REVIEW

CENTRAL ECONOMICS

Bill Adongo's Definition:

Central Economics is a new invention of mine and is infinitesimals( items or values in sequential) interval proportionate change in material ( wealth) well-being of people for goods and services. It is one of my new creation which is used to perfectly predict infinitesimals(items or values in sequential) interval proportionate change in average (point) price, average (point) income, average (point) cost, average (point) quantity demand, and average (point) revenue. In Central Economics, all curves are linear (or para-linear) even though they may still considered as curves in economic term.

ADONGO'S FIRST LAW OF CENTRAL ECONOMICS

My law states that for all average (point) materials well-being of people for goods and services; all averages (points) values are convertible to non-averages if the sum of averages (points) is divided by the observed averages (points).

POINT ELASTICITY

At a point, we can talk about an infinitesimal interval proportionate change in quantity to an infinitesimal interval proportionate change in price. These types of elasticity are called Central curve elasticity.

The most convenient measure in the case of change in point price is the point elasticity of demand. The point elasticity of demand of commodity X is defined as:

E_*D=P_ix∆D_x/2P_fxD_ix

E_*D be point elasticity demand

P_ix be intial price

∆D_x be change in quantity demand

P_fx be final price

D_ix be initial quantity demand

For example, if price P_ix falls from 1.6 to 1.5, and the amount demanded by the individual, D_ix increase from 50kg to 55kg. Hence, we have:

The initial quantity D_ix=50kg

Change in quantity ∆D_x=55-50=5g

Final price P_fx=1.60

Initial price P_ix=1.50

The point elasticity demand is:

E_*D=P_ix∆D_x/2P_fxD_ix

E_*D=1.50*5/2*1.60*50

E_*D=0.047

We can also substitutes and complements; we saw that the point amount demanded of one good may be responsive to a change in the point price of another good. This responsiveness is measured by the point cross-elasticity of demand E_*c, defined as:

E_*c=P_iy∆D_x/2P_fyD_ix

For example, when the price Y, P_fy, falls from 0.90 to 0.80, the amount of X demanded by the individual, D_fx decrease from 45kg to 41kg. Hence, we have:

E_*c=P_iy∆D_x/2P_fyD_ix

E_*c=0.80*4/2*0.9*41

E_*c=0.044

To measure the responsiveness of the amount demanded to changes in point money income, we can employ the term point income-elasticity of demand, defined as:

E_*m=M_iX∆D_x/2M_fXD_ix

TABLE:

M(Cedis)	1,000	1,100	1,200	1,300
Dx(kg)	50	55	58	60

In table 1.0 when income increase from 1,000 to 1,100, the amount demanded increase from 50 to 55, so that

E_*m=1000*5/2*1100*50

E_*m=0.045

As in the case of demand, the concept of point elasticity may be used to measure the degree of responsiveness of supply to point price. In the case of point elasticity of supply of a good X is defined as:

 E_*s=P_iX∆S_x/2P_FxS_ix

THE CENTRAL LAW OF DIMINISHING MARGINAL RATE OF SUBSTITUTION

In general, infinitesimal interval proportionate marginal changes, we can give an infinitesimal interval proportionate marginal rate of substitution of labour for capital as:

MRSl_{* for k}=∆k/2L_f

MRSl_{* for k}=∆k/2L_i

Applying the general principle of central Economics, we have:

MRSl _{for k}=[∆k/2L_f+∆k/2L_i]/2

For an infinitesimal prediction of MRSl _{for k}, we have:

MRSl _{for k}=[l_a(∆k/2L_f)+l_s(∆k/2L_i)]/2

or

MRSl _{for k}=[l_s(∆k/2L_f)+l_a(∆k/2L_i)]/2

For each l_a=2, 3, 4, …, correspondence to l_s=0, -1, -2, ….,

 CENTRAL ELASTICITY OF DEMAND AND THE POWER OF MONOPOLY

The aim of monopolist in this context is to raise an infinitesimal interval proportionate in price of his product by restricting output. Since I cannot apply slope principle here, it is better to derive this result directly in terms of point elasticity.

I have shown without too much difficulty that point marginal revenue, point price elasticity is related as:

∆R_*/∆q_*ED=2P

∆R_*/∆q_*ED=2P/e_D

Applying the general law, we have:

∆R/∆q=P(1+1/e_D)

∆R/∆q=[l_a(P)+l_s(P/e_D)]

∆R/∆q=[l_s(P)+l_a(P/e_D)]

For each l_a=2, 3, 4, …., correspondence to l_s=0, -1, -2,….,

If we denoted by ∆C_*/∆q_*eD, the profit maximization monopolist would put marginal point cost equal to marginal point revenue.

∆q_*=∆C/2P

∆q_*eD=∆C_*e_D/2P

Hence the price is:

P=(∆C/∆q)/(1+1/e_D)

Applying the general law gives;

∆q=[∆C+∆C_*e_D]/4P

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

CREDIT CREATION: BANKS

Bank deposits constitute the larger part of the money supply; we used the bank deposit multiplier to explain the process of money creation. This tells us how the volume of bank deposits is affected by an increase in cash base. But currency can constitute a major component of the money supply, especially in poor countries where a large proportion of the population does not have ready access to banks.

