Economic Modelling of Farm Production Systems

Authors: Barrie Ridler and Warren Anderson

Introduction

Farming is primarily for profit and maths provides the key to understanding how to make the most profit. But the significance of the interactions and interrelationships that are part of any farm system has been blurred by over simplification of the data.

This simplification process relies on averaged data which reduces detail, yet detail is required to model the farm as a system. Without detail attempts to accurately model the production, but more significantly the economics of production, become questionable.

Linear Programming provides the mathematical procedures to solve complex farm systems with the added advantage of providing economic insights into what, how and why change occurs.

Deriving Knowledge from Modelling

Farming can be deconstructed to maths which makes modelling farms quite simple. The figures that represent a farming system can be quite precise (number of stock,
animal production, feed demand for specific animals and production level, cost of inputs, price of product) and a farmers monitoring provides most figures on a regular schedule. But the multiple relationships that combine the use of resources for production and profit make understanding or more importantly for modelling, conceiving these processes, difficult. The reaction by many has been to simplify the picture by presenting averaged rather than actual data.

This has led to ratios, outputs or inputs per cow, per hectare, per kgMS; which are raw averages. These have become extension terms for technology transfer purposes and have been accepted because so many research and extension workers are unaware of their shortcomings.
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Farms are now judged for many different purposes on the basis of a factor (production, debt, profit, input or output /ha or /cow) without understanding that details about inputs, the cow or the hectare are paramount in any useful systems analysis. Averaged figures and ratios are now readily accepted in farming and compared (through “benchmarking”) as if they contain all the information relevant to profitable farm decision making across all individual farm environments.

Modelling and Production Model Limitation

Arithmetic calculations are used in an attempt to define the production of a farm and can give some insight into the relationship between the resources, but few models are able to account for the non-uniform relationships that exist within farm systems.

Modelling of a farm business can take many forms and is done for many purposes. Accounting for taxation purposes is the most common form of mathematical modelling applied to farm businesses, albeit historical. Financial modelling in the form of partial budgets, cost/benefit analysis and benchmarking are all in common use. They mainly employ spreadsheet techniques which limit the number of variables
that can be altered during the analysis. Each change or series of changes is determined before the computation begins.

However, detail is required to identify constraints. The use of averages of data within a deterministic production model makes it impossible to identify future constraints.

There is limited or no capability to reference or modify calculations as the model runs, yet in a systems context continual re-evaluation must be occurring to assess possible substitutions of resources which will make the system increasingly more efficient and profitable. Without this facility, constraints become unknowns with a future cost.

A range of model runs can be undertaken but this will increase the time and cost of the modelling process without expanding knowledge about the system. Averages, ratios and benchmarks hide detail and therefore constraints cannot be identified. The benefit from modelling a system is in being able to identify constraints and overcome them before they prevent progress and create expense.

Linear Programming (LP)

This is a mathematical technique used to handle far more complex problems than those of production solutions, financial or partial budgeting. Component models split the system into discrete areas to simulate. Such simulated results should not be directly added back into the original system due to the flow-on effect to the system as a whole. LP can include a myriad of variables yet is able to manipulate each of variable as a component of the whole as the LP progresses.

Allocating 70 different people to 70 different jobs has the potential to provide so many possible solutions that the capability of any calculator is exceeded. This is why managers tend to use ‘rules of thumb’. Comparative analysis and benchmarks are used for a similar reason as it seems too hard to consider all the options.

That is unless they use LP as it only takes a moment to find the optimal solution by posing the problem as a linear programme. The theory behind LP allows it to drastically reduce the number of possible optimal solutions that must be checked, so cuts out unnecessary ‘clutter’. The result is a highly efficient modelling tool especially when allied with low cost computing power.
Mathematical algorithms provide a continual re-evaluation of the value of each component of a system as the LP progresses towards an optimal solution within a single computation.

