1. AAMP Training Materials
Module 1.3: Profitability of Fertilizer
Shahidur Rashid and Nick Minot (IFPRI)
This is the third section of the Smallholder Productivity Module which is part of the AAMP Training Materials.
Exercises in this presentation are found in the excel spreadsheet entitled:
Module 1.3 – Profitability of Fertilizer.xls

2. Module Outline Objectives Background Materials
Fertilizer Profitability, Case Studies and Exercises
Fertilizer Crop Model Exercises
Conclusions

3. Objectives Assess farm-level profitability of fertilizer use
Fertilizer cost components
Output response of fertilizer applications
Profitability of fertilizer use
Risk and the value/cost ratio (VCR)
Use Fertilizer Response Model
Evaluate the impact of price and policy changes on fertilizer use, crop output, and consumer and producer benefits

4. Background Material Review of markets & prices
From cost curves to the supply curve

5. Q: What determines the process of exchange?
Markets and Prices
Market
Price
Process of exchange
Outcome
The process of exchange is determined by several factors:
The number of traders, producers, and consumers
Infrastructure, information, institutions, coordination, technology
Law, regulations, contract enforcement
Q: What determines the process of exchange?

6. Demand & Supply DEMAND SUPPLY PRICE
Consumers maximize satisfaction from what they buy given their income
Producers maximize their profits given certain technology
DEMAND
SUPPLY
PRICE

7. From Cost Curves to the Supply Curve
Average Total Cost (ATC) is a firm’s total cost divided by the quantity produced.
Marginal Cost (MC) is the change in total cost for a change in output, or the cost of the “next” unit produced. A firm’s MC also acts as its supply curve.

8. The Individual Firm and the Market

9. Fertilizer Profitability
Fertilizer cost
Crop response to fertilizer application
Profitability of fertilizer use
Risk and the value/cost ratio
Exercises on fertilizer profitability

10. Fertilizer cost build ups
Fertilizer costs in Africa are often double the world price, because of high transport costs (particularly to landlocked, interior countries), small markets and consequent inability of traders to benefit from large economies of scale in procurement and shipping. For example, fertilizer prices in Uganda in 1999 were $600 per ton at farmgate. When Ugandan importers were able to combine their import orders with large importers in Kenya, the retail price of urea in Uganda dropped by more than $300 per ton (Morris et al. 2007, p.57).
Even after fertilizer arrives in country, internal distribution costs are high. The above data from Ethiopia show that internal distribution costs raise farmgate prices by 25 to 30% above the already high CIF import price.

11. Case study of maize profitability
As these budgets show, fertilizer costs account for over 90% of cash costs in maize production.

12. Fertilizer responsiveness on maize (maize yields (qt/ha)
These data demonstrate that maize yields increase by an average of 40% on plots where farmers apply fertilizer. In very arid regions, such as SNNP, the response is not high, because most fertilizers are highly dependent on adequate moisture. In well watered regions, such as Oromia, yields increase by 50% on fertilizer fields compared to those using no fertilizer at all.

13. Ethiopia Fertilizer – Yield Response Elasticities
These data indicate that improved seeds also increase fertilizer responsiveness. The first row indicates that a 1% increase in fertilizer (together with improved seeds and adequate water) increases maize yields by 0.26% to 0.35%. The second row indicates that a 1% increase in fertilizer (with local seeds) increases maize yields by about half as much. Clearly, crop responsiveness to fertilizer applications varies by location, by crop, and according to the amount of complementary inputs (such as improved seeds).

14. Key Factors Behind Fertilizer Profitability
Fertilizer Price
Highly Variable
RISK
Output Price
Current Yield
Weather Uncertain
Fertilizer use in Africa is risky because of highly variable rainfall, output prices and fertilizer prices. In a bad rainfall year, a farmer may lose her whole crop. Farmers who apply fertilizer in a bad drought years therefore lose all the money they invested in fertilizer. For this reason, farmers typically require “average” gains to fertilizer to be significantly greater than “average” benefits of applying additional fertilizer. The value/cost ratio provides an empirical guideline as to how much more.
Level of Use
Lack of Public Goods
Transaction Costs
High Prices

15. Value/cost ratio (VCR)
VCR = value of increased crop output cost of fertilizer applied = P(crop)*Q(additional crop production) P(fert)*Q(fertilizer applied)

16. Risk and fertilizer use
Fertilizer use is highly risky in Africa because of highly variable weather
Drought  crop losses
Drought  heavy financial losses when purchased inputs (like fertilizer) applied

17. Risk and VCR
Rule of thumb: given normal risks, VCR > 2 necessary for farmers to use fertilizer
High risk production environments: VCR > 3-4 necessary for farmers to use fertilizer
See Morris et al. (2007), p.46.

