Jack and Jill are the only two residents in a neighbourhood, and they would like to hire a security guard. The value of a security guard is $50 per month to Jack and $90 per month to Jill. Irrespective of who pays the guard, the guard will protect the entire neighbourhood and charge $120 per month for the service. Suppose Jack earns $4,000 per month and Jill earns $8,000 per month.
a. With a proportional tax of 1 percent on income, how much would Jack and Jill pay, and would it be enough to pay for the security guard?
Jack would pay $ ___.
Jill would pay $ _.
This tax _ be enough to pay for the security guard.
b. Suppose instead that Jack proposes a payment scheme under which Jack and Jill would each receive the same net benefit from hiring the guard. How much would Jack and Jill pay now?
Jack would pay $ _.
Jill would pay $ _.
Would both Jack and Jill vote for this scheme? ___

Would both Jack and Jill vote for this scheme? __No___ Jack will feel cheated by Jill in the sum of $3. Jack will likely prefer the 1% based on income.

Explanation:

a) Data and Calculations:

Value of a security guard for Jack = $50 per month

Value of a security guard for Jill = $90 per month

Total value of a security guard for both Jack and Jill = $140 ($50 + $90)

Cost of hiring a guard = $120 per month

Jack's monthly earnings = $4,000

Jill's monthly earnings = $8,000

Total monthly earnings for both Jack and Jill = $12,000

a. Proportional tax of 1 percent on income = $120 ($12,000 * 1%)

Jack will pay $4,000 * 1% = $40

Jill will pay $8,000 * 1% = $80

Total = $120

b. Net benefit scheme:

Jack will pay $50/$140 * $120 = $43

Jill will pay $90/$140 * $120 = $77

Total = $120