LP provides information on the relative value of the resources used, which resources are most limiting, (or in excess), the price that can be paid for a limiting resource (within a critical time period), the robustness of the resource use and the opportunity cost of selecting one resource allocation over another.

The barrier to the use of LP in farming has been the requirement to describe, then construct a full farm systems model with all its integrated economic constraints and variables; determine the objective function and provide a framework to incorporate all applicable constraints into the model accurately and efficiently.

Farm Systems Economic Modelling

Simplicity brings a dislocation from the reality which farm systems models must retain. Any model must be transparent and it must coincide with the reality of farmer experience of the specific farm yet still be able to challenge preconceived ideas. This makes the data used and the input of that data extremely important.

Production economics is a science in itself and those who have some knowledge in the field will realize that robust Farm Systems Economic Modelling does not result from simply adding $ values to the physical inputs and outputs of a model for farm production, then comparing them.

The concept of diminishing returns to added inputs, marginal responses and analysis, substitution, opportunity costs and partial budgets must all be addressed to validate a farm systems economic outcome. LP provides an ideal framework for integrating these complex interrelationships between resource options in a manageable format.

As any input is added to a system, there is usually an initial positive response. This tapers off until a “tipping point” is reached where there is no additional response or it becomes negative. This is known as “diminishing returns”.

As an example, the response to the application of increasing amounts of nitrogen (N) to pasture on a bull beef unit is shown in Table1 (columns 1 and 2) and Figure1 (Appendix)

Economic values are added to the physical input of kg N/ha. and the subsequent production of bull beef to provide a $ input and $ return sequence. From a purely production point of view, maximum production of pasture and beef occurs at about the 80-90kgN applied level.

The highest total revenue (TR) figure in Column 4 also corresponds to this level. It is unfortunate that this point is often chosen for the economic input figure due to the ease in obtaining it. At times even the Total Revenue (TR) minus Total Cost (TC) figure (95kgN applied in Table 1 or where the two lines intersect in Fig.2) has been wrongly used.
Analysis of Table 1 shows that somewhere between 40 and 50 kgN/ha. applied, a point is reached where the extra pasture grown and converted to beef at $4/kg carcass weight does not pay for the extra nitrogen used to achieve this result. $Marginal Cost ($MC) and $Marginal Return ($MR). The diminishing return to additional nitrogen as shown in Fig1 can no longer economically justify continuing to add more of this input and this is illustrated in Fig 3 as is the relationship between the TC and TR figures, MC and MR columns.

The clarity provided by data from each additional 10kg of N applied can be lost when an averaged response ratio is applied. Economic accuracy is destroyed, resources are poorly used and this impacts on the wider environment.

As an example of this, when 610kgDM are produced from 90kg of N the averaged ratio of 6.8:1 (90kgN producing total 610kgM) apparently justifies the cost of the N. (15 kgDM is converted to 1 kg carcass weight (CW) in this case; a kg CW is worth $4 and a kilogram of N costs $1.67; the return for the averaged kgN response of
6.8KgDM is 0.45KgCW which at $4/KgCW is worth $1.81 and covers the cost of the
N).

However in reality, the actual response from increasing from 80 to 90kgN/ha was negative (620kg DM reduced to 610kgDM) and means the averaged calculation provided a nonsense result due to an averaged ratio being used instead of considering the marginal response to an additional input. This highlights the need to understand diminishing returns and the economic insight that comes from application of marginal cost (MC) and marginal return (MR) that is a consequence of diminishing returns.

The LP process allows input and output relationships to be progressively tested for optimal economic outcome at each stage of the simulation, not just when a single simulation has been completed. This latter method may by chance provide a similar answer to that from a farm systems economic model but without the clarity of resource use limits and sensitivity analysis that LP provides.

Without reference to the marginal response to inputs and an understanding that diminishing returns will apply to any increasing use of a resource, any economic analysis will be flawed. It is difficult (and far more expensive) to identify constraints, the importance of each constraint and the variation likely around the “tipping point” of MC vs. MR without the use of LP.

