# LM Curve

General Equilibrium in Money Market Or Financial Sector of the Economy

Introduction:

According to Keynes in money market equilibrium takes place at the rate of interest where Md = Ms. From this idea Hicks, in 1937, presented the concept of LM curve. According to Hicks, corresponding to such interest rate where Md = Ms, there is some particular level of NI . Thus LM curve establishes a relationship between rate of interest and NI through Md and Ms. The LM is the abbreviation of “Liquidity for Money”. Again, in LM, the L represents the demand for money and M represents the supply of money.

Definition of LM Curve

Now we define LM curve. “It is the curve which shows different combinations of rate of interest (i) and NI(Y) where Md = Ms”.

As demand for money (Md) has two components, i.e., Md = Msd ± Mtd. And Mtd = kY, Msd = – mi, where, k = proportion of cash,             m = slope of Msd curve

Note: Msd equation can also be shown as :               Msd = mo mi
where mo represents Msd at zero interest rate.

Thus                            Md = – mi + kY
At equilibrium Md = Ms = Mo

where                Mo = Ms = supply of money is fixed

Ms = Md          and Mo = kY — mi

. kY Mo

or                      mi = kY — Mo

m m, This is an equilibrium rate of interest.

On the same pattern we can get different values of Y where Ms = Md. Now with the help of Fig. 17, we construct LM curve.

In the p’art(1) of this fig. we have Mtd curve which is positively sloped, i.e., Mtd increases alongwith increase in Y. In part(2) there is Msd curve which slopes downward, i.e., Msd = f (i). In part (3) Z—Z curve shows fixed supply of money which is required for Mtd and Msd. In part(4), we have derived LM curve. The point E shows the combination of Oil and Y1. At this Oil , Msd is Msd3, while at

OY, , Mtd is Mtdi. Summing these two demands for money we get the point C where Md (Mtd, + Msd3) = MS. The, F shows the combination of 0i2 and 0Y2. At 0i2, Msd is Msd2 while at 0Y2, Mtd is Mtd2. Summing these• both demands for money, we get the point B where Md(Mt2 Msd2) = M s. The point G shows the combination of 013 and 0Y3. At 013, Msd is ‘Msd, while at 0Y3, Mtd is Mtd3. Summing these two demands for money, we get the point A where Md (Mt, + Msdi) = M.

Thus, by joining the points like; E, F and G we get LM curve which slopes upward. All the points of LM curve show that money market is in equilibrium — Md = Ms. Any’point below the LM curve like K, shows that money market is not in equilibrium, because, here Md > Ms. As, at the point K, rate of interest remaining the same, the level of income has increased to 0Y2. The increased income would raise the demand for money (Mtd)  as Mtd2. Supply.of money remaining the same Md > Ms. As a result, the rate of interest will go up. This would have the effect of decreasing Msd. The increased Mtd and decreased Msd will be able to maintain equality between Md and Ms at F. Any point above LM curve like J, shows that money market is not in equilibrium, because, here Md < Ms. As, at J, the level of income remaining the same, the interest rate has gone up to 012. The increased rate of interest would decrease the demand for money (Msd) —as Msd2, Supply of money remaining the same Md < Ms. As a result, the circulation of money will increase which will have the effect of increasing the level of NI. The increased level of NI (0Y2) will lead to increase Mtd — as Mtd2..

The decreased Msd and increased Mtd will be able to maintain equality between Md and Ms at the point F. Thus, we find, any deviation from the LM curve will ultimately take it on LM curve where money market is in equilibrium.

Derivation of LM Curve —An Alternative Method

In part (1) of Fig.18, the basic; equilibrium takes place at E, where Md, = Ms. Alonnwith Mdi, the level of income is Y1. Taking 0i1 rate of interest and level of income OY, in part (2) of this fig, we get the point B. Alongwith increase in income to 0Y2 , the demand for money rises to Md2. As the curve Md2 (Y2) shows. Here, new equilibrium takes place at E2 where 0i2 is the rate of interest. Taking 0i2 and 0Y2 , in part (2) of this fig. we get the point C. Because of decrease in income, the demand for money curve shifts downward as Mdo(Yo). Now money market is in equilibrium at Oio. At Oio rate of interest, the level of income is 0Yo. Thus, by joining A, B and C we get LM curve which slopes positively.

Direct Derivation of LM Curve Slope of LM Curve

In Fig.19, we take point A on LM curve where Md = Ms and the point A establishes relation-ship between Oil and 0Y1. If the level of income is raised from Yl to Y2 shown by point G. Hence there would be excess of demand for cash with high income , people would want more currency and demand deposits to cover their transaction demand. Hence, people would be less willing to lend at same i

and some other try to have more. This would lead to raise i, ultimately equilibrium is attained at H. The point H shows a situation where equilibrium has been attained by raising i which could offset the effect of higher income and demand for money.Thus, we find that LM curve has a positive slope.

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