Model
What a commitment really saves
A multi-year commitment is a bet against price deflation, and the bet is usually not stated.
How it behaves
One input on the horizontal axis, the others held fixed.
Data table
| List prices fall per year | Real saving over the term |
|---|---|
| 0 | 40% |
| 0.004 | 39.8% |
| 0.008 | 39.5% |
| 0.011 | 39.3% |
| 0.015 | 39.1% |
| 0.019 | 38.9% |
| 0.023 | 38.6% |
| 0.026 | 38.4% |
| 0.03 | 38.2% |
| 0.034 | 37.9% |
| 0.038 | 37.7% |
| 0.041 | 37.5% |
| 0.045 | 37.2% |
| 0.049 | 37% |
| 0.053 | 36.7% |
| 0.056 | 36.5% |
| 0.06 | 36.3% |
| 0.064 | 36% |
| 0.068 | 35.8% |
| 0.071 | 35.5% |
| 0.075 | 35.3% |
| 0.079 | 35% |
| 0.083 | 34.8% |
| 0.086 | 34.5% |
| 0.09 | 34.3% |
| 0.094 | 34% |
| 0.098 | 33.8% |
| 0.101 | 33.5% |
| 0.105 | 33.2% |
| 0.109 | 33% |
| 0.113 | 32.7% |
| 0.116 | 32.5% |
| 0.12 | 32.2% |
| 0.124 | 31.9% |
| 0.128 | 31.7% |
| 0.131 | 31.4% |
| 0.135 | 31.1% |
| 0.139 | 30.8% |
| 0.143 | 30.6% |
| 0.146 | 30.3% |
| 0.15 | 30% |
| 0.154 | 29.8% |
| 0.158 | 29.5% |
| 0.161 | 29.2% |
| 0.165 | 28.9% |
| 0.169 | 28.6% |
| 0.172 | 28.4% |
| 0.176 | 28.1% |
| 0.18 | 27.8% |
| 0.184 | 27.5% |
| 0.188 | 27.2% |
| 0.191 | 26.9% |
| 0.195 | 26.6% |
| 0.199 | 26.3% |
| 0.202 | 26% |
| 0.206 | 25.7% |
| 0.21 | 25.4% |
| 0.214 | 25.1% |
| 0.217 | 24.8% |
| 0.221 | 24.5% |
| 0.225 | 24.2% |
| 0.229 | 23.9% |
| 0.232 | 23.6% |
| 0.236 | 23.3% |
| 0.24 | 23% |
| 0.244 | 22.7% |
| 0.247 | 22.4% |
| 0.251 | 22.1% |
| 0.255 | 21.7% |
| 0.259 | 21.4% |
| 0.263 | 21.1% |
| 0.266 | 20.8% |
| 0.27 | 20.5% |
| 0.274 | 20.1% |
| 0.277 | 19.8% |
| 0.281 | 19.5% |
| 0.285 | 19.1% |
| 0.289 | 18.8% |
| 0.292 | 18.5% |
| 0.296 | 18.1% |
| 0.3 | 17.8% |
Worked examples, recomputed
Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.
- 40% discount, prices −20%/year → ≈ 26% over three years
- over-committing costs 100%, under-committing 40%: 2.5×
Where it appears
Each mechanism states it in its own names. The general symbol each name stands for is shown with it.
- Cost Mechanics
What is metered, and what is the smallest increment you are charged for?