To this needs to be added the distinction between fixed and variable costs and the “lumpy inputs” such as labour and some machinery which at times straddles the two. Fixed costs (FC) are those incurred whether there is enterprise activity or not; variable costs (VC) are incurred by the enterprise and they would not be incurred if the enterprise was not undertaken. Examples of FC are rates, interest, principal
repayments and living expenses.

Within any analysis FC and VC need to be carefully separated, especially where averaged ratios are used (cost/cow or worse still costs per kgMS). Again, as with the need to distinguish additional cost and income within the LP framework, correctly identifying the impact of other economic factors also becomes part of the LP solution.
The same principal applies to all additional input and output scenarios; the tipping point for each must be correctly defined. This is not possible where averaged figures
or ratios provide the economic input or where a single computational procedure works through a series of defined steps to reach a conclusion. This fact is sidestepped by taking a production model result then using an optimisation routine about the solution or applying partial budgeting techniques as a comparative analysis technique.

The important point to note is that neither of these options of providing economic results is able to identify or respond to constraints or identify the tipping point for a specific resource within individual systems. Nor does this approach acknowledge that an outcome almost always involves a number of contributing resources or performance criteria which cannot be identified within ratios, benchmarks or comparative analysis of merged data. This limits the ability to establish even the constraints that apply to physical outputs. Without this core function, correct economic solutions will only be found by chance (or by following the clues provided by LP models).

LP allows substitution between resource uses without user intervention, but can be constrained by user preference. Substitution may occur when the MC vs. MR of any number of inputs reaches (or approaches) the tipping point of MC>MR and allows the novel solutions that can occur in LP models but are not possible from other formats.

A Partial Budget, as the name suggests, considers the physical and financial effects of a change to a firm, while leaving out of the analysis factors not pertaining to the change. Although applying partial budgets to specific parts of a system may be
helpful in some cases, using them as a general tool for systems analysis suffers from the same weakness of not being able to clearly identify constraints and their relationship to each other and to the system.

Analysis is limited to a few alternatives, none of which may be a near optimal solution. Trying to expand the range of options suffers from time and preconception constraints. Partial budgets are therefore limited in scope and may not be addressing the real constraint to the system (similar to choosing between traffic lights or roundabouts on a motorway off-ramp without recognizing that this does not solve the major constraint of the Symonds Street Interchange).

So just where is it best to spend money for best return?

LP quickly identifies the best place to apply a quantified resource but can allow for preference or risk by restricting resource use at the users discretion. This process also establishes a very clear economic comparison between two options after the restriction has been imposed.

LP results are sometimes euphemistically labelled “counter intuitive” because they do not conform to current perceptions. It may require some modification of the input data or, more likely, up-skilling knowledge bases and management expertise to take advantage of a new opportunity.

The GSL linear programming (LP) model:

GSL uses data from each farm as it is currently functioning. This may be in the form of actual monitored data or a combination of monitored data and that calculated from actual farm performance over 2 weekly periods.

Within GSL a number of simultaneous equations describe the resources available. If some are known accurately and others are not, the process of running the LP will mathematically fill in the gaps with enough clarity to be able to complete the initial run and provide the means to ask further questions highlight constraints and indicate where additional data will provide greater accuracy.

This same process enables detail such as stock reconciliations, breed, weight changes, production, dry-off options, cull options plus cost and income data to build from 2 weekly through to year by year solutions.

This methodology allows ranging of input numbers or a full optimisation which is extremely useful for nitrogen fertiliser, crops, supplementary feeding or stocking rate issues. The LP user can limit inputs or some output functions (e.g. greenhouse gas emissions) where a cap may be seen as useful.

The GSL LP format also allows multiple resource use options to be selected and can run varying performance herds or flocks within the same analysis in order to determine the relative profitability between them under the same farm resource conditions.

