Is lm model

What Is the LM Model?

The LM model, or "Liquidity Preference-Money Supply" model, is a fundamental component of the IS-LM framework, a widely used tool in Macroeconomic Models to represent short-run economic equilibrium. It specifically illustrates the relationship between interest rates and the level of aggregate Output in the economy, where the Demand for Money equals the Money Supply. The LM model is crucial for understanding how monetary conditions influence the real economy by linking the financial market with the goods market.

History and Origin

The LM model's conceptual roots lie in John Maynard Keynes's The General Theory of Employment, Interest and Money, published in 1936. Keynes introduced the concept of "liquidity preference" to explain how the Interest Rates are determined by the supply and demand for money, rather than solely by Saving and Investment.

Building upon Keynes's insights, British economist John Hicks developed the IS-LM model in 1937, presenting it in his seminal paper "Mr. Keynes and the 'Classics': A Suggested Interpretation." Hicks's model provided a simplified, graphical representation of Keynesian theory, integrating the goods market (IS curve) and the money market (LM curve) into a single analytical framework.²⁵, ²⁶, ²⁷ This framework quickly became a cornerstone of Keynesian Economics and the leading macroeconomic analysis tool from the 1940s to the mid-1970s.²⁴

Key Takeaways

• The LM model (Liquidity Preference-Money Supply) represents the Equilibrium in the money market.
• It illustrates combinations of interest rates and Gross Domestic Product (GDP) where the demand for money equals the money supply.
• The LM curve typically slopes upward, indicating that higher income levels increase the demand for money, leading to higher interest rates to maintain equilibrium.
• Changes in the money supply, largely controlled by the Central Bank, cause shifts in the LM curve.
• Despite its simplifying assumptions, the LM model remains a foundational teaching tool for understanding the interaction of monetary policy and economic activity.

Formula and Calculation

The LM curve is derived from the condition that the total demand for money equals the total supply of money. The nominal money supply ((M^{S)) is typically assumed to be exogenously determined by the central bank. The demand for money ((M}D)) is a function of income (Y) and the interest rate (i), reflecting the concept of Liquidity preference.

The money market equilibrium is expressed as:

Where:

• (M^S): Nominal Money Supply, controlled by the central bank.
• (P): Price Level, often assumed fixed in the short run within the basic IS-LM framework.
• (L): Liquidity Preference function, representing the real demand for money.
• (Y): Real Output or Income.
• (i): Interest Rate.

The real money supply ((M^S/P)) is influenced by Monetary Policy. The demand for money, (L(Y, i)), has two main components based on Keynes's theory of liquidity preference:

1. Transactions and Precautionary Demand: Positively related to income (Y). As income rises, people need more money for transactions and unexpected expenses.
2. Speculative Demand: Negatively related to the interest rate (i). When interest rates are high, the opportunity cost of holding money (instead of interest-bearing assets like bonds) is high, so people hold less money for speculative purposes.²³

Rearranging the equilibrium equation can express the interest rate as a function of output and real money supply:

This relationship shows how, for a given real money supply, an increase in income leads to a higher interest rate to balance the money market, resulting in the upward slope of the LM curve.

Interpreting the LM Model

The LM model is interpreted as a graphical representation of money market equilibrium. The upward slope of the LM curve indicates a positive relationship between the level of output (income) and the interest rate. When Economic Growth leads to higher output, the demand for money for transactions and precautionary purposes increases.²¹, ²² With a fixed money supply, this increased demand for money puts upward pressure on interest rates, as individuals and firms compete for the available Liquidity.

Conversely, if the central bank increases the Money Supply through expansionary monetary policy, the LM curve shifts to the right. This means that at any given level of output, the equilibrium interest rate will be lower because there is more money available in the economy. A decrease in the money supply would shift the LM curve to the left, leading to higher interest rates for any given output level.

The intersection of the LM curve with the IS curve (representing goods market equilibrium) determines the simultaneous equilibrium levels of interest rates and output in the economy. This point signifies a state where both the goods market and the money market are in balance.

Hypothetical Example

Consider a simplified economy where the central bank maintains a fixed nominal money supply of $1,000, and the price level is assumed to be 1. The real money supply is thus $1,000.

The demand for money (L(Y, i)) can be represented by the equation:
(L(Y, i) = 0.5Y - 100i)

To derive the LM curve, we set money demand equal to money supply:
(1000 = 0.5Y - 100i)

Now, let's find the interest rate (i) for different levels of output (Y):

• If (Y = 1000):
  (1000 = 0.5(1000) - 100i)
  (1000 = 500 - 100i)
  (500 = -100i)
  (i = -5%) (This result suggests that at very low output levels, the model may imply negative interest rates, which are rare in reality but possible in theoretical contexts or a liquidity trap scenario.)