My central deposit multiplier is given as:

∆D_*=∆C/2r

∆D_*=∆C/2c

Applying the general law gives;

∆D=[∆C/2r+∆C/2c]/2

∆D=[∆C/r+∆C/c]/4

∆D=[l_a(∆C/r)+l_s(∆C/c)]/4

or

∆D=[l_s(∆C/r)+l_a(∆C/c)]/4

For each l_a=2, 3, 4, …, correspondence to l_s=0, -1, -2, ….,

The modified bank deposit multiplier gives;

∆M_*=∆C(1+c)/2r

∆M_*=∆C(1+c)/2c

Applying the general law gives;

∆M=[∆C(1+c)/r+∆C(1+c)/c]/4

∆M=[l_a∆C(1+c)/r+l_s∆C(1+c)/c]/4

or

∆M=[l_s∆C(1+c)/r+l_a∆C(1+c)/c]/4

For each l_a=2, 3, 4, …., correspondence to l_s=0, -1, -2, …,

Example let considered Central Bank issue change in currency of $20. If r=0.1 and c=0.4. Set the Bank money supply.

∆M_*=∆C(1+c)/2r

 ∆M_*= 20(0.50)/2(0.1)

∆M_*=$50

∆M_*=∆C(1+c)/2c

∆M_*=20(0.50)/2(0.4)

∆M_*=$12.5

∆M=(50+12.5)/2

∆M=$31.25

We can predict an infinitesimal estimate ∆M_{* relation to r}  and ∆M_{* relation to c}  as:

∆M_{* relation to r}=50, 100, 150, 200, ….,

∆M_{* relation to c}=12.5, 0, -12,5, -25, …,

∆M=(50+12.5)/2; (100+0)/2; (200-12.5)/2; (200-25)/2; ……;

COMPARING:

The Central Economics is not only good in predicting an infinitesimal values, but is of great accuracy. Comparing my earlier calculation on point elasticity of demand is E_*D=0.047 and point income elasticity of demand E_*M=0.045.

Also, applying the existing concept (theory) of income elasticity of demand is E_*D=1.6 and income elasticity of demand is E_*M=1.0. In real sense E_*D≈E_*M since quantity demand increase from 50kg to 55kg in relation to the price and income, making my theory perfectly accurate than the existing.

CERTAINTITY PROPORTION THEORY

Consider W_d to be proportion of debt capital and W_e be the proportion of equity capital in the firm’s target capital structure. If the overall cost of capital is r_c=W_dr_d+W_er_e, then there is independent prediction of the cost of equity capital r_e and the cost of debt capital r_d.

r_ei=rc/2w_ei

r_d=rc/2w_di

W_e=1-W_d

(r_ei, r_di)=[(r_c/2w_ei,  rc/2w_ei  + r_c/2w_ei,..); (r_c/2w_di,  r_c/2w_di  - r_c/2w_di,..)]

Where;

r_c=overall cost of capital

W_d=the proportion of debt capital in the firm’s capital structure

r_d=the cost of debt capital

W_e=the proportion of equity capital in the firm’s capital structure

r_c=the cost of equity capital

EXAMPLE

If a bag of sugar has a target capital structure of 60 percent this year, if we expected the overall cost to be $10.4 next year.

a)what will be the cost of equity capital r_c and the cost of debt capital r_d next year.

W_d=1-0.60

r_e1=10.4/2(0.40)=13.0000

r_di=10.4/2(0.60)=8.6667

Hence, the cost of equity capital and the cost of debt capital are $13.00 and $8.67 respectively.

PROOF!

0.60r_di+0.40r_ei=10.4

0.60(8.6667)+0.40(13.0000)=10.4

5.20+5.20=10.4

10.4=10.4

SUPPLY PRICE OF MARGINAL EFFICIENCY

Given the supply price, S and rate of marginal efficiency of capital r. there is independent prediction of the annual prospective yield from the capital asset, R₁,R₂, R₃, and R_n if the supply price is

S=R₁/(1+r) + R₂/(1+r)²+……+R_n/(1+r)ⁿ. Two years prospective yield from the capital asset is:

R₁=C(1+r)²/2

R₂=C(1+r)/2

(R₁, R₂)=[( C(1+r)²/2, C(1+r)²/2+ C(1+r)²/2, …);( C(1+r)/2, C(1+r)/2  -  C(1+r)/2,…)]

EXAMPLE:

Suppose it costs 3000 Rupees to invest in Certainty machinery and the life of the machinery is two years. If the rate is 10%,

a)what will be the prospective yield from the capital asset, of the two years.

SOLUTION

R₁=3000(1.10)2/2=1815

R₂=3000(1.10)/2=1650

PROOF!

S=R₁/(1+r) + R₂/(1+r)2

3000=1650/(1.10)+1815/(1.10)

3000=1500+1500

3000=3000