Pack-Size Elasticity: The Math Behind Shrinkflation & the Incentive Curve

Within a single brand's portfolio, pack sizes are substitutes. When the price of one size changes, consumers may switch to an adjacent size rather than switch brands. This internal competition is measured by cross-size elasticity.

Cross-size elasticity is the percentage change in volume of Pack B when the price of Pack A changes by 1%. Positive cross-size elasticity means Pack B gains volume when Pack A gets more expensive (they are substitutes). Negative cross-size elasticity means Pack B loses volume when Pack A gets more expensive (they are complements, which is rare within a portfolio).

Typical cross-size elasticities in FMCG:
- Adjacent sizes (e.g., 200g and 300g): +0.3 to +0.8 (strong substitution)
- Non-adjacent sizes (e.g., 200g and 750g): +0.05 to +0.2 (weak substitution)
- Different formats (single vs multi-pack): +0.1 to +0.4 (moderate substitution)

The incentive curve directly governs cross-size elasticity. A steep section of the curve (large PPU drop between adjacent sizes) generates high cross-size elasticity because consumers have a strong incentive to switch. A flat section generates low cross-size elasticity because there is no price-based reason to switch sizes.

Understanding cross-size elasticity is essential before changing any price in the portfolio, because the volume you lose on one size may partially appear on another — or it may leave the brand entirely.

Cross-Size Elasticity (A to B):
E(A,B) = (% Change in Volume of B) / (% Change in Price of A)

Net Portfolio Impact of Price Change on Pack A:
Delta Revenue = Delta Revenue(A) + Sum(E(A,i) x Volume(i) x Price(i) x % Price Change(A)) for all other packs i

Cannibalization Rate:
CR = Volume gained by other own-brand packs / Volume lost by Pack A
If CR > 0.5: most of the "lost" volume stayed within your brand (cannibalization, not brand loss)
If CR < 0.3: most volume left the brand (competitive loss)

Portfolio-Optimal Price:
The price that maximizes total portfolio revenue, not single-SKU revenue.
Requires solving: Max Sum(Price(i) x Volume(i, P)) subject to cross-elasticity constraints.

This is why SKU-level pricing decisions made in isolation are suboptimal — they ignore the cross-size volume flows that determine true portfolio impact.

A frozen pizza brand increased the price of its 350g standard pizza by 5% ($4.99 to $5.24). They expected a volume decline of 8% (own-price elasticity of -1.6).

Actual results over 12 weeks:
- 350g volume: -10% (slightly worse than expected)
- 200g convenience volume: +2% (minimal cross-size effect)
- 700g twin-pack volume: +18% (massive cross-size effect)

The cross-size elasticity from 350g to 700g was +0.9 — far higher than the assumed 0.3. The $0.25 increase on the 350g made the 700g twin-pack ($8.99 for 700g vs $5.24 for 350g) look even better value, triggering a large trade-up effect.

Net portfolio impact:
- 350g revenue: -$180K
- 700g revenue: +$310K
- 200g revenue: +$15K
- Total portfolio: +$145K

The price increase appeared to lose money on the 350g but actually improved total portfolio revenue by $145K. Without cross-size analysis, the brand might have reversed the increase based on the 350g decline alone. This is why portfolio-level analysis is essential — individual SKU results can be deeply misleading.

Cross-size elasticity is difficult to measure precisely because price changes rarely happen in isolation. Practical approaches:

Controlled price tests: Change the price of one pack in a subset of stores and measure the volume response on adjacent sizes. This is the gold standard but requires retailer cooperation and takes 8-12 weeks.

Historical analysis: Identify past price changes on individual packs and measure the simultaneous volume change on adjacent sizes. Requires careful control for seasonality, promotions, and competitor activity.

Scanning data analysis: Use weekly scan data to model the relationship between own-brand pack prices and cross-size volume flows. Econometric models (multinomial logit, nested logit) can estimate cross-elasticities from observational data.

Rules of thumb when precise measurement is not possible:
- Adjacent sizes within 50% of each other (e.g., 200g and 300g): assume cross-elasticity of 0.4-0.6
- Adjacent sizes more than 50% apart (e.g., 200g and 500g): assume 0.2-0.3
- Non-adjacent sizes: assume 0.1 or lower

Always model cross-size effects before making price changes. A price increase on the 400g that shifts 30% of its lost volume to the 250g (at higher PPU) may actually improve total portfolio revenue — but you would never know without the cross-size analysis.

Cross-lesson connection — Pricing Lesson 6 (Cross-Elasticity / Private Label Asymmetry): cross-size elasticity within a brand is a special case of the cross-elasticity matrix introduced in Pricing L6. The Private Label Asymmetry Law (consumers trade DOWN to private label or smaller packs 2-2.5× faster than they trade UP to branded premium or larger packs) applies directly here. When the curve is broken upward (Upsize RSP/kg above Routine), the resulting trade-down to Routine, to private label, or to a competitor's better-priced Upsize runs 2-2.5× faster than a symmetric cross-size model would predict. Apply a 1.2× conservatism multiplier to any same-brand cannibalization estimate when the curve is in a broken state — initial models systematically under-estimate the real-world flow.