BILL ADONGO

LIFE TIME:

BILL ADONGO(1983-present) is the greatest Actuary and Economist of all time. He is known by his Central Point Law and Point Values Interval Law which has great influence in economics and many areas of studies. Below is one of his applications in his diary.

BILL ADONGO INCOME ELASTICITY AND BUDGET THEORY

Consider that consumer has an income equal to M that spent on the good X and Y. If we represent P_x and P_y to be the prices of two goods X and Y respectively: The income increased by ∆M and the price of the two goods increased by ∆Q_x and ∆Q_y, at budget constraint equation

∆M=P_x∆Q_x + P_y∆Q_y:  there is independent prediction of the prices P_x and P_y which is given as;

P_xi=∆M/2∆Q_xi

P_yi=∆M/2∆Q_yi

[P_xi, P_yi]=[(∆M/2∆Q_xi, ∆M/2∆Q_xi+∆M/2∆Q_xi, ...);(∆M/2∆Q_yi, M/2∆Q_yi - ∆M/2∆Q_yi, ..)]

Let us, also considered that income elasticity of demand equation K_xe_xi + K_ye_yi=1 where K_x denote proportion of income spent on good Y, e_xi for good X, and e_yi for income elasticity of demand for good Y. Then, there is independent forecasting of e_xi and e_yi. This is defined as:

e_xi=1/2k_xi

e_yi=1/2k_yi

K_yi=1-K_xi

(e_xi, e_yi)=[(1/2k_xi, 1/2k_xi + 1/2k_xi,…..); (1/2k_yi, 1/2k_yi - 1/2k_yi,…..)]

EXAMPLE:

a)      Given two commodities, rice and milk. If the rice accounts for 75%, what would be the income elasticity of rice and milk?

b)      Predict the independent correspondence of income elasticity e_xi and e_yi.

e_x1=1/2(0.75)=2/3

e_y1=1/2(0.25)=2

(e_xi, e_yi) = [(2/3,  2/3 +2/3,  2/3 +2/3+2/3, ….); (2,  2-2,  2-2-2, ….)]

(e_xi, e_yi) = [(2/3,  4/3,  2,  …); (2,  0,  -2,  ….)]

PROOF!

K_xe_xi + K_ye_yi=1 …………(*)

075e_xi + 025e_yi=1

From the solution above;

e_x1=2/3 when e_y1=2

Substituting the value e_x1=2/3 and e_y1=2 into they equation (*)

075(2/3) + 025(2)=1

  

1/2 +1/2 = 1

2/2=1

1=1

From the solution above;

e_x2=4/3 when e_y2=0

Substituting, e_x2=4/3 and e_y2=0 in equation (*)

075(4/3) + 025(0)=1

1 + 0 = 1

1=1

From the solution above:

e_x3=2 when e_y3=-2

Substitution; e_x3=2 and e_y3=-2 in equation (*)

075(2) + 025(-2) =1

3/2-1/2 = 1

(3-1)/2 = 1

2/2=1

1=1

NOTE:

Those who said my works are not original, to proof them wrong: there is no where in economics, we can predict the value of income elasticity e_xi and e_yi for goods X and Y respectively without assume value for e_xi or  e_yi.  There is no any other Law in Economics that is value than the Central Point Law and Point Values Interval Law.