Answer to Question #251964 in Microeconomics for lisa

Question

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

MB_Mike=200-2Q_M

MB_Rosie=100-Q_R

MB_Shobber=100-2Q_S

where Q_M represents the quantity of street lights consumed by Mike, Q_R is the quantity of street lights consumed by Rosie and Q_S 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.

a.     In what sense, if any, do street lights qualify as a public good? What is the relationship between Q_M, Q_R, and Q_S (i.e., greater than, less than or equal to) likely to be when the Mayor installs the lights? Why?

Answer 1

$MB_{Mike}=200-2Q_M \\ MB_{Rosie}=100-Q_R \\ MB_{Shobber}=100-2Q_S$

street lights = $150

Total marginal benefits = $MB_{Mike} + MB_{Rosie} + MB_{Shobber}$

$= 200-2Q_M + 100- Q_R + 100 -2Q_S \\ = 400 -5Q$