    # LM Equation - Alter Method Illustration 133

The following equations describe an economy:

C         =          50 + 0.5Y

I           =          175 – 40i

Formulate the equations for IS curve and represent it graphically assuming rates of interests to be (1) 3%, (2) 1.5%

Solution

IS Curve explains the equation for commodity market symmetry at several combinations of level of earnings and rate of interest.

Y         =          AD      =          C + I

=          50 + 0.5Y + 175 – 40i

Y – 0.5Y         =          50 + 175 – 40i

(1-0.5) Y         =          225 – 40i

0.5Y    =          225 – 40i

Y         =          (225 – 40i)
0.5

=          450 – 80i

Alter Method

Alternate method to get IS curve is to directly use IS curve equation and fill in it the values of several parameters and variables.

The equation for IS curve is provided by:
_
Y         =          1          (A – di)
1-b
_          _
Where A = a+ I that is sum of autonomous consumption (a) and investment outlay (I), b is marginal propensity to consume, d is sensitivity of investment to variations in rate of interest, Y and i are level of earnings and rate of interest correspondingly.

Substituting, the values of several parameters we have the subsequent IS Equation:

Y         =                1          [(50 + 175) – 40i)
1 - 0.5

=          1          (225 – 40i)
0.5

Y         =          450 – 80i

Or Equation for IS curve: Y = 450 – 80i

Graphic representation:

We can represent the IS equation graphically by taking some values of interest and compute the level of earnings using IS equation.

(1) Presume rate of interest as 3%. Substituting this value of interest in IS equation we have

Y        =          450 – 80i

=          450 – 80 * 3

=          450 – 240        =          210

At rate of interest being 3%, level of earnings is 210

(2) Rate of interest with 1.5%.

Y          =          450 – 80i

=          450 – 80 *1.5

=          450 – 120        =          330

At rate of interest being 1.5% level of earnings is 330 Illustration 134

For a nation’s economy the following functions are provided

C          =          150 + 0.5Y

S          =          -150 + 0.3Y

I           =          180 – 3i

MS       =          180

MD       =          0.3Y – 6i

Determine the following:        (1) IS Equation, (2) LM Equation (3) Symmetry level of earnings and interest rate

Solution
_
IS Curve:         Y         =          1          (a + I)
1-b
_
Where b = MPC, a and I are self governed investment correspondingly d is sensitivity of investment demand to variations in rate of interest i.

Substituting the values of several parameters we have

Y         =          1          [(150 + 180) – 6i]
1 – 0.5

=          1          330 – 6i
0.5

Y          =          660 – 12i

Therefore, IS curve is:

Y          =          660 – 12i                                 ….. Equation (1)

Derivation of LM Equation:

For money market symmetry

MD       =          MS

0.3Y – 6i          =          180

6i         =          -180 + 0.3Y

i           =          -180 + 0.3Y
6

i           =          -30 + 0.05Y                             ….. Equation (2)

Substituting the value of i in the IS equation (1) we have

Y          =          660 – 12i

=          660 – 12 (-30 + 0.05Y)

=          660 + 360 – 0.6Y

=          1020 – 0.6Y

Y + 0.6Y         =          1020

1.6Y    =          1020

Y         =          637.5

Therefore, the symmetry level of earnings is 637.5. To procure the symmetry rate of interest we substitute the value of Yin LM Equation (2), we get the following

i           =          -30 + 0.05Y

=          -30 + 0.05 (637.5)

=          - 30 + 31.875

i           =          1.875

Therefore, symmetry rate of interest is 1.875%

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