# 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%

**Online Live Tutor Alter Method, Derivation of LM Equation: **

We have the best tutors in Economics in the industry. Our tutors can break down a complex Alter Method, Derivation of LM Equation problem into its sub parts and explain to you in detail how each step is performed. This approach of breaking down a problem has been appreciated by majority of our students for learning Alter Method, Derivation of LM Equation concepts. You will get one-to-one personalized attention through our online tutoring which will make learning fun and easy. Our tutors are highly qualified and hold advanced degrees. Please do send us a request for Alter Method, Derivation of LM Equation tutoring and experience the quality yourself.

**Online Synthesis of Monetary and Real Factor Help: **

If you are stuck with an Synthesis of Monetary and Real Factor Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Synthesis of Monetary and Real Factor help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Synthesis of Monetary and Real Factor Homework Help. Please do send us the Synthesis of Monetary and Real Factor problems on which you need help and we will forward then to our tutors for review.

**Other topics under Macro Economics For Management:**

- Aggregates and Dimension of National Earnings
- Consumption and Investment in Management
- Cost Push Inflation
- Economic Alleviation Under Economic Strategy
- Economic Alleviation Under Financial Strategy
- Establishment of National Earnings By Keynes
- International Linkages and Mundell Fleming Model
- Investigation of Trade Cycles
- Issues and Concepts
- Money Market Symmetry, Demand and Supply of Money
- Multiple Modular Sectors
- Nature and Costs Under Inflation
- Reparation Financial Strategy