Question

Big changes can happen to wealth distribution. In the twentieth century those were WWII and the Reagan presidency. Both profoundly changed wealth distribution. Below we have an economy undergoing such a transition in periods A, B. Given are decile distributions (example, for the poorest 20% of the population system A pays 4% of the country’s wealth to this segment whereas B pays 2%).

CAUTION: The deciles below are cumulative, hence any change is carried forward and felt long after. For example decile 30% have a 3 (9-6) difference. However the difference really is only 1 (9-4 versus 62).

% Population % Income A               % Income B

10                            1                              1

20                            4                              2

30                            9                              6

40                            16                           12

50                            25                           20

60                            36                           31

70                            49                           44

80                            64                           60

90                            81                           78

100                         100                         100

1.Despite both 10% being paid the same, system _ pays more to decile 20% through _ %.

a.How many of the middle deciles are paid the same?

b.These same paid deciles are:

2.The biggest difference between the two systems is what is paid to decile _ %. 5.Of all data in both systems, the decile paid the most is _ % in system _

3.System _ has a more equitable wealth distribution.

Answer 1

Statement Showing the calculation of required Information:

A = Given    D = % Income A of Current Decile - % Income A of previous Decile

B = Given E = % Income B of Current Decile - % Income B of previous Decile

C = Given F = Difference of Data calculated in D & E Column

A	B	C	D	E	F
% Population	% Income A   (Cumulative Data)	% Income B   (Cumulative Data)	% Income A   (Individual Data)	% Income B   (Individual Data)	Difference of Coloumn D & E
10	1	1	1	1	0
20	4	2	3	1	2
30	9	6	5	4	1
40	16	12	7	6	1
50	25	20	9	8	1
60	36	31	11	11	0
70	49	44	13	13	0
80	64	60	15	16	-1
90	81	78	17	18	-1
100	100	100	19	22	-3

Answers

(i) Despite both 10% being paid the same, system A pays more to decile 20% through 2 % ( Difference Column - F )

(ii) & (iii) "2" middle deciles are paid the same at 60% % 70%, as the difference between both the income A & B is 0 ( Difference Column -F  )

(iv) The biggest difference between the two systems is paid at decile 100%. i.e., 3% ( Difference Column - F )

(v) Of all data in both systems, the decile paid the most is 22% in system B at 100% decile ( % Income Of Individual Data - Column E Value )

(vi) System "A"  has a more equitable wealth distribution as at every next % of Population system A increase its wealth distribution by 2 % however system "B" has no such systematic increase in the Wealth Distribution.