1. The document discusses macroeconomic models used to measure and analyze gross national product (GNP) through equations representing aggregate supply and demand. 2. It presents equations incorporating various GNP components like consumption (C), investment (I), government spending (G), exports (X), and imports (M) to determine how they impact the multiplier (k) and overall GNP (Y). 3. Through examples calculating k under different scenarios, it demonstrates how components like G, I, and X that increase aggregate demand have a multiplier effect, raising k and Y, while M is a leakage that decreases k. The overall models show how external factors influence a country's total output.

1. MICRO-MACRO-INTERNATIONAL
SYSTEM OF ALGEBRAIC MODEL EQUATIONS
Sophremiano B. Antipolo, PhD, EdD, CES
Professorial Lecturer

2. Measuring Aggregate Income:
Gross National Product (GNP)
GNP
• a measure of the total value of final goods and
services produced by the economy, say, in a
given year.
NB: We are not concerned here with the details of national
income accounting (This belongs to the NSCB; now:
Philippine Statistical Authority -- PSA). But we need to
understand and appreciate National Income Accounting
for purposes of international comparison, using this
economic indicator.

3. Analyzing the GNP Components:
National Income Determination Model
Equation 1: Aggregate Aggregate
Supply = Demand
Y = C + I + G + (X-M)
where: Y = National Income
C = Consumption
I = Investment
G = Gov’t Expenditure
X = Export
M = Import

4. The Consumption Function
Using simple linear equations:
Equation 2
Y = C
But: C = a + bY
where: a = level of C at Y=0
b = marginal propensity to
consume
= ΔC/ΔY

5. Analyzing C-function
Simplifying
Equation 2: Y = C
Y = a + bY
Y - bY = a
Y[1-b] = a
Y = a/1-b
or: Y = [a] [1/1-b]
where: [1/1-b] = multiplier = k

6. Exercise #1: Multiplier Value
when Y = C
If mpc = b = 0.2, compute for k.
Solution:
k = [1/1-b]
k = 1/1-0.2
k = 1/0.8
Thus: k = 1.250 (Note this k-value as
our reference. Compare later when
Y-model has an added component.

7. Expanding the Aggregate Demand:
Incorporating “S” & “I”
Eq 3: S = I (Leakage=Injection)
Eq 4: Y = C + S (at eq’m: S =I)
Thus: Y = C + I
But: I = e + iY
where: e = level of I at Y = 0
i = marginal propensity to invest
= ΔI/ΔY

8. Substituting & simplifying Eq 4:
Y = C + I
Y = a + bY + e + iY
Y -bY -iY = a + e
Y [1-b-i] = a + e
Y = [a+e]/[1-b-i]
or: Y = [a+e] [1/1-b-i]
where: [1/1-b-i] = new multiplier =k

9. Exercise #2: Multiplier Value
When there is “S” & “I”
Find the new value of k, if b=0.2 and i = 0.1?
Solution:
k = 1/1-b-i
k = 1/1-0.2-0.1
k = 1/0.7
Thus: k = 1.428
(Note: the new k is HIGHER)

10. Incorporating “G”– Govt Expenditure
Eq. 5 Y = C + I + G; G=autonomous
Simplify: Y = a +bY + e + iY + G
Y-bY-iY = a +e +G
Y(1-b-i) = [a+e+G]
Y = [a+e+G]/1-b-i
Or: Y = [a+e+G] [1/1-b-i]
where: [1/1-b-i] = k (Note: k has not
changed; but Y increases due to (+G)

11. Exercise # 3: What if G is a function of Y?
Specifically: G=g+jY
where:
g=level of G at Y=0
j=marginal propensity to spend by the Govt
Assuming j=0.1, find the new value of k?
Note: For consistency, maintain the previous
assumptions on b and i.

12. Simplifying & Substituting:
Y=C+I+G
Y=a+bY+e+iY+g+jY
Y-bY-iY-jY=a+e+g
Y(1-b-i-j)=a+e+g
Y=(a+e+g)/1-b-i-j
Y=(a+e+g) (1/1-b-i-j)
where: (1/1-b-i-j)=k = new k

13. Solve for the new k, assuming: b=0.2; i=0.1; j=0.1
Solution:
k=1/1-b-i-j
k=1/1-0.2-0.1-0.1
k=1/0.6
k=1.67 Note: The new k is higher. PROOF
that G is an INJECTION. The higher the G,
the higher the Y (the GNP).

14. OPEN ECONOMY MODEL
Eq. 6: Y = C + I + G + [X-M]
To simplify, assume that X is autonomous
But: M = m + zY
where: m = level of M at Y=0
z = marginal propensity to
import
= ΔM/ΔY

15. Simplify: Y= a+bY+e+iY+G+[X-M]
Y= a+bY+e+iY+G+[X-(m+zY)]
Y= a+bY+e+iY+G+X-m-zY
Y-bY-iY+zY= a+e+G+X-m
Y(1-b-i+z) = a+e+G+X-m
Y= [a+e+G+X-m]/1-b-i+z
or: Y= [a+e+G+X-m][1/1-b-i+z]
where: [1/1-b-i+z] = the new multiplier = k

16. Exercise #4: Multiplier Value
with C+I+G+[X-M]
Solve for k, if b=0.2, i=0.1, and z=0.2?
Solution: k = 1/1-b-i+z
k = 1/1-0.2-0.1+0.2
k = 1/0.9
Thus: k = 1.11 (Note: the new value of
k DECREASES. Proof that M is a
leakage not an injection.)

17. Exercise # 5: What if X is a function of Y
and M is autonomous
Specifically: X=x+wY
where: x=level of X at Y=0
w=marginal propensity to export
Assume w=0.2, find the new value of the
multiplier (k)?
Note: Again, for consistency, maintain the
assumed values of b and i.

18. Simplifying & Substituting:
Y=C+I+G+(X-M)
Y=a+bY+e+iY+g+jY+(x+wY-M)
Y-bY-iY-jY-wY=a+e+g+x-M
Y(1-b-i-j-w)=a+e+g+x-M
Y=(a+e+g+x-M)/1-b-i-j-w)
Y=(a+e+g+x-M)*(1/1-b-i-j-w)
where: 1/1-b-i-j-w)=k=new multiplier

19. Solution:
k=1/1-b-i-j-w
k=1/1-0.2-0.1-0.1-0.2
k=1/0.4
k=2.5 Note: The new value of k has
increased from 1.26 when Y=C to 1.428 when
there is S=I; further to 1.67 when T=G; and
finally to 2.5 when we boost our X. The
higher the X, the higher the GNP.

20. THE END