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Calvo Pricing and Sticky Prices

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New Keynesian Economics FrameworkPrice Discrimination→→Phillips Curve Derivation in New Keynesian Models
pricing sticky-prices nominal-rigidities

Core Idea

Calvo pricing assumes firms can adjust prices only randomly (with constant probability each period), creating a realistic form of price rigidity. Unlike menu-cost models, Calvo pricing leads to tractable equilibria and is widely used in DSGE models. The key insight is that firms optimally reset prices but must sometimes sell at stale prices, creating nominal inertia. This staggered pricing structure causes monetary shocks to have real effects on output and employment in the short run.

Explainer

From the New Keynesian framework, you know that nominal rigidities — the failure of prices and wages to adjust instantly — are what give monetary policy its real effects. The question is how to model this rigidity in a way that is both realistic and analytically tractable. Guillermo Calvo's 1983 pricing model provides the standard answer used in modern macroeconomics. The core assumption is elegantly simple: in each period, every firm faces a fixed probability (1 − θ) of being able to reset its price, and a probability θ of being stuck with its current price. This probability is independent of how long the firm has been stuck — a memoryless process, like a coin flip each period.

Think of it as a lottery. Each period, a fraction (1 − θ) of firms "win" the right to change their price, while the remaining fraction θ must continue selling at whatever price they last set. If θ = 0.75, then on average a firm goes four periods between price adjustments. The firms that get to reset their price do so optimally: they look forward, anticipating that they may be stuck at this new price for several periods, and set a price that is optimal on average over the expected duration. This forward-looking price-setting is critical — firms do not just set today's ideal price, they set a price that accounts for expected future inflation and demand conditions, because they know they may not get another chance to adjust soon.

The power of the Calvo setup is what it implies in aggregate. At any moment, the economy contains a mix of firms: some just reset their prices (reflecting current conditions), while others are stuck at prices set one, two, or many periods ago (reflecting past conditions). The aggregate price level is therefore a weighted average of current optimal prices and stale historical prices. When the central bank increases the money supply, firms that are stuck at old prices cannot raise their prices immediately. Their goods become temporarily cheap in real terms, boosting demand for their output and increasing real economic activity. This is how monetary shocks generate real effects — not because firms are irrational, but because the staggered structure of price adjustment creates unavoidable nominal inertia.

Aggregating the Calvo pricing decisions across all firms yields the New Keynesian Phillips Curve (NKPC): current inflation depends on expected future inflation and a measure of real marginal cost (often proxied by the output gap). This equation is one of the three core building blocks of the standard New Keynesian model, alongside the IS curve and a monetary policy rule. The Calvo parameter θ governs how flat or steep the Phillips curve is — higher θ (stickier prices) means inflation responds more sluggishly to changes in economic conditions, giving monetary policy more traction over real output. The elegance of Calvo pricing is that a single parameter captures the degree of nominal rigidity in the entire economy, making it the workhorse specification for policy analysis at central banks worldwide.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Center of Mass → Conservation of Linear Momentum → Elastic Collisions → Inelastic Collisions → Coefficient of Restitution → Collision Analysis and Real-World Applications → Two-Body Collisions in the Center-of-Mass Frame → Reduced Mass and Two-Body Problems → Kinematics in Two Dimensions → Projectile Motion → Circular Motion: Kinematics → Simple Harmonic Motion → Introduction to Differential Equations → Solow Growth Model → Capital Accumulation and the Golden Rule → Investment Demand and Capital Formation → Aggregate Demand → The AS-AD Model → The Phillips Curve → New Keynesian Economics Framework → Calvo Pricing and Sticky Prices

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