In a Calvo pricing economy with θ = 0.75, a central bank unexpectedly cuts interest rates. What happens in the immediate period after the cut?
AAll prices fall immediately by the same proportion as the interest rate cut
BOnly 25% of firms can reset prices; the rest are stuck, so real output temporarily rises as the same nominal demand buys more at sticky prices
CFirms anticipate the cut in advance and adjust prices before it happens, so no real effects occur
DNo real effects occur because prices are fully flexible when firms have the option to change them
With θ = 0.75, only a fraction (1 − θ) = 25% of firms can reset their prices in any given period. The remaining 75% are stuck at old prices. When the central bank cuts rates and demand rises, sticky prices mean the same nominal demand buys more real output at those unchanged prices. This is the monetary transmission mechanism: real effects occur precisely because not all prices adjust immediately. If all firms could adjust instantly (θ = 0), the price level would fully absorb the demand stimulus and real output would not change.
Question 2 Multiple Choice
When a firm gets a Calvo 'green light' to reset its price, why does it typically set a price above its currently optimal level?
AFirms are irrational and always overshoot their target price
BGovernment regulations require a minimum markup over production costs
CBecause it may be stuck with this price for multiple periods, the firm sets a forward-looking price weighted toward future desired prices, which are higher if it expects inflation to continue
DFirms set high prices now to compensate for being forced to keep prices low in past periods
A Calvo-resetting firm knows it faces a lottery about when it will get to reset again. It will not simply choose the price that maximizes profit today; it chooses the price that maximizes expected profit over the uncertain number of periods it will be stuck with this price. If the firm expects the aggregate price level to rise (inflation), then future desired prices will be higher than today's desired price, so the optimal reset price is a weighted average tilted above the current optimum. This forward-looking price-setting behavior is exactly what makes the New Keynesian Phillips Curve forward-looking.
Question 3 True / False
In the Calvo model, a firm that has been unable to reset its price for the past 3 periods is no more likely to reset next period than a firm that just reset.
TTrue
FFalse
Answer: True
This is the defining feature of Calvo pricing: the reset probability (1 − θ) is constant and memoryless — independent of how long the firm has been stuck or how misaligned its price has become. This is sometimes called the 'Calvo lottery.' It is mathematically convenient (it generates a tractable, stationary distribution of price vintages) and is the key assumption that makes DSGE models analytically solvable. The assumption is a simplification — in reality, firms with severely misaligned prices are more likely to update — but it is tractable and empirically reasonable on average.
Question 4 True / False
The Calvo model predicts that firms adjust prices frequently in small increments, keeping prices nearly generally close to their optimal level.
TTrue
FFalse
Answer: False
The Calvo model predicts the opposite: firms adjust prices infrequently (only when they receive a random 'green light') and in large increments when they do adjust, because their prices may have drifted far from optimal during the period of being stuck. The realistic feature of Calvo pricing is that it generates lumpy, infrequent price changes, not continuous small adjustments. This matches empirical evidence showing prices are often unchanged for months before jumping by several percentage points when they do change.
Question 5 Short Answer
Explain why the Calvo pricing mechanism implies that current inflation depends on expected future inflation, not just current economic conditions.
Think about your answer, then reveal below.
Model answer: When a firm resets its price, it will be stuck with that price for an uncertain number of future periods. To maximize expected profit over this horizon, it must choose a price that is optimal not just today but on average across all future periods it might be stuck. If the firm expects higher inflation in future periods — meaning the aggregate price level will be higher — then the currently optimal reset price must be set above the current optimum to avoid being underpriced in future periods. Since a fraction of all firms is resetting today and each is forward-looking in this way, aggregate inflation today reflects the collective forward-looking price-setting decisions, which embed expectations about future inflation. This is the mechanism behind the New Keynesian Phillips Curve: πₜ = βEₜπₜ₊₁ + κxₜ.
The key insight is that price stickiness makes today's pricing decisions implicitly about the future. A fully flexible firm would only optimize for today; a Calvo firm must hedge across an uncertain future duration of price freezing, embedding expectations into current inflation.