Methodology
This page documents the analytical framework behind the Fertilizer Affordability Model, including the formulas used, how results should be interpreted, and important notes on data comparability.
Fertilizer affordability refers to the ability of farmers to purchase fertilizer relative to the income they can generate from selling their crops. When fertilizer prices rise faster than crop prices, farmers face a deteriorating economic environment that may reduce fertilizer use, lower yields, and threaten food security.
This model quantifies affordability using two indicators: the Barter Ratio and the Affordability Index. Together, they provide a standardized, time-comparable measure of how many units of crop output a farmer must sell to purchase one unit of fertilizer input.
The Barter Ratio (BR) measures how many units of a crop a farmer must sell to purchase one unit of fertilizer. It is calculated as:
Barter Ratio Formula
Barter Ratio (BR) = Fertilizer Price (per ton) ÷ Crop Price (per ton)
For example, if DAP fertilizer costs $600/ton and corn costs $200/ton, the Barter Ratio is 3.0 — meaning a farmer must sell 3 tons of corn to buy 1 ton of DAP.
Higher Barter Ratio
Fertilizer is less affordable. More crop output is required to purchase the same amount of fertilizer.
Lower Barter Ratio
Fertilizer is more affordable. Less crop output is required to purchase the same amount of fertilizer.
The Affordability Index (AI) normalizes the Barter Ratio against a selected base period, enabling comparison of affordability across different time periods on a common scale. The base period is assigned an index value of 100.
Affordability Index Formula
Affordability Index (AI) = (Base Period Barter Ratio ÷ Current Period Barter Ratio) × 100
For example, if the base period Barter Ratio was 3.0 and the current period ratio is 4.0, the Affordability Index is (3.0 / 4.0) × 100 = 75 — indicating affordability has declined by 25% relative to the base period.
Index Above 100
Fertilizer is more affordable than the base period. The farmer needs fewer crop units to buy fertilizer.
Index Below 100
Fertilizer is less affordable than the base period. The farmer needs more crop units to buy fertilizer.
The base period can be configured by administrators in three ways:
| Type | Description | Use Case |
|---|---|---|
| Single Year | Uses the annual average Barter Ratio for a specific year | Standard long-term comparison |
| Single Month | Uses the Barter Ratio for a specific month and year | Monthly or seasonal analysis |
| Average Period | Uses the average Barter Ratio across a range of years | Smoothed baseline for volatile markets |
The following considerations are critical when interpreting Barter Ratio and Affordability Index results across different datasets:
- 1Prices must be expressed in the same currency and unit (e.g., both in USD per metric ton) for the ratio to be meaningful.
- 2Fertilizer prices may reflect different market levels (farm gate, wholesale, retail, CIF port). Comparisons across markets require consistent price definitions.
- 3Crop prices should represent the price received by farmers, not consumer retail prices, to accurately reflect the farmer's economic position.
- 4Seasonal price variation can significantly affect monthly Barter Ratios. Annual averages provide more stable comparisons.
- 5Currency fluctuations affect cross-country comparisons. Consider using local currency prices for domestic analysis.
- 6The model does not account for fertilizer application rates, crop yields, or profitability — it measures price relationships only.
| Indicator | Formula | Higher Value Means | Lower Value Means |
|---|---|---|---|
| Barter Ratio | Fert. Price ÷ Crop Price | Less affordable | More affordable |
| Affordability Index | (Base BR ÷ Current BR) × 100 | Better than base period | Worse than base period |