AD-AS Model Notes

The AD-AS Model

Overview

The AD-AS model expands upon the IS-LM model by incorporating supply-side considerations and long-run dynamics where prices are not fixed. It integrates aggregate demand (AD) and aggregate supply (AS) to determine output and price levels in both the short and long run.

1. Aggregate Demand (AD) Curve

  • Represents the negative relationship between the aggregate price level (P) and the level of output (Y).

  • Derived from the IS-LM model, where P affects the LM curve: \frac{M}{P} = L(Y, r)

1.1. IS-LM Model and AD Curve

The AD curve represents all (Y, P) points where the IS-LM model is in equilibrium (both goods and money markets).

  • IS curve: r = \frac{C0 + I0 + G - cT}{b} - \frac{1 - c}{b}Y

  • LM curve: r = \frac{k}{h}Y - \frac{1}{h}\frac{M}{P}

Substituting for r and solving for Y with A := C0 + I0 + G - cT yields the AD curve:

Y = \frac{h}{bk + h(1 - c)}A + \frac{b}{bk + h(1 - c)}\frac{M}{P}

  • Changes in P lead to movements along the AD curve.

  • Note: i \neq r (Fisher equation) because P can change. Assume \pi^e (expected inflation) is constant for now.

1.2. Intuition Behind the AD Curve

P \uparrow \implies \frac{M}{P} \downarrow \implies \frac{M}{P} < L(Y, r) (Excess demand for money)

  • Individuals sell bonds (Theory of Liquidity Preference) \implies r \uparrow \implies I \downarrow \implies Y \downarrow

  • This downward slope is due to an "Interest rate effect" or "Keynesian effect," where changes in the interest rate cause the downward slope.

1.3. Wealth Effects

The downward slope of the AD curve can also be attributed to the "Wealth Effect."

  • Consumption depends on Y and wealth \left(\frac{M}{P}, A\right): C = C\left(Y - T, \frac{M}{P}, A\right)

  • P \downarrow \implies \frac{M}{P} \uparrow \implies C \uparrow (feel wealthier) \implies IS curve shifts to the right \implies Y \uparrow

1.4. Policy and the AD Curve

  • Expansionary policy (G \uparrow, T \downarrow, M \uparrow) shifts the AD curve to the right.

  • Contractionary policy (G \downarrow, T \uparrow, M \downarrow) shifts the AD curve to the left.

2. Aggregate Supply (AS) Curve

2.1. Classical Case (Long Run)

  • Prices are fully flexible.

  • Supply is determined by technology: \overline{Y} = F(K, L)

  • Natural Rate Hypothesis: In the long run, the economy is at the Natural Level of Output (Milton Friedman).

  • Output depends on capital, labor, and technology, not the aggregate price level.

  • Changes in AD lead to inflation/deflation only.

  • Economic policies have no effect on output.

  • This always applies in the long run.

2.2. Keynesian Case (Short Run)

  • Prices are fixed.

  • AS curve is horizontal.

  • Output determined by AD (IS-LM).

  • Economic policies can shift the economy towards full employment.

  • As full employment is reached, increased demand results only in increased prices.

  • Output is determined by AD in the short run and by supply-side factors at full employment.

2.3. Upward Sloping AS Curve
2.3.1. Long Run (LRAS)

  • Classical case holds; the LRAS curve is vertical.

2.3.2. Short Run (SRAS)

  • Positively sloped SRAS curve.

  • Models explaining the positive slope:

    1. Sticky Wages

    2. Sticky Prices

    3. Lucas’ Imperfect Information Model

2.3.3. Sticky Wages

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

  • Nominal wages (W) are sticky (fixed for the duration of a wage contract) in the short run.

  • Labor markets are competitive (workers paid the value of their marginal product).

  • Real wage (\frac{W}{P}) matters for firms and workers.

  • Increase in the price level decreases the real wage, causing firms to hire more workers and produce more output.

  • Firms and workers bargain over the nominal wage, and they form expectations about the future price level (P^e): W = \omega \times P^e, where \omega is the real wage target.

    • If P < P^e \implies Realized real wage > target \implies Firm hires fewer workers \implies Y < \overline{Y}

    • If P > P^e \implies Realized real wage < target \implies Firm hires more workers \implies Y > \overline{Y}

    • If P = P^e \implies Realized real wage is as anticipated \implies Firm hires the number of workers needed to obtain the natural level \implies Y = \overline{Y}

Implied SRAS curve:

Y = \overline{Y} + \alpha(P - P^e), where \alpha > 0

Or, equivalently:

P = P^e + \frac{1}{\alpha}(Y - \overline{Y}) (Lucas Aggregate Supply)

  • SRAS is a relationship between output and unexpected movements in the aggregate price level.

  • Embeds:

    • Classical case: P = P^e

    • Keynesian case: \alpha \rightarrow \infty

2.3.4. Sticky Prices

  • Some firms can change prices quickly (flexible prices), while others set prices in advance (contracts, menu costs).

  • Market structure is monopolistic competition \implies firms are price-setters.

  • Desired price level depends on:

    • Aggregate price level: P \uparrow \implies Costs \uparrow \implies Wants to set a higher price.

    • Aggregate output: Y \uparrow \implies Demand \uparrow \implies Wants to set a higher price.

  • Expressed 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 their prices based on expectations: p = P^e + a(Y^e - \overline{Y})

  • Proportion of firms with sticky prices: s. Proportion with flexible prices: (1 - s)

  • Aggregate price: P = sP^e + (1 - s)P + (1 - s)a(Y - Y^*)

After manipulation:

P = P^e + \frac{1 - s}{s}a(Y - Y^*)

  • SRAS is a relationship determined by unexpected changes in demand and the proportion of firms having sticky prices.

2.3.5. Lucas’ Imperfect Information Model

  • Firms know their own price but not the overall price level.

  • All wages and prices are fully flexible.

  • If firms observe an increase in demand for their good, they don't know if it’s due to a preference shift or increased aggregate demand.

  • y(z) = \overline{y}(z) + \gamma(p(z) - P)

    • y(z) - quantity produced by firm z

    • p(z) - price charged by firm z

    • P - aggregate price

  • Increase in demand for firm z: only p(z) \uparrow and so y(z) \uparrow

  • Increase in total demand: both p(z) and P \uparrow and so y(z) unchanged.

  • Firms form an expectation of the aggregate price level when making production choices: y(z) = \overline{y}(z) + \gamma(p(z) - P^e)

  • If firms observe p(z) \uparrow, they are uncertain whether it's due to increased firm demand or increased aggregate demand.

  • They place a probability q that it’s due to increased aggregate demand and a probability 1 - q that it’s due to increased specific demand.

  • Firms’ expectations, in general, will not be correct, i.e. they will over/underestimate the general price level at any particular moment, and thus y(z) will vary above/ below the natural level.

Aggregating all firms:

P = P^e + \beta(Y - Y^*)