 = 11.67 > 10, not possible

socially efficient light Q = 12.5

if each behaves independently,

then PA = 60 = 65-Q

QA* = 5,

store B & C will not buy lights, bcoz Maximum WTP is less than 60

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