Page 109 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
2 2 1 2 1
–1
Also C = A =
1 1 2 1
1 2 2 1
P 1 1 2 1 1
Further, =
P
2 1 2 2 1 2 1 2

Thus equilibrium prices are P 1 2 2 1 and P 2 1 1 2 .
1 2
1 2 2 1 1 2 2 1
On substituting these prices either in demand or in supply equation, we can obtain the equilibrium
quantities of the two commodities.
The two-commodity model can be easily generalised to the case of n-commodities. It will
consist of n equations in n prices as shown below:
a P + a P + ..... + a P = g
11 1 12 2 1n n 1
a P + a P + ..... + a P = g
21 1 22 2 2n n 2
......................................................
a P + a P + ..... + a P = g
n1 1 n2 2 nn n n
National Income Model

The simplest form of the Keynesian model of national-income determination is given by the
following system of equations:
Y = C + I
0
C = a + bY (a > 0, 0 < b < 1)
We note here that Y (the level of national income) and C (the level of national consumption) are
endogenous variables. The above equations must be rearranged so that all the endogenous
variables appear only on the L.H.S of the equations.
Thus, we have
Y – C = I
0
–bY + C = a
Using matrix notation, the above equations can be written as

1 1 Y I 0
=
b 1 C a
Applying Cramer’s rule, we get

I 0 1 1 I 0
a 1 I a b a a bI
Y = 0 and C 0 .
1 1 I b 1 b 1 b
b 1

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