Answer to Question #254759 in Microeconomics for Burak

Question

Mike, Rosie, and Shobber live in separate houses along a dark and windy road. The following represent their marginal benefits for street lights:

MBMike=200-2QM

MBRosie=100-QR

MBShobber=100-2QS

where QM represents the quantity of street lights consumed by Mike, QR is the quantity of street lights consumed by Rosie and QS is the quantity of street lights consumed by Shobber. The Mayor of their town considers street lights to be a public good and is charged with purchasing the optimal number of street lights from Boone’s Light Shop. Boone’s is willing to sell street lights for $150 per light.

 

 

 

 

b. What quantity of street lights should the Mayor purchase? Why? Suppose the Mayor is able to implement a pricing scheme to charge users for the illumination services.

c.  How much should each individual be charged? Does the tax revenue cover the total cost of providing the optimal number of streetlights?

Answer 1

b.)

we have ,

$Mb = Mc\\ 200 - 2Q+ 100 -Q + 100 - 2Q = \$150\\ 400 -150 = 5Q \\ Q = 50$

therefore, no. of streetlights purchased by mayor = 50 

Because the equilibrium or maximum utility or satisfaction will be ,

when Marginal benefit = Marginal cost .

c.)

Individuals will pay according to their marginal benefit/ satisfaction.

Mike will pay = 200 - 2Q  = $ 100

Rosie will pay = 100 - Q = $ 50

and Shobber will pay = 100 - 2Q = $ 0 

so,

yes the tax revenue cover the total cost of providing optimum no. of streetlights.