EQUILIBRIUM IN NATIONAL-INCOME ANALYSIS

By Saad Bin Abbas

Even though the discussion of static analysis has previously been regulated to Market Models in various guises-linear and nonlinear, one commodity and multicommodity, specific and general-it. Obviously, has solicitations in other areas of economics also.

MATHEMATICAL EXPLANATION OF NATIONAL-INCOME MODEL:

We may cite the simplest Keynesian National-Income model:

C = a + bY (1 < b > 0, a > 0)

Where Y and C outlooks for Endogenous Variables National-Income and (calculated) consumption expenditure, respectively, and I∘ and G∘ denote the exogenously determined investment and government expenditures. The first equation is an equilibrium condition:

(National-Income = Total planned Expenditure)

Second, the consumption function is behavioral. The two parameters in the consumption function, a and b stand for the autonomous consumption expenditure and the marginal propensity to consume, respectively.

It is quite clear that these two equations in two endogenous variables are neither functionally dependent upon nor inconsistent with, each other. Thus we would be able to find the equilibrium values of income and consumption expenditure, Y* and C*, in terms of the parameters a and b and the exogenous variables I∘ and G∘.

Substitution of the second equation into the first will reduce to a single equation in one variable, Y:

OR (1 — b) Y = a + I ∘ + G ∘ (collecting terms involving Y)

To find the solution value of Y (Equilibrium National Income), we only have to divide by (1- b):

Note, again, that the solution value is expressed entirely in terms of the parameters and the exogenous variables, the given data of the model. Putting Y* into the Second equation will yield than the equilibrium level of consumption expenditure:

This is again expressed entirely in terms of the given data.

Both Y* and C* have the expression (1 — b) in the denominator; thus a restriction b ≠ 1 is necessary, to avoid division by zero. Since b, the marginal propensity to consume has been assumed to be a positive fraction, this restriction is automatically satisfied. For Y* and C* to be positive, moreover, the numerators in equations must be positive. Since the exogenous expenditures, I∘ and G∘ are normally positive, as is the parameter a (the vertical intercept of the consumption function), the sign of the numerator expressions will work out, too.

As a check on our calculations, we can add the C* expression in the above equation to (I∘ + G∘) and verify the sum is equal to the Y* expression.

NATIONAL-INCOME MODEL DETERMINATION:

This model is obviously one of the extreme simplicity and crudity, but other models of National -Income determination, in varying degrees of complexity and sophistication, can be constructed as well. In each case, however, the principals involved in the construction and analysis of the model are identical to those already discussed.

For this main reason, we shall not go in further discussions here. A more comprehensive National-Income model, involving the simultaneous equilibrium of the money market and the goods market, will be discussed further.

Originally published at https://www.studentsofeconomics.com.