Intermediate Macroeconomics: The IS-LM Model (Goods and Money Market equilibrium)

Transition from AD-AS to the IS-LM Model

The standard Aggregate Demand (AD) and Aggregate Supply (AS) model often treats aggregate demand as a somewhat opaque "black box." The IS-LM model serves to unpack this, explaining exactly what determines aggregate demand in the short run. By modeling the interaction between two primary markets—the Goods Market, represented by the IS curve, and the Money Market, represented by the LM curve—one can determine the equilibrium levels of Output ($Y$) and the Real Interest Rate ($r$). A fundamental assumption of this model in the short run is that the price level ($P$) remains fixed.

The Goods Market Equilibrium and the IS Curve

The goods market is considered to be in equilibrium when planned spending is exactly equal to actual output. In the context of a closed economy, this equilibrium condition is expressed by the formula $Y = C + I + G$. The model identifies several functional components of this equation. First, the Consumption Function indicates that consumption depends positively on disposable income, defined as $C = C_0 + c(Y - T)$, where $c$ represents the Marginal Propensity to Consume (MPC). This value is constrained such that $0 < c < 1$. Second, the Investment Function posits that investment depends negatively on the real interest rate, expressed as $I = I_0 - br$. In this function, $b$ represents interest sensitivity, where $b > 0$.

The intuition behind these relationships is straightforward: a higher interest rate ($r \uparrow$) increases borrowing costs, which reduces investment ($I \downarrow$), leading to lower aggregate demand ($AD \downarrow$) and lower output ($Y \downarrow$). Conversely, higher output ($Y \uparrow$) increases disposable income, which in turn raises consumption ($C \uparrow$). Key variables in this market include exogenous policy variables such as government spending ($G$) and taxes ($T$), which constitute fiscal policy.

The Keynesian Cross and the Multiplier Effect

The Keynesian Cross is a diagrammatic representation showing how equilibrium income or Gross Domestic Product (GDP) is determined in the short run. Equilibrium occurs at the point where Planned Expenditure ($AE$) equals Actual Output ($Y$). At this intersection, desired spending equals total production, meaning firms are producing exactly what is demanded and there are no unintended inventory changes. The diagram utilizes a 45-degree line to represent all points where $AE = Y$, while the $AE$ line (sloping upward and representing $AE = C + I + G$) shows actual planned spending.

A critical component of this model is the Multiplier Effect. When an autonomous factor like government spending ($G$) increases, the $AE$ line shifts upward, leading to a new intersection with the 45-degree line and a resulting increase in equilibrium income. The increase in income is larger than the initial increase in spending because the process is iterative: higher spending leads to higher income, which leads to higher consumption, which then leads to further increases in income.

Derivation and Dynamics of the IS Curve

The IS curve is derived from the Keynesian Cross by observing how changes in the interest rate affect equilibrium output. Each specific interest rate ($r$) corresponds to a different level of investment. Because each level of investment shifts the aggregate expenditure ($AE$) line to a different position, different equilibrium outputs are produced. Specifically, a high interest rate leads to low investment and low output, while a low interest rate leads to high investment and high output.

Consequently, the IS curve traces out the various combinations of the real interest rate ($r$) and aggregate output ($Y$) where the goods market is in equilibrium. The curve slopes downward because a reduction in the interest rate increases investment and aggregate demand, raising equilibrium output. Movements along the IS curve are caused by changes in the real interest rate. Conversely, the IS curve shifts when autonomous factors other than the interest rate (such as changes in consumption, investment, government spending, consumer confidence, or financial frictions) cause aggregate demand and equilibrium output to change.

The Money Market Equilibrium and the LM Curve

The money market is in equilibrium when the supply of real money balances equals the demand for money, expressed as $\frac{M}{P} = L(r, Y)$. In this model, the supply of real money balances ($\frac{M}{P}$) is treated as exogenous or fixed. The Money Demand Function, denoted as $M^d = L(r, Y)$, depends positively on income ($Y$) and negatively on the interest rate ($r$). Higher income ($Y \uparrow$) necessitates more transactions, which increases money demand ($L \uparrow$). A higher interest rate ($r \uparrow$) increases the opportunity cost of holding cash, thereby decreasing money demand ($L \downarrow$). The three primary motives for holding money are transactions, precautionary reasons, and speculative purposes.

Derivation and Dynamics of the LM Curve

The LM curve illustrates the combinations of interest rates and output levels where the money market is in equilibrium. It slopes upward because an increase in income raises the demand for money; for the market to restore balance given a fixed money supply, the interest rate must rise. The intuition is that as people need more money for transactions due to rising income, money demand rises, and since supply is fixed, the cost of money (the interest rate) must increase to bring the market back to equilibrium.

Movements along the LM curve are driven by changes in income ($Y$). In contrast, the LM curve shifts when there are changes in real money balances ($\frac{M}{P}$) or changes in money demand (liquidity preference). For instance, an increase in the money supply ($M \uparrow$) shifts the LM curve to the right, while an increase in the price level ($P \uparrow$) reduces real balances and shifts the LM curve to the left. Other factors that can shift the LM curve include changes in preferences, uncertainty, or technological shifts that affect how much money people choose to hold.

Short-Run Equilibrium and Policy Interpretation

The economy is in short-run equilibrium at point $E$, where the IS curve and the LM curve intersect. At this specific point, both the goods market and the money market are in equilibrium simultaneously, determining the equilibrium output ($Y^<em>$) and the equilibrium interest rate ($r^</em>$). Mathematically, this is represented by the condition $IS(Y, r) = LM(Y, r)$.

Fiscal policy and monetary policy are the primary tools used to influence this equilibrium. Fiscal policy works through the goods market and is reflected in the IS curve. Expansionary fiscal policy ($G \uparrow$ or $T \downarrow$) shifts the IS curve to the right, increasing both output and the interest rate. Contractionary fiscal policy ($G \downarrow$ or $T \uparrow$) shifts the IS curve to the left, decreasing both output and the interest rate. Monetary policy works through the money market and is reflected in the LM curve. Expansionary monetary policy ($M \uparrow$) shifts the LM curve to the right, lowering the interest rate and increasing output. Contractionary monetary policy ($M \downarrow$) shifts the LM curve to the left, raising the interest rate and decreasing output.

Detailed Mechanisms of Policy Actions

Expansionary fiscal policy, such as an increase in $G$ or a decrease in $T$, shifts the IS curve right because aggregate demand rises at any given interest rate. This higher level of income increases the demand for money. With a fixed money supply, this creates an excess demand for money, causing a movement along the LM curve and a subsequent rise in the interest rate. While output increases, the resulting rise in the interest rate may reduce investment, a phenomenon known as "crowding out." Thus, while fiscal policy raises $Y$, the effect is somewhat weakened by the rising $r$.

Expansionary monetary policy involves the central bank increasing the money supply ($M$), which shifts the LM curve to the right. This creates an excess supply of money, lowering the interest rate required to clear the market. The lower interest rate encourages investment, leading to a rise in aggregate demand and aggregate output until the excess supply is eliminated. The chain of events can be summarized as: $M \uparrow \Rightarrow r \downarrow \Rightarrow I \uparrow \Rightarrow AD \uparrow \Rightarrow Y \uparrow$. In summary, the IS-LM model determines aggregate demand, which then interacts with the AD-AS model to determine the price level and final output.