• If (Y = 2000):
  (1000 = 0.5(2000) - 100i)
  (1000 = 1000 - 100i)
  (0 = -100i)
  (i = 0%)

• If (Y = 3000):
  (1000 = 0.5(3000) - 100i)
  (1000 = 1500 - 100i)
  (-500 = -100i)
  (i = 5%)

• If (Y = 4000):
  (1000 = 0.5(4000) - 100i)
  (1000 = 2000 - 100i)
  (-1000 = -100i)
  (i = 10%)

Plotting these points (Y, i) would show the upward-sloping LM curve. As Output increases, the equilibrium Interest Rates also rise, demonstrating the LM curve's positive relationship.

Practical Applications

The LM model is widely used in macroeconomics to analyze the effects of Monetary Policy on the economy. For instance, if a central bank aims to stimulate Economic Growth by lowering interest rates, it would typically increase the Money Supply through tools like open market operations. This action shifts the LM curve to the right, leading to a new equilibrium with lower interest rates and higher output.²⁰

The Federal Reserve, as the central bank of the United States, uses various tools to manage the money supply and influence interest rates, which is consistent with the LM model's underlying principles. These actions are designed to promote maximum employment and stable prices.¹⁹ For example, the Federal Reserve's adjustments to the federal funds rate target range affect broader interest rates and financial conditions, influencing borrowing and spending decisions by households and businesses.¹⁸ Understanding the LM curve's dynamics helps policymakers anticipate how changes in money supply affect the Equilibrium interest rate and, consequently, aggregate demand and output.

Limitations and Criticisms

While the LM model provides a valuable simplified framework for understanding macroeconomic interactions, it faces several significant limitations and criticisms:

• Static Nature and Short-Run Focus: The basic LM model is largely static and focuses on short-run equilibrium, often assuming fixed prices.¹⁷ It does not adequately account for dynamic adjustments over time, including time lags in policy implementation or the evolution of expectations.¹⁶ This limits its ability to explain phenomena like inflation.¹⁵
• Simplistic View of Financial Markets: The model typically aggregates all non-money financial assets into a single "bond" category, overlooking the complexity of diverse financial instruments and various market segments.¹³, ¹⁴ It also assumes an exogenous money supply determined solely by the central bank, often neglecting the role of bank lending and the endogenous nature of money creation in the modern financial system.¹²
• Neglect of Expectations: The traditional LM model does not explicitly incorporate forward-looking expectations of economic agents, which are crucial in determining investment, consumption, and financial decisions in the real world.¹¹
• Relevance to Modern Monetary Policy: Many modern central banks, including the Federal Reserve, primarily target interest rates rather than the money supply directly.¹⁰ While the LM model can still be adapted to analyze interest rate targeting, its original formulation, based on money supply control, becomes less directly applicable.⁹
• Closed Economy Assumption: The most basic IS-LM models assume a closed economy, ignoring international trade and capital flows, which significantly influence domestic interest rates and output in open economies.

Economists like John Hicks, the model's creator, himself referred to it as a "classroom gadget" and expressed dissatisfaction with its simplifications over time.⁸ Critics argue that these simplifications can obscure more complex economic realities and may lead to unreliable policy judgments, particularly when economic policy changes.⁶, ⁷

LM Model vs. IS Model

The LM model is intrinsically linked to the IS Model as part of the broader IS-LM framework. While both models aim to determine the equilibrium of interest rates and output in an economy, they represent different sectors:

Confusion often arises because both curves interact to determine a single Equilibrium point for interest rates and output. The LM model describes the financial side of the economy, while the IS model describes the real side. Together, they provide a snapshot of how these two critical sectors interact to reach a short-run macroeconomic balance.

FAQs

What does "LM" stand for in the LM model?

"LM" stands for "Liquidity Preference–Money Supply." It reflects John Maynard Keynes's concept of Liquidity preference, which refers to the public's desire to hold wealth in liquid forms (money), and the economy's overall Money Supply.

Why does the LM curve slope upward?

The LM curve slopes upward because as the level of national Output (income) increases, people and businesses need more money for transactions. This increased demand for money, with a given money supply, drives up the Interest Rates to maintain Equilibrium in the money market.

³### How does the central bank influence the LM curve?
The Central Bank primarily influences the LM curve through its Monetary Policy actions, which control the Money Supply. An expansionary monetary policy (e.g., increasing the money supply) shifts the LM curve to the right, leading to lower interest rates. A contractionary policy shifts it to the left, resulting in higher interest rates.

²### Is the LM model still used today?
While the basic IS-LM model, including the LM curve, has limitations and has been augmented or superseded by more complex models in advanced macroeconomic research, it remains an important pedagogical tool. It is widely used in undergraduate macroeconomics courses to introduce students to the fundamental interactions between financial and real markets and the effects of Fiscal Policy and monetary policy.¹