Theory-Based Models

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Theory-Based Models

AD-AS Model

A short-run demand and supply framework showing how price level and output move when demand or cost conditions shift around long-run capacity.

Introductoryshift equilibrium

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Theory-Based Models

Proof

Route section

Read the derivation as a document, with the math typeset directly and the intermediate chains tucked behind expandable steps.

Sections

Setup and notation

The route writes aggregate demand and short-run aggregate supply as linear schedules around a long-run output anchor.

P = AD_0 - AD_1 Y

P = AS_0 + AS_1 Y

Y = Y^*

Aggregate demand schedule

A higher price level reduces real balances and dampens demand, so the AD schedule slopes downward.

\frac{\partial P}{\partial Y}\Big|_{AD} = -AD_1

Short-run supply schedule

Short-run supply is upward sloping because marginal cost rises as firms push output above normal utilization.

\frac{\partial P}{\partial Y}\Big|_{SRAS} = AS_1

Short-run equilibrium

Equilibrium is the crossing of AD and SRAS.

AD_0 - AD_1 Y = AS_0 + AS_1 Y

Y^* = \frac{AD_0 - AS_0}{AD_1 + AS_1}

P^* = AD_0 - AD_1 Y^*

Long-run anchor and adjustments

When output differs from potential, the model treats that as a gap relative to the long-run capacity line.

gap = Y - Y^*

Capacity anchor

The long run is not another short-run curve shift. It is the level of output consistent with capacity.

Back to explore Open compare

Theory-Based Models

Loading Theory-Based Models

Theory-Based Models

AD-AS Model

A short-run demand and supply framework showing how price level and output move when demand or cost conditions shift around long-run capacity.

Introductoryshift equilibrium

Catalog Overview Explore Proof Compare

Theory-Based Models

Proof

Route section

Read the derivation as a document, with the math typeset directly and the intermediate chains tucked behind expandable steps.

Sections

Setup and notation

The route writes aggregate demand and short-run aggregate supply as linear schedules around a long-run output anchor.

P = AD_0 - AD_1 Y

P = AS_0 + AS_1 Y

Y = Y^*

Aggregate demand schedule

A higher price level reduces real balances and dampens demand, so the AD schedule slopes downward.

\frac{\partial P}{\partial Y}\Big|_{AD} = -AD_1

Short-run supply schedule

Short-run supply is upward sloping because marginal cost rises as firms push output above normal utilization.

\frac{\partial P}{\partial Y}\Big|_{SRAS} = AS_1

Short-run equilibrium

Equilibrium is the crossing of AD and SRAS.

AD_0 - AD_1 Y = AS_0 + AS_1 Y

Y^* = \frac{AD_0 - AS_0}{AD_1 + AS_1}

P^* = AD_0 - AD_1 Y^*

Long-run anchor and adjustments

When output differs from potential, the model treats that as a gap relative to the long-run capacity line.

gap = Y - Y^*

Capacity anchor

The long run is not another short-run curve shift. It is the level of output consistent with capacity.

Back to explore Open compare