Question

Assume there are four people in a city. Person A owns nothing, person B owns a chicken shack worth $10,000, person C owns a small garden worth $130,000 and person D owns a cottage worth $240,000. They want to finance a public children’s zoo, a local public good. The zoo will cost $56,000 and should be financed by a property tax with equal tax rates per property value. Calculate the tax rate (in %) for the following cases
a. all four people live in the city.
b. there is a city of four B-like people.
c. there is a city of four C-like people.
d. there is a city of four D-like people.
e. there is a city of only one A, one B and one C (D has left).

Answer 1

Answer:

a) X = 14.7%

b) X = 140%

c) X = 10.76%

d) X = 5.83%

e) X = 40%

Explanation:

As per the data given in the question,

a) Let the tax rate be = X%

then 0+(X × 10,000)÷100+(X × 130,000)÷100+(X × 240,000)÷100 = $56,000

100X+1,300X+2,400X = $56,000

X = $56,000÷3,800

= 14.7%

b) ((X × 10,000)÷100)× 4 = $56,000

400X = $56,000

X = 140%

c) ((X × 130,000)÷100)×4 = $56,000

5,200 X = $56,000

X = 10.76%

d) ((X × 240,000)÷100 )×4 = $56,000

9,600 X = $56,000

X = 5.83%

e) X× 0+(X × 10,000)÷100+(X × 130,000)÷100 = $56,000

1,400 X = $56,000

X = 40%