18. Fertilizer Profitability Example
Elasticity estimate for fertilizer response = 2.6
Therefore, a 10% increase in fertilizer use  2.6% increase in yield response
Average fertilizer use is 80kg/ha, so…
10% increase in fertilizer use  8kg/ha additional use of fertilizer
Cost of additional fertilizer = 8kg * 4 Birr/kg = 32 Birr
Average yield is 1700 kg/ha. Using our elasticity estimate,
Expect a 2.6% increase in additional output  44.2 kg/ha
Additional value of extra production  44.2 kg/ha * 2.5 Birr/kg = 110 Birr/ha
Extra revenue due to fertilizer  – 32 = 78.5 Birr

19. Profitability Exercise 1
Exercise 1 Data
Maize production per hectare
1000 kg
Maize price
2.67 Birr/kg
Average fertilizer use
80 kg/ha
Fertilizer price
5 Birr/kg
Fertilizer response elasticity
0.3
10% increase in fertilizer use  8 kg/ha additional use of fertilizer.
Cost of additional fertilizer = 8 kg/ha * 5 Birr/kg = 40Birr/ha
10% increase in fertilizer use  3.0% increase in yield
3.0% increase in yield  30 kg/ha
Value of additional yield  30 kg/ha * 2.67 Birr/kg = 80.1 Birr/ha
Extra revenue from 10% increase in fertilizer: 80.1 Birr/ha – 40 Birr/ha = 40.1 Birr/ha
VCR = 80.1/40.1 = 2
Yes, it is profitable to increase fertilizer use by 10% in this scenario.
Question 1: Given the data above, will it be profitable for a farmer to increase fertilizer use by 10%

20. Profitability Exercise 2
Exercise 2 Data
Maize production
1,000,000 MT
Maize price
2.67 Birr / kg
% increase in maize production 6%
% increase in fertilizer use
20%
Fertilizer price
5 Birr/kg
Price elasticity of supply
0.5
Average fertilizer use
80 kg/ha
Price elasticity of supply = %∆ supply / %∆ price  0.5 = .06 / x  x = .12
The decline in the maize price is 12% for a 6% increase in maize supply.
If the previous maize price was 2.67 Birr/kg, the new price after the price drop is 2.35 Birr/kg.
The country gains 60,000 MT extra production with it’s 20% increase in fertilizer, yielding approximately 141,000,000 Birr.
The country uses 20% more fertilizer. The original usage was 80,000 MT. The additional fertilizer is 16,000 MT. The value of the extra fertilizer is 16,000 MT * 5000 Birr = 80,000,000 Birr
Profit: 141,000,000 – 80,000,000 = 61,000,000
Question 2: Suppose the country increases fertilizer use by 20%, which leads to a 6% increase in maize supply. If the price elasticity of supply is 0.5, what will happen to maize price? What will happen to profitability?

21. Using a Fertilizer Crop Model
Review
What is a model?
Example of a simple model
Comparative Statics
Understand fertilizer response curve
Discuss crop supply and demand

22. What is a model?
A model is a set of equations that represents some aspect of reality and converts data and assumptions into useful results.
Data
Assumptions
Model
Results

23. Example of a simple model
Data: Distance from
Livingstone to
Lusaka is 472 km
Assumption: Can drive at 60 kph on that route
MODEL:
Time = Distance/speed
Results: Time=7.9 hours

24. Comparative statics
Running a model repeatedly with some difference and comparing results
Alternative data
Alternative
assumptions
Base data
Base assumptions
Model
Model
Base results
Alternative results
Example: If we could increase our speed from 60 to 70 kph, it would take us
15% less time or 6.7 hours.

25. A fertilizer-crop model
Assumptions: relationship between fertilizer use and crop yield, farmer behavior and elasticity of demand.
Data: current crop production, crop consumption, crop price, fertilizer price (before subsidy), subsidy rate, & fertilizer use.
Model
Results: fertilizer use, crop production, crop consumption, & crop price, given a change in data or assumptions

26. Fertilizer response curve
Yield is positive even with no fertilizer
Yield rises with more fertilizer, but the rate of increase declines
Too much fertilizer will reduce yield

27. Fertilizer response curve
a is the yield with no fertilizer (a>0)
b determines the steepness of the curve at the beginning (b>0)
c determines how quickly it turns down (c<0)
Yield = a + b*F + c*F2

28. Fertilizer response curve (in value terms)
If we multiply yield by crop price, we get the curve of the value of production per hectare
It has the same shape
We can add cost of fertilizer per hectare (red line)
Profit from using fertilizer is vertical distance
Profit

29. Fertilizer response curve (in value terms)
Black box maximizes yield
Blue box maximizes profit
Red box is where a risk-averse farmer might choose to produce

30. Fertilizer response curve (in value terms)
Fertilizer subsidy lowers the angle of the red line (dashed red line)
This increases optimum amount of fertilizer and increases yield

31. Fertilizer supply and demand
Fertilizer subsidy lowers the retail price (red lines)
This increases fertilizer use from 25 to 33 kg/ha

32. Crop supply and demand
Fertilizer subsidy increases crop supply (shift to right)
This lowers price if non-tradable

33. Crop supply and demand
Benefit to consumers is reduction in price multiplied by quantity consumed
Benefit to farmers: is area between supply curves (red) below equilibrium price

34. Fertilizer Response Exercises (Notes)
Only yellow cells should be changed
Generally we want to change the “after” cells so we can compare “before” and “after” results
Don’t forget to return changed numbers to their original values before doing the next exercise.
The model does not account for rationing, late delivery, targeting, leakage, rent seeking, or differences between farmers and regions etc. Nor has it been calibrated using real-world data. Therefore, it should be considered a training tool, nothing more.

