Lecture 15

Announcements

• Graded Homework will be posted today.
• Due on Section week of March 24.

Summary of Lecture 14

• Monetary Policy Tools
• Effects of Monetary Policy, Romer dates
• Taylor Rule
• Sticky Price Model
• Phillips Curve
• Reading: Mankiw, Chapters 15

The AD/AS – IS/LM Model

• Goods Market and Money Market interact.
• IS Curve: Represents equilibrium in the goods market.
• LM Curve: Represents equilibrium in the money market.
• The IS-LM Model leads to the AD Curve in the AD/AS Model.
• Production Function & Labor Markets: Consider price rigidities and sticky wages, forming the AS Curve.

Spatial Dynamics in the AD/AS Model

• Graph Relationships:
  • Y-axis: Interest Rate (r)
  • X-axis: Output (Y)
• Effects of Price Reduction:
  • Shifts the LM curve to the right
  • Increases output (Y)
  • Higher output is associated with lower prices (P).

Short Run Aggregate Supply (SRAS)

• Initial assumption of a flat SRAS (i.e. all prices are predetermined) is updated to be more realistic.
• Sticky Price Model:
  • Firms set a desired price through
    $ext{ln } p_{desired} = ext{ln } P + b( ext{ln } Y - ext{ln } \bar{Y})$
    where $b > 0$.
• Types of Firms:
  • Flexible Prices: Set prices according to the equation above.
  • Sticky Prices: Set prices based on expected prices and output before knowing actual values:
    $ext{ln } p = ext{ln } P<em>e + b( ext{ln } Y</em>e - ext{ln } \bar{Y})$.
• Average Price Level:
  • Aggregate price level defined as
    $ext{ln } P = s ext{ln } P<em>{sticky} + (1 - s) ext{ln } P</em>{flex}$
  • Flex prices modeled as
    $ext{ln } P<em>{flex} = ext{ln } P + b( ext{ln } Y - ext{ln } \bar{Y})$ and sticky prices as $ext{ln } P</em>{sticky} = ext{ln } P<em>e + b( ext{ln } Y</em>e - ext{ln } \bar{Y})$.

Solving for P

• Aggregated price leads to:
  $ext{ln } P = ext{ln } P_e + \frac{1-s}{s} b( ext{ln } Y - ext{ln } \bar{Y})$
• Implications:
  • High expected price (P_e) → leads to high P
  • Higher output (Y) leads to higher price levels.
  • As the fraction of sticky firms (s) increases, the SRAS curve flattens.

Aggregate Output

• Relationship defined by:
  $ext{ln } Y = ext{ln } \bar{Y} + a( ext{ln } P - ext{ln } P_e)$
• Where $a = \frac{1-s}{s b}$.
• This models short-run frictions implying that the SRAS takes a defined form.

The Phillips Curve

• Represents empirical relationship between inflation and unemployment.
• Basic Principle:
  • Higher inflation corresponds to lower unemployment rates.
  • This relationship is derived from the SRAS model.
• Equation of Phillips Curve:$ext{ln } P<em>t = ext{ln } P</em>{t-1} + \frac{1}{a}( ext{ln } Y_t - ext{ln } \bar{Y})$
  • Where the actual inflation $π_t$ relates to expected inflation and outputs.

Okun’s Law

• Definition: Every 1% increase in unemployment is associated with a 2% decrease in economic growth.
• Approximation: $ext{ln } Y<em>t - ext{ln } \bar{Y} ≈ -2(u</em>t - u_N)$
  • Where $u_N$ is the natural rate of unemployment.

The Accelerationist Phillips Curve and Adaptive Expectations

• Establishes the relationship between changes in inflation ($∆π$) and unemployment ($u$).
• NAIRU (Non-Accelerating Inflation Rate of Unemployment) is defined in this context.
• Using adaptive expectations, we derive the relationship: $∆π<em>t = -θ(u</em>t - u_N)$
  • Sacrifice Ratio: Tied to GDP losses to reduce inflation.

Economic Scenarios from Monetary Policy

1. Unexpected increase in the money supply: Initial effects on GDP, unemployment, and inflation.
2. Expected increase in prices: Examine how anticipations affect economic outcomes, specifically GDP and unemployment.

Summary of Lecture 15

• Inclusion of Sticky Price Model
• New derivation and understanding of SRAS
• Phillips Curve Dynamics
• Interaction of IS-LM, AS-AD, and Phillips Curve to analyze output, interest rates, and unemployment.
• Explore effects of anticipated versus unanticipated monetary shocks.