The IS/LM Analysis

The Investment/Saving and Liquidity Preference/Money Supply Equilibrium Model

In this section, we consider the standard Keynesian model of the investment/saving and liquidity preference/money supply equilibrium (IS/LM) framework, which incorporates the equilibrium conditions for the goods market and the money market. This model is called the IS/LM model.

The IS curve shows all combinations of interest rate r and income Y that satisfy income identity, the consumption function, and the investment function. The LM curve shows all combinations of interest rate r and income Y that satisfy the money demand relationship for a fixed level of money supply and a predetermined value of the price level.

In addition to Eqs. (2.1) and (2.2), the model may be summarized by the following two equations:

Equation (2.8) is an investment function. The IS/LM model considers private investment as an endogenous variable that is determined by the rate of interest. Investment decreases with the rate of interest, r,(P > 0). Since the rate of interest is the cost of borrowing investment money, this assumption is plausible. Equations (2.1), (2.2), and (2.8) provide equilibrium in the goods market. The combination of Y and r that satisfies these equations determines the IS curve. Thus, substituting Eqs. (2.2) and (2.8) into Eq. (2.1), we have

Fig. 2.2 IS and LM curves

This is the IS curve, which shows the combination of income and interest rate that equilibrates the goods market.

Equation (2.9) is an equilibrium condition for the money market. M denotes money supply and L denotes money demand. Money demand increases with income, reflecting the demand of economic transactions, and decreases with the interest rate and the opportunity cost of money holdings, (e > 0, у > 0). The combination of Y and r that satisfies Eq. (2.9) determines the LM curve. Thus, from Eq. (2.9), we can obtain the LM curve, which denotes the combination of income and interest rate that is consistent with equilibrium in the money market.

The IS/LM model consists of two equations, (2.9) and (2.10). When compared with the simple 45-degree line model in Sect. 1, this current model makes investment endogenous as a decreasing function of interest. In addition, the model introduces money in order to determine the rate of interest.

Figure 2.2 shows the IS and LM curves. The vertical axis denotes interest rate and the horizontal axis denotes income. The IS curve given by Eq. (2.10) is downward sloping, while the LM curve given by Eq. (2.9) is upward sloping. Suppose Y increases; then, r should be reduced to maintain the equilibrium of the goods market by stimulating investment demand. Thus, the IS curve is downward sloping. However, in order to maintain the equilibrium condition of the money market, r should rise so as to depress money demand. Thus, the LM curve is upward sloping. The intersection of the curves determines the initial equilibrium point, E0.

 
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