AS-AD Model Notes Part A

The AS-AD Model

8-1 Aggregate Supply

• The aggregate supply (AS) relation captures how output affects the price level, derived from wage and price behaviors.

• Wage determination:
  W = P^eF(u, z)
  Where:

  • W = Nominal wage
  • P^e = Expected price level
  • u = Unemployment rate
  • z = Catch-all variable

• Price determination:
  P = (1 + µ)W
  Where:

  • P = Price level
  • µ = Mark-up over cost

Derivation of Aggregate Supply

1. Eliminate the nominal wage (W):
   P = (1 + µ)P^eF(u, z)
   The price level depends on the expected price level and the unemployment rate, assuming \mu and z are constant.

2. Express unemployment rate (u) in terms of output (Y):
   u = \frac{U}{L} = \frac{L - N}{L} = 1 - \frac{N}{L} \approx 1 - \frac{Y}{L}
   Where:

   • L = Labor force
   • N = Employment
   • U = Number of unemployed

   For a given labor force, higher output implies a lower unemployment rate.

3. Substitute unemployment rate into the price level equation:
   P = P^e(1 + µ)F(1 - \frac{Y}{L}, z)
   The price level P depends on the expected price level P^e, the level of output Y, and constants \, µ, z, and L in the short run.

Properties of the AS Relation

• An increase in output leads to an increase in the price level due to:

  1. Increase in output leading to increased employment.
  2. Increase in employment leads to a decrease in the unemployment rate.
  3. Lower unemployment rate leads to an increase in the nominal wage.
  4. Increase in the nominal wage leading to an increase in prices.
     Y \uparrow \implies N \uparrow \implies u \downarrow \implies W \uparrow \implies P \uparrow

• An increase in the expected price level leads to a one-for-one increase in the actual price level. This is because if wage setters expect a higher price level, they set a higher nominal wage, leading to increased costs and prices.
  P^e \uparrow \implies W \uparrow \implies P \uparrow

AS Curve Properties

• The AS curve is upward-sloping: higher output leads to a higher price level.

• The AS curve goes through the point where Y = Yn and P = P^e (where Yn is the natural level of output).

• An increase in the expected price level shifts the AS curve upward, while a decrease shifts it downward.

• Summary:

  • AS relation derived from wage and price determination in the labor market.
  • For a given expected price level, the price level is an increasing function of output.
  • Increases in the expected price level shift the AS curve up; decreases shift it down.

8-2 Aggregate Demand

• The aggregate demand (AD) relation captures the effect of the price level on output, derived from equilibrium conditions in goods and financial markets (IS/LM model).
  • IS relation: Y = C(Y - T) + I(Y, i) + G Where:
    • Y = Output
    • C = Consumption
    • T = Taxes
    • I = Investment
    • i = Interest rate
    • G = Government spending
  • LM relation: \frac{M}{P} = YL(i) Where:
    • M = Nominal money supply
    • P = Price level
    • L(i) = Liquidity preference function

From IS/LM to AD

• An increase in the price level shifts the LM curve to the left, leading to a decrease in output.
• Some groups in the economy are not protected from price increases, shifting the IS curve to the left.
• An increase in the price level leads to a decrease in output.
  P \uparrow \implies \frac{M}{P} \downarrow \implies i \uparrow \implies Y \downarrow

Shifts in Aggregate Demand

• Changes in monetary or fiscal policy (or any variable other than the price level that shifts the IS or LM curves) shift the AD curve.

• The AD is downward sloping
  Y = Y(\frac{M}{P}, G, T)
  Where:

  • \frac{M}{P} = Real money supply
  • G = Government spending
  • T = Taxes
    (+, +, -): Indicates the sign of the effect of each variable on output.

• An increase in government spending increases output at a given price level, shifting the AD curve to the right.

• A decrease in nominal money decreases output at a given price level, shifting the AD curve to the left.

• Summary:

  • AD relation derived from equilibrium conditions for goods and financial markets.
  • The level of output is a decreasing function of the price level.
  • Changes in monetary or fiscal policy shift the AD curve.

8-3 Equilibrium in the Short Run and in the Medium Run

• Equilibrium depends on the value of P^e, which determines the position of the AS curve.

  • AS relation: P = P^e(1 + µ)F(1 - \frac{Y}{L}, z)
  • AD relation: Y = Y(\frac{M}{P}, G, T)

• Equilibrium is given by the intersection of the AS and AD curves.

• At the equilibrium point, the labor market, goods market, and financial market are all in equilibrium.

• The AS curve is drawn for a given value of P^e. The higher the level of output, the higher the price level.

• The AD curve is drawn for given values of M, G, and T. The higher the price level, the lower the level of output.

From the Short Run to the Medium Run

• If output is above the natural level of output (Y > Y_n), then the actual price level is above the expected price level (P > P^e).

• Wage setters will revise upward their expectations of the future price level, causing the AS curve to shift upward.

• Expectation of a higher price level also leads to a higher nominal wage, which in turn leads to a higher price level.

• If output is above the natural level, the AS curve shifts up over time until output falls back to the natural level.

• The adjustment ends once wage setters no longer have a reason to change their expectations.

• In the medium run, output returns to the natural level of output, and P = P^e.

• Summary:

  • In the short run, output can be above or below the natural level.
  • Changes in variables that enter the AS or AD relation lead to changes in output and the price level.
  • In the medium run, output eventually returns to the natural level through changes in the price level.