1. MATH ASSIGNMENT
APPLICATIONS OF LINEAR ALGEBRA IN ECONOMICS
BY:- AMIT GARG

2. Economics is the branch of knowledge concerned with the
production, consumption, and transfer of wealth .
Many economic relationships can be approximated by linear
equations and others can be converted to linear relationships.
So the analysis of many economic models reduces to the study
of systems of linear equations.
Relationship between Linear algebra
and Economics ….
What is Economics ????

3. Applications of linear algebra in economics...
• Leontiff Input-Output Model
It is a model that show interdependencies between
different branches of
economy
• Developed by :- Wassily Leontief
He devided the economy ito different sectors
(like :- coal industry ,
agricultural industry , manufacturing industry etc).
• Use of Linear Equation
For each sector , he wrote linear equation
describing how sector distributes
Output to the other sectors

4. Leontiff Input-Output Model…….
Consumption Matrix
A consumption matrix shows the quantity of inputs needed
to produce one unit of a good.
FromTo Agriculture Manufacturing Labour
Agriculture 0.25 0.083 0.2
Manufacturing 0.25 0.167 0.4
Labour 1.25 0.4167 0.2
Represents
Producing
Sector of the
economy
Represents
Consuming
Sector of the
economy

5. TOTAL PRODUCTION , INTERNAL DEMAND , FINAL DEMAND...
Acc to Leontiff model
= +
Total
product
produced
Internal
demand .
Final
Demand
(F)(X)
• f is demand from the non-producing sector of the economy.
• x is the total amount of the product produced.
• They both can be represented as vectors (combining demands
from different industries) .

6. MATHEMATICS INVOLVED……
The internal demand is equal to the consumption matrix
multiplied by the total production vector .
X (Amount produced)]= [Cx] + final demand [F]
Therefore :-
x = cx +f _ _ _ _ _ (1)
By using the algebric properties of Rn.
Ix = Cx + f _ _ _ _ _ (2)
(I-C)x = f _ _ _ _ _ (3)

7. Let C be the consumption matrix for an economy, and let f
the final demand. If C and f have nonnegative entries, and
if C is economically feasible, then the inverse of the matrix
(I-C) exists and the production vector:
X = (I - C)^-1*f .......(4)
Therefore there exist a nonnegative entries and
is the unique solution of the equation :-
X = Cx +f

8. USES OF INPUT – OUTPUT MODEL…
DEMAND SUPPLY PRICE
PREDICTION OF THESE THREE THINGS …..

9. REFERENCES :- (1) Research Paper of Sir Lucas Davidson .
(2) WIKIPEDIA .