Suppose that the community of Twainville consists of three people with the following marginal benefits (MB) for street lights provided in quantity q:
Tom:MB = 1,500 - 5q for 0 # q # 300, MB = 0 elsewhere,
Sally: MB = 2,100 - 7q for 0 # q # 300, MB = 0 elsewhere,
Huck: MB = 2,100 - 5q for 0 # q # 420, MB = 0 elsewhere
a. If the marginal cost of streetlights is $3,150 what is the optimal number of lights to install in the city?
b. Compute each person’s marginal benefit at the optimal number of streetlights. Check to make sure that the marginal benefits for the three residents sum to the marginal cost.
c. If we finance the streetlights with a lumps-sum tax of $1,050 where each resident pays one-third of the marginal cost, how will each resident react? (compare each resident’s MB to the tax price of 1,050.)