Interactive modelAdvanced Macro & Growthintermediate

Fisher Equation

Nominal rates, real rates, and expected inflation, the identity underneath monetary policy.

Equilibrium: πᵉ* = 3.0, i* = 5.0

Current equations

i = r + πᵉ: i = 2 + 1·πᵉπᵉ: πᵉ = 3

Lenders care what their money will BUY when repaid. So nominal rates carry expected inflation on top of the real rate: i = r + πᵉ. Slide expectations right and watch nominal rates rise one-for-one.

Shift the curves

Real interest rate (r)0

The real rate is what lenders actually earn after inflation, it anchors the whole line.

Expected inflation (πᵉ)0

Nominal rates rise one-for-one with expected inflation, the Fisher effect.

The Fisher Equation model, in writing

Definition

The split between real and nominal interest: the nominal rate equals the real rate plus expected inflation, so lenders quote nominal but care about real.

i = r + πe (exactly: 1+i = (1+r)(1+πe))

The intuition

If you lend at 5% while inflation runs at 3%, your purchasing power grows only 2%. When expected inflation rises, lenders demand compensation and nominal rates rise roughly one-for-one (the Fisher effect). Surprise inflation, though, transfers wealth from lenders to borrowers because the contract was written before anyone knew.

Exam tip

Ex-ante (expected) versus ex-post (actual) real rates is the distinction markers reward: unexpected inflation is what redistributes between borrowers and lenders.

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IS-LM →Mundell-Fleming (Open-Economy IS-LM) →Government Budget Constraint & Seigniorage →Solow-Swan Growth Model →