Week 6

IS-LM Model Overview

• Instructor: Valerio Pieroni

• Focus: Combination of two previous lectures covering:

  • The IS-LM model in equilibrium

  • Fiscal and monetary policy within the IS-LM framework

  • Coordination of fiscal and monetary policies

  • Special cases: "Liquidity trap" and "classical-monetarist" case

Equilibrium in the IS-LM Model

• IS-LM Model Definition:

  • A description of the economy in the short run (with fixed prices).

  • General equilibrium model: All market interdependencies are considered (goods and money markets).

  • Focus is on aggregate demand; supply dynamics are not directly modeled.

  • With fixed prices, output depends entirely on demand; firms produce according to demand levels.

IS Curve

• Equation:

  • r = C0 + I0 b - c bT + G b - (1 - c) b Y

• Characteristics:

  • Shape: Linear

  • Slope: Downward, steepness depends on investment sensitivity to interest rates:

    • If b increases:

      • Investments sensitive to r changes → IS curve becomes flatter (more elastic).

    • If b decreases:

      • Investments less sensitive to r→ IS curve becomes steeper (more inelastic).

LM Curve

• Equation:

  • r = k hY - (1/h) M/P

• Characteristics:

  • Shape: Linear

  • Slope: Upward, steepness depends on the interest rate sensitivity of money demand:

    • If h increases:

      • Money demand sensitive to r changes → LM curve is flatter (more elastic).

    • If h decreases:

      • Money demand less sensitive to r changes → LM curve is steeper (more inelastic).

IS-LM Model: Equilibrium

• Equilibrium Conditions:

  • Occurs at the combination of Y and r where both markets (goods and money) are in balance.

  • Unique equilibrium as curves are linear; one curve has a positive slope (LM) and the other a negative slope (IS).

Equilibrium Algebra

• Equations to Solve for Equilibrium:

  • IS Curve: r = C0 + I0 b - c bT + G b - (1 - c) b Y

  • LM Curve: r = k hY - (1/h) M/P

• Results:

  • Y*_equilibrium and r*_equilibrium derived from the equilibrium equations.

IS-LM Equilibrium Stability

• Questions:

  • Is the IS-LM equilibrium stable?

  • Will the economy return to equilibrium if displaced?

• Answer: Yes, in disequilibrium, market forces generally adjust the economy back to equilibrium.

Desirable Equilibrium

• Definition:

  • Full employment equilibrium occurs when unemployed workers equal job vacancies; all unemployment is voluntary.

  • Natural Level of Output exists at full employment.

Impact of Fiscal Policy in IS-LM Model

• Effects on Output (Y):

  • ∂Y/∂G = h bk + (1 - c)h > 0 ⇒ Increase in G raises Y.

  • ∂Y/∂T = -ch bk + (1 - c)h < 0 ⇒ Increase in T lowers Y.

• Effects on Interest Rate (r):

  • ∂r/∂G = k bk + (1 - c)h > 0 ⇒ Increase in G raises r.

  • ∂r/∂T = -ck bk + (1 - c)h < 0 ⇒ Increase in T lowers r.

Crowding Out

• Definition:

  • An increase in G raises interest rates, which can "crowd out" private investment.

• Dependency Factors:

  • Higher crowding out occurs with:

    1. Inelastic LM curve (steeper)

    2. Elastic IS curve (flatter)

IS-LM and Monetary Policy

• Impact of Changes in M:

  • ∂Y/∂M = b bk + (1 - c)h/P > 0 ⇒ Increase in M raises Y.

  • ∂r/∂M = -1 - c/bk + (1 - c)h/P < 0 ⇒ Increase in M lowers r.

Liquidity Trap

• Key Characteristics:

  • Interest rates approach zero; horizontal LM curve (perfectly elastic).

  • Investment relies on "animal spirits" rather than r.

• Consequences:

  • Traditional monetary policy fails; unable to stimulate the economy.

• Escape Strategy:

  • Requires superior demand increase through effective fiscal policy (G increases leading Y to rise).

Recent Quantitative Easing

• Post-GFC Quantitative Easing:

  • Can affect Y through changes in expectations when M increases.

Classical-Monetarist Case

• Model Characteristics:

  • Demand for money mainly driven by transactional motives; inelastic LM curve.

  • Effective monetary policy, ineffective fiscal policy due to high crowding out.