Theory question 102
Tools of Economic AnalysisA village consists of twenty (20) households with the following annual incomes:
Incomes ($00)
30 | 20 | 50 | 40 | 60
40 | 40 | 50 | 20 | 60
80 | 40 | 20 | 20 | 70
40 | 70 | 30 | 40 | 80
(a) Determine the (i) mean income; (ii) modal income; (iii) median incomes
(b) What is the range of the income distribution?
(c) Calculate the total tax that could be generated from the village if (i) a flat rate tax of 7% is imposed on all households; (ii) a flat rate tax of 15% is imposed on all households earning $4,000 per annum and above.
Show the model answer
(a)(i) Total = 900 ($00) = $90,000; mean = 900 ÷ 20 = 45, i.e. $4,500
(ii) 40 occurs most often (6 times): mode = $4,000
(iii) Arranged in order, the 10th and 11th values are both 40: median = $4,000
(b) Range = 80 − 20 = 60, i.e. $6,000
(c)(i) 7% × $90,000 = $6,300
(ii) Households earning $4,000 and above: 6 × 40 + 2 × 50 + 2 × 60 + 2 × 70 + 2 × 80 = 760 ($00) = $76,000; 15% × $76,000 = $11,400
Remember the figures are in hundreds of dollars.