35. Fertilizer Response Exercises
Evaluate the effect of a new seed variety that is more responsive to fertilizer.
Change the “b” coefficient (cell E14) from 25 to 30.
What is the effect of a new seed variety that gives a higher yield without fertilizer, but gives same response to fertilizer?
Change the “a” coefficient to 900, but leave “b” and “c” as is.
What is the effect of an increase in the crop price on fertilizer use?
Change the crop price from US $250 to US $300.
A more responsive seed variety means that the optimum use of fertilizer increases from 34 kg/ha to 44 kg/ha. This increase in fertilizer application is accompanied by an increase in yield, from 340 kg/ha to 409 kg/ha. Simultaneously, the demand for fertilizer shifts outward, and the supply of crop expands.
The new variety of fertilizer boosts yields without fertilizer, therefore the farmer’s optimal fertilizer application rate is the same as before. Consequently, there is no increase in demand for fertilizer, but there is an outward shift in supply of crop.
If the price of crop output increases, demand for fertilizer increases. This happens because farmers are able to offset the cost of extra fertilizer due to the extra revenues they collect from selling crops. The supply of crop also increases in response to the increase in price.

36. Fertilizer Response Exercises
What would be the effect of a program that made farmers less risk averse?
Reduce the VCR (Cell E11) from 2 to 1.5
What is the effect of a 40% subsidy on fertilizer utilization? Do farmers use more or less than the economic optimum? What about 50%? And 60%? Which gives the largest net impact on the country?
Suppose farmers were not risk averse and were economically rational. What is the net impact of a fertilizer subsidy?
Hint: set VCR=1 in before and after columns.
Risk averse farmers do not produce at the economic optimum due to a number of factors. If a program were put in place that reduced risk, the farmers would produce more.
A 40% subsidy on fertilizer increases the demand for fertilizer and boosts crop supply. The farmer utilizes just slightly less fertilizer than is needed to achieve the economic optimum. A subsidy of 50% further reduces the price, leading the farmer to purchase exactly the right amount of fertilizer to achieve economic optimum. A 60% increase, however, pushes the farmer beyond the previous economic optimum, dropping price substantially. The largest net impact is the lowest (40%) subsidy.
If farmers are not risk averse, they produce the amount of crop that achieves economic optimum. An increase in the fertilizer subsidy will make very little difference to the price of crop in the country, but the cost of the program would be quite significant.

37. Fertilizer Response Exercises
What is the net effect of a 50% fertilizer subsidy if the administrative costs are 40% of the direct subsidy costs? How about 50% or 60%?
What is the distribution of gains from a fertilizer subsidy between farmers and consumers? Why is one larger than the other? What would be the distribution be if the demand for the crop were highly elastic (e.g. elasticity of demand=-20)? What kind of crops have a highly elastic demand?
Administrative costs reduce the net impact on the country substantially. The higher the administrative costs, the lower the net impact. At 60% admin costs, a 50% subsidy gives the country a negative impact because the costs of the program outweigh the benefits.
In this scenario, the subsidy benefits consumers more than producers in the country. This has to do with the steepness of the supply and demand curves, or the price elasticity of supply and demand. When the elasticity of demand is very high (-20), such as in the case of a crop for which there is a readily available substitute, this situation reverses because consumers will only purchase a very small additional amount of the crop when the price decrease.

38. Conclusions
In order to simulate impact of fertilizer policies, one needs:
Data on current use by crop and yield responsiveness
Estimates of supply and demand elasticities for fertilizer & crop
Assumptions about farmer decision making process (what is minimum VCR?)
Fertilizer demand can be affected by:
Yield response of crop (maize & rice respond more than cassava)
Yield response of variety (modern varieties respond more)
Price of fertilizer (subsidy or lower price  higher demand)
Risk aversion of farmers (lower risk aversion higher demand)
Crop price (higher price makes fertilizer more profitable)

39. Conclusions Increased fertilizer use causes:
Increase in supply of crop with benefits to farmers
Reduced price of crop (if non-tradable) with benefits to consumers
Distribution of benefits of higher fertilizer use depends on elasticity of demand for the final output (maize, cotton, etc)
Inelastic crop demand means price falls more, larger benefits for consumers, smaller benefits for farmers
More elastic crop demand means price falls less, smaller benefits for consumers, larger benefit for farmers
If tradable crop, price fixed by world markets and no benefits for consumers, all benefits to farmers

40. References
Kelly, V Factors affecting the demand for fertilizer in sub-Saharan Africa.” ARD Discussion Paper No. 23. The World Bank. Washington, DC.
Morris, M. et al Fertilizer use in Africa. The World Bank. Washington, DC.