AD-AS Model Notes

The AD-AS Model

Overview

The AD-AS model builds upon the IS-LM model by incorporating supply-side economics and allowing prices to be flexible in the long run. It aims to determine how output and aggregate prices are determined in both the short run and the long run.

Motivation

• The IS-LM model primarily focuses on aggregate demand as the main determinant of output, neglecting the role of supply.
• Classical economics emphasized supply-side economics, with Say’s Law stating that "Supply creates its own demand."
• Say's Law is more applicable in the long run when prices are flexible.
• The AD-AS model combines demand-side (Keynesian) and supply-side insights.

Upward Sloping AS Curve

Long Run

• In the long run, the classical case holds, resulting in a vertical long-run aggregate supply curve (LRAS).

Short Run

• The short-run aggregate supply curve (SRAS) is positively sloped. Three main economic models explain this:
  1. Sticky Wages
  2. Sticky Prices
  3. The Lucas’ Imperfect Information Model

Sticky Wages

• Output is represented by a production function: $Y = F(K, L)$

• In the short run, nominal wages (W) are sticky due to factors like fixed wage contracts.

• Labor markets are assumed to be competitive, with workers paid the value of their marginal product: $\frac{W}{P} = MPL$

• Labor demand decreases with the real wage: $LD = g(\frac{W}{P})$ and g' < 0

• Firms and workers bargain over the nominal wage (W) based on expectations about the future price level (Pe):
  $W = ω × Pe$
  Where ω is the real wage target ensuring labor demand equals labor supply at full employment, leading firms to produce at the natural level ($\overline{Y}$).

• If P < Pe, the realized real wage exceeds the target, leading to fewer workers hired and Y < \overline{Y}.

• If P > Pe, the realized real wage is less than the target, leading to more workers hired and Y > \overline{Y}.

• If $P = Pe$, the realized real wage matches expectations, resulting in the natural level of employment and $Y = \overline{Y}$.

• Implied SRAS curve:
  $Y = \overline{Y} + α(P − Pe)$, where α > 0

  Or, rewritten as:

  $P = Pe + \frac{1}{α}(Y − \overline{Y})$ (Lucas Aggregate Supply)

  The SRAS curve illustrates the relationship between output and unexpected changes in the aggregate price level. The difference $(Y - \overline{Y})$ is the output gap.

Sticky Prices

• Assumes monopolistic competition where firms are price-setters.

• Some firms can quickly change prices (flexible prices), while others set prices in advance for a specific period (sticky prices).

• Desired price level depends on:

  • Aggregate price level: An increase in $P$ leads to an increase in costs, resulting in a desire to set a higher price.
  • Aggregate output: An increase in $Y$ leads to an increase in demand, resulting in a desire to set a higher price.

• Can express this as: $p = P + a(Y − \overline{Y})$ , where a > 0

• Flexible price firms set their price according to: $p = P + a(Y − \overline{Y})$

• Sticky price firms set prices based on expectations: $p = Pe + a(Ye − \overline{Y})$

• Assume $Ye = \overline{Y}$ and that the proportion of firms with sticky prices is $s$, and with flexible prices is $(1 − s)$.

• Aggregate price:

  $P = sPe + (1 − s)P + (1 − s)a(Y − \overline{Y})$

• After manipulation:

  $P = Pe + \frac{1-s}{s} a(Y − \overline{Y})$

  The SRAS is a relationship determined by unexpected changes in demand and the fraction of firms with sticky prices.

Lucas’ Imperfect Information Model

• Firms know their own price but are uncertain about the overall price level of competitors.
• All wages and prices are fully flexible.
• When firms observe an increase in demand, they are uncertain whether it is due to a preference for their good or an increase in aggregate demand.
• $y(z) = \overline{y}(z) + γ(p(z) − P)$
  • $y(z)$ - quantity produced by firm z
  • $p(z)$ - price charged by firm z
  • $P$ - aggregate price
• If there is an increase in demand for firm z, only $p(z) \uparrow$ and $y(z) \uparrow$.
• If there is an increase in total demand, both $p(z) \uparrow$ and $P \uparrow$ and $y(z)$ is unchanged.
• Firms form an expectation when making production choices:
  $y(z) = \overline{y}(z) + γ(p(z) − Pe)$
• Firms place a probability $q$ that an observed price increase is due to aggregate demand, and a probability $(1 − q)$ that it’s due to specific demand.
• If we aggregate all the firms together we get: $Y = \overline{Y} + γ(P − Pe)$

Aggregate Supply (AS)

• Given \beta > 0, the short-run aggregate supply (AS) curve is:

  $P = Pe + β(Y − \overline{Y})$

• The slope of the aggregate supply:

  • Sticky wage model: $\beta = \frac{1}{α}$
  • Sticky price model: $\beta = a(\frac{1 − s}{s})$
  • Lucas’s imperfect information model: $\beta = \frac{1}{γ}$

• Changes in expectations change the intercept of the AS curve.

Expectations

• Expectations, particularly price expectations ($P^e$), significantly influence economic behavior.
• Two main approaches to how expectations are formed:
  1. Adaptive Expectations
  2. Rational Expectations

Adaptive Expectations

• Agents base expectations on past observations of the variable:

  $P<em>{et+1,t} = P</em>{et,t−1} + λ(P<em>t − P</em>{et,t−1})$

  Where $\lambda ∈ (0, 1)$

• Systematic forecast errors: $P<em>t − P</em>{et,t−1}$

• If $\lambda = 1$ then $P<em>{et+1,t} = P</em>t$

Rational Expectations

• Agents use all available information to form expectations:

  $P<em>{et+1,t} = E(P</em>{t+1}|Ω<em>t) = E</em>t(P_{t+1})$

  Where $E<em>t$ denotes the mathematical expectation of $P</em>{t+1}$ conditional on the information set $\Omega_t$. It contains all relevant information that can be used to form an expectation.

• Individuals do not make systematic errors:

  $E<em>t(P</em>{t+1} − E<em>tP</em>{t+1}) = 0$

AS-AD Model

• Components:
  • Downward sloping AD curve (derived from IS-LM).
  • Upward sloping SRAS curve (based on sticky prices, sticky wages, or Lucas’ Imperfect Information).
  • Vertical LRAS curve (based on the Quantity Theory of Money).

AS-AD Model: Shocks

• Demand shocks (AD):
  • Positive: Shifts AD to the right (e.g., unexpected tax cut).
  • Negative: Shifts AD to the left (e.g., unexpected tax increase).
• Supply shocks (AS):
  • Positive: Shifts SRAS to the right (e.g., unexpected decrease in production costs).
  • Negative: Shifts SRAS to the left (e.g., unexpected shock to energy prices).

AS-AD Model: Positive Demand Shock

• Short-run: Higher demand puts upward pressure on prices, P{e2} = P1 < P_2, leading to an increase in both $P$ and $Y$.
• Long-run: Expectations adjust as firms realize the high demand has increased prices, $P_e \uparrow$, shifting the SRAS upward, resulting in $Y=Y^*$ and $P \uparrow$.

AS-AD Model: Economic Policy

• The economy always returns to the natural level of output in the long run.
• Economic policy can be used to:
  • Expedite recovery from a recession.
  • Limit inflation during an economic boom.
• If $AD \downarrow$, monetary policy can be employed to offset the shock and stabilize the economy. The challenge is implementing policy interventions before expectations adjust and shift the SRAS curve.