# IS And LM Functions

__Illustration 64__

Presume the consumption and Investment Functions as below:

C = 200
+ 0.75Y

I = 500 – 5r

Determine the equation of the IS curve.

__Solution__

The equation of the IS curve is:

Y = C + I

Y = 200 + 0.75Y + 500 – 5r

Y – 0.75Y = 200 + 500 – 5r

0.25Y = 700 – 5r

Y = __700 – 5r__

0.25

** Y = 2,800 – 20r**

__Illustration 65__

Presume that the supply of money is $800. The transactions and speculative demand for money functions are given below.

m1 = 0.25Y

msp = 200 – 4r

Determine the equation of the LM curve.

md = m1 + msp

md = 0.25Y + 200 – 4r

In symmetry, md = ms

Therefore,

0.25Y + 200 – 4r = 800

0.25Y = 800 – 200 + 4r

0.25Y = 600 + 4r

Y = __600
+ 4r__

0.25

**Y = 2,400
+ 16r**

Hence the function of Y = 2,400 + 16r.

__Illustration 66__

Presume the consumption and investment function as below:

C = 200
+ 0.75Y

I = 500 – 5r

Also presume that the money supply is $ 560. The money demand function is as below:

md = 0.25Y – 4r

- Determine the equation of IS Curve
- Determine the equation of the LM curve
- Determine the concurrent symmetry for the IS Curve and LM curves

__Solution__

- IS Equation is as follows:

Y = C + I

Y = 200 + 0.75Y + 500 – 5r

Y – 0.75Y = 700 – 5r

0.25Y = 700 – 5r

Y = __700 – 5r__

0.25

** Y = 2,800 – 20r**

- LM Equation is as follows:

md = 0.25Y – 4r

ms = 560

In Symmetry,

md = ms

Therefore,

0.25Y – 4r = 560

0.25Y = 560 + 4r

Y = __560
+ 4r__

0.25

**Y = 2,240
+ 16r**

- Concurrent Equation for the IS Curve and LM curves are as follows:

IS = LM

2,800 – 20r = 2,240 + 16r

2,800 – 2,240 = 32r

560 = 32r

** r = 17.5%**

Hence,

Y = 2,800 – (20 *17.5)

= 2,800 – 350

** Y = 2,450**

**Concurrent symmetry for the IS Curve and LM curves subsists when Y = 2,450 and
r = 17.5%.**

__Illustration 67__

Presume the consumption, investment and money demand and supply functions are as below:

C = 0.75Y

I = 215
million dollars – 0.25r

md = 0.25Y – 5r

ms = 160 million dollars

Ascertain the following:

- The symmetry earnings and the interest rate

- The symmetry earnings and the interest rate when self-governing investment enhances to 270 million dollars.

__Solution__

- Symmetry earnings and the interest rate are as below:

Symmetry of the IS Curve = Y = C + I

Y = 0.75Y + 215– 5r

Y – 0.75Y = 215 – 5r

0.25Y = 215 – 5r

Y = __215 – 5r__

0.25

** Y = 860 – 20r**

Equation of the LM curve is as follows:

In Symmetry, md = ms

Therefore,

0.25Y – 5r = 160

0.25Y = 160 + 5r

Y = __160
+ 5r__

0.25

** **

** Y = 640
+ 20r**

Concurrent symmetry for the IS and LM curves are as below:

IS = LM

860 – 20r = 640 + 20r

40r = 220

r = 5.5%

Y = 860 – 20r

= 860 – (20*5.5)

= 860 – 110

** Y = 750**

**Concurrent symmetry for the IS and LM curves subsists when Y = 750 and r = 5.5%**

- The symmetry earnings and the interest rate when self governing investment enhances to 270 million dollars and the equation of the new IS curve will be as below:

Y = C + I

Y = 0.75Y + 270 – 0.25r

Y – 0.75Y = 270 – 0.25r

0.25Y = 270 – 0.25r

Y = __270 – 0.25r__

0.25

** Y = 1,080 – 1r**

Equation of the LM curve:

Y = 640 + 20r

Concurrent symmetry for the IS curve and LM curve:

IS = LM

1,080 – r = 640 + 20r

21r = 440

** r = 21%**

Y = 1,080 – 21

** Y = 1,059**

**Concurrent symmetry for the IS curve and LM curve subsists when Y = 1,059 and
r = 21%.**

__Illustration 68__

Presume that the value of k is 0.25.

Determine the direction and volume of movement in the LM curve when,

- The increase in the supply of money is $20 millions and

- The decrease in the supply of money is $50 millions.

__Solution__

- The direction and the volume of movement in the LM curve when the increase in the supply of money is at $ 20 millions:

Volume of Movement in the LM curve:

__ 1 __ *
20

0.25

** = 80**

**As there is an enhancement in the supply of money, the LM curve will move to
the right.**

- The decrease and the volume o movement in the LM curve when the decrease in the supply of money is $50 millions.

Volume of movement in the LM curve:

__ 1 __ * 50

0.25

** = 200**

**As there is a decrease in the supply of money, the LM curve will move to the
left.**

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