Menu Costs: When Prices Won't Move

In micro, an out-of-place price moved at once. In macro, the cost of changing price tags holds prices still.

Changing a price means reprinting the menu. Shops hate that cost, so they put up with small losses. Only a shock past the threshold below makes them move. While prices stay frozen, sales and jobs take the hit instead.

For example, ✏️ pencils at the 🏪 stationery shop cost 500 won. Costs creep up a little, but the owner leaves the tag alone. Rewriting every tag is more trouble than the small loss. Instead, the shop simply stocks fewer pencils.

\pi(p) = \pi^* - k(p - p^*)^2

\delta^* = \sqrt{F / k}

Part of these learning paths

Examples & Exercises

The market's ideal price fell by $1$ .

A restaurant with a menu cost of $4$ — does it reprint its price list? (Standing still loses $2\delta^2$ .)

Small shock

\delta = 1

, menu cost

4

— price stays.

Show proof

Standing still loses $2 \cdot 1^2 = 2$ . That is less than the menu cost $4$ , so reprinting would lose more than it saves — the rational choice is to leave the price alone.
Profit is $100 - 2 = 98$ , nearly intact: near the top of the profit hill the ground is flat, so a small miss barely hurts.
Quantity absorbs it instead: the now-too-high price sheds $5$ customers, and volume falls from $50$ to $45$ . The price is spotless while the quantity is bruised — the face of a short-run macro fluctuation.
(The band's edge is $\sqrt{4 / 2} \approx 1.41$ : any smaller shock is swallowed whole.)

This time the ideal price fell by $3$ .

What does the same restaurant, menu cost $4$ , do now?

Big shock

\delta = 3

, menu cost

4

— price adjusts.

Show proof

The loss grows with the square: $2 \cdot 3^2 = 18$ . Triple the shock, nine times the loss.
That towers over the menu cost $4$ , so cutting the price wins. After adjusting, profit is $100 - 4 = 96$ , far better than the $100 - 18 = 82$ from standing still.
The price moved from $10$ to $7$ , so volume recovers to $50$ . Big shocks are absorbed by prices and leave quantities whole; small shocks are absorbed by quantities and leave prices whole — which side takes the hit depends on the shock's size.

6. The Two Faces of Wages, and Unemployment