Application of the LP

The applications can be broad or detailed. Between farm systems, within farm systems, limiting use of a specific resources or inputs or the examination of a specific use of an input to identify at what period of time it is most valuable.

Examples would be:

  • Herd or Flock replacement rates
  • Production and effect on profit
  • High input vs. low input systems
  • The value of irrigation or specific crops within systems.
  • The impact of disease (as reflected through costs, culling and production. changes within a herd structure) on a farm system.
  • Grazing off.
  • Impact of increasing production per cow on profit
  • Reduction of greenhouse gases.
  • Mitigation strategies that impose least cost solutions (Ridler et al 2010).
  • Capping levels of use of nitrogen and other nutrients

This last example highlights the detail offered through LP. The GSL model was used to identify the periods in which N applications to pasture appeared to have the least economic impact on particular farms. The GSL LP model was then allowed to optimise for N use and eliminated almost 35% of the N applied. In this case economic
performance of the farm also improved (as the MC vs. MR of the additional N being used was negative.)

This example highlights that all dry matter (setting aside the factors of quality and utilisation) is not equal and that “calculating” average economic values for feed is misguided. It will all depend on how valuable that feed is to the overall system when overcoming a particular constraint (now or in a week or months time) and how much more efficient the system will become should that constraint be overcome. This is what decides the “value” of feed. It can only be assessed for a specific system and for specified changes within that system. Any wider application will be guesswork.

There will be some changes identified by the LP modelling system that, due to their very high economic impact on any system, are likely to have industry wide impact.

In dairy these are:

  • increasing production per cow (MC/MR limits apply).
  • reducing replacement rate
  • improving herd longevity.

Although not immediately obvious without a full understanding of production systems, all the above changes will lead to an increase in the average kgMS production per cow. This is another example of how averaged figures fail to correctly identify how or why change occurs and can lead to incorrect conclusions about causal relationships.

What farm systems models show is that there is far more flexibility available for management than many prescriptive decision rules allow.

Pasture can be flowed forward as average pasture cover or as harvested supplement and can be managed to avoid quality and utilisation issues. This provides the opportunity to reduce a constraint in the future by taking some action now. It also means that the simplistic calculations that prevail for value of winter grazing-off or heifer grazing off can provide the wrong conclusions.

The GSL LP provides breakeven prices for all such options taking into account the resources specific to each individual farm. By comparison, partial budgets are often completed without reference to the periods before and after neither the budget nor the impact of change on the overall system.

The GSL LP provides far more than a series of solutions. It provides a window into understanding what has occurred, how it has occurred, but most importantly why it has occurred. It is effectively a blueprint for connecting dots forward rather than continually rearranging how the dots may have connected backwards.

Summary

 

  •  Averaging data destroys detail.
  •  Detail is required to identify constraints.
  • The solution finding algorithm of LP is able to perform multiple analyses using stable detailed data to identify constraints whilst moving towards a final optimal solution.
  • This process also reveals information about the timing and location of the constraint.
  •  The process itself can be used to fill in “data gaps”.
  • It provides an economic answer to the benefit of overcoming each constraint and the resource combination that best suits the overall system including  the manager’s objectives and attitude towards risk.

When taken to the core functions, farming is all about applied maths. The key to the application however is the level of management expertise that understands and implements the correct figures at the correct time.

Appendix:
Table 1: Marginal Cost and Marginal Return Table:

Image 13

Fig.1: Diminishing Returns Curve. Pasture Dry Matter response to added
Nitrogen (from Table 1 data).

Image 14

Fig.2: Total Revenue vs. Cost of added Nitrogen (from Table 1 data).

Image 15

Fig.3: Marginal Cost and Marginal Return to additional nitrogen (from Table 1 data).

Image 16

Condensed from the Paper:

Farm systems economic modelling

B.J.Ridler:  2bjr@xtra.co.nz

W.J.Anderson: W.J.Anderson@massey.ac.nz

 

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