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19 January, 15:52

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).

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  1. 19 January, 16:03
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    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%
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