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Substitutability Theory

Substitutability Theory

The substitutability thesis keeps that short term and long term securities are substitutes for borrowers and lenders. When buyers and sellers of securities are involved in arbitrage and switching functions, they are likely to get rid of inconsistencies among long term and short term interest rates in the short run.

For such operations, the thesis presumes maximising mannerism on the part of buyers ad sellers and relatively free and unobstructed markets. For example, prices of short term securities will be followed by a drop in the prices of long term securities and vice versa.

The forces which tend to such parallel moments among short term and long term interest rates are as follows:

  1. The substitutability of surrogate investment chances on the part of lenders and the surrogate means of financing on the part of borrowers and

  2. By inclination for variations in credit and monetary stipulations to have a concurrent contact on the financial market.

The substitutability thesis is significant for performing monetary policy when by arbitrage and switching process variations are broadcasted from one division of the financial market to the other by the central bank. Nevertheless, it is uncertain if investors will readily toggle over from short term to long term securities. Thus, the perfect substitutability presumed among the two types of securities smashes down.

Let us see few illustrations which help to know unambiguously the term structures of interest rates for the set demand for money.

Illustration 56

The money demand function is specified as follows:

                        Md      =          1.0Y – 500i

If for instance Central Bank of the nation has specified money supply equal to $3,040 millions, ascertain the following.

  1. The rate of interest when money market is in symmetry and

  2. Presuming the level of earnings is $8,000 millions

Solution

For money market to be in symmetry the following has to be in equal levels, i.e.

                                                Md      =          Ms
Hence,
                                    1.0Y – 500i     =          3,040

                                                Y         =          8,000
Therefore,
                        1 * 8,000 – 500i         =          3,040

                        8,000 – 3,040            =          500i

                                    4,960             =          500i

Hence,
                                              i           =          4,960 / 500

                                              i           =          9.92%

Illustration 57

Below given is the set money demand function of a financial system.

                                    MD      =          0.8Y – 160i

Presume earning of the financial system is $4,800 millions and the central bank has fixed money supply equal to $1,600 millions.

  1. If at a point of time interest rate equal to 8% per annum prevails, will the money market be in symmetry?

  2. How the interest rate will vary if it is not the symmetry interest rate?

Solution

Money market is at symmetry when;

                                 MD     =          MS

Demand for money    MD    =          0.8Y – 160i

Specified that interest i      =          8%

Earnings                   Y        =          $4,800 dollars

Hence,
                                    MD      =          0.8 * 4,800 – 160 * 8

                                                =          3,840 – 1,280

                                                =          1,260 million dollars

1,260 is lesser than 1,600 and hence the given money supply of $1,600 millions at 8% rate of interest demand for money lowers supply of money. This lower demand for money will lead to decline in interest rate to the level where money demand equals the specified money supply.

Illustration 58

Specified demand for money function is Md = 0.6Y – 60i

Assume an income of an economy to be $5,000 millions and the Central Bank has specified money supply equal to 2,500 millions. With these data given ascertain the following:

  1. In case if the interest rate per annum is 5%, what will be the equilibrium in the money market?

  2. Also in order to meet the equilibrium level in the money market, decide whether the interest rate has to be declined or enhanced.

Solution

The first condition to be in equilibrium has to be follows:

                                    Md      =          Ms

And the demand for money function is
                       
                                    Md      =          0.6Y – 60i

Given that interest rate i is 5% and income to be 5,000 million dollars

                                    Md      =          0.6(5,000) – 60(5)

                                    Md      =          3,000 – 300

                                    Md      =          2,700

2,700 > 2,500, therefore, the specified money supply of $2,500 millions at 5 percent rate of interest, demand for money goes beyond supply of money. This surpasses demand for money will tend to enhance in interest to the level where money demand equals the given money supply.

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