Question

The accompanying table below shows the marginal benefits (willingness to pay) that accrue to Ted, Barney and Marshall from different numbers of police officers providing protection (a public good) to their neighborhood. The marginal cost of one police officer is $1,600.

	Ted	Barney	Marshall
Q	MB	MB	MB
1	$1,000	$1,200	$1,500
2	$800	$1,000	$1,200
3	$600	$800	$900
4	$400	$600	$600
5	$200	$400	$300
6	$0	$200	$0
7	$0	$0	$0

Question 3 of 4

6 Points

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What follows is a numeric fill in the blank question with 3 blanks.

Using Lindahl pricing, what share of the tax burden should each of the three individuals pay?
Ted should pay $   per officer
Barney should pay $   per officer
Marshall should pay $   per officer  

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Answer 1

Solution:

To answer about the Lindahl pricing share, first we find the optimum number of police officers chosen. (Social) Marginal cost is given to be constant at $1600 per officer. Optimum occurs where social marginal benefit at a quantity of public good equals its social marginal cost (SMC).

We are given private marginal benefits at different levels, and social marginal benefit (SMB) can be derived simply by summation of private marginal benefit. Then, social marginal benefit at:

1 officer = 1000 + 1200 + 1500 = $3700

2nd officer = 800 + 1000 + 1200 = $3000

And so on...

At 4th officer, SMB = 400 + 600 + 600 = $1600 = SMC

So, optimally 4 officers will be chosen. Then, share of Lindahl tax falling on:

Ted = 400/1600 = 25%, Barney = 600/1600 = 37.5%, Marshall = 600/1600 = 37.5%

With marginal cost of $1600 per officer, total cost = 1600*4 = $6400

So, Ted share is 25%*6400 = $1600 on 4 officers or 1600/4 = $400 per officer

Barney share is 37.5%*6400 = $2400 on 4 officers or 2400/4 = $600 per officer

And Marshall share is 37.5%*6400 = $2400 on 4 officers or 2400/4 = $600 per officer.