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IS And LM Functions

 IS and LM Functions General Equilibrium Product and Money Market

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

  1. Determine the equation of IS Curve

  2. Determine the equation of the LM curve

  3. Determine the concurrent symmetry for the IS Curve and LM curves

Solution

  1. 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

  1. 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

  1. 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:

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

Solution

  1. 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%

  1. 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,

  1. The increase in the supply of money is $20 millions and
  1. The decrease in the supply of money is $50 millions.

Solution

  1. 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.

  1. 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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