Farm systems economic modelling

B.J.Ridler:  2bjr@xtra.co.nz
W.J.Anderson: W.J.Anderson@massey.ac.nz

Abstract:

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 a simplification of the data.

This simplification process involved averaging data which reduced detail, yet detail is required to model the farm as a system. Without this 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.

Introduction

Farming can be deconstructed to maths which should make modelling farms quite simple.

The figures that apply to farming can be quite precise (number of stock, animal production, feed demand for specific animals and production level, cost of inputs, price of product) and monitoring provides most figures on a regular schedule. But the multiple relationships that combine use of resources with 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.

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.

Use of Data

We could apply this same process to roads. (And throughout this process apply the objections you have back to farms.)

There are about 540 vehicles per 1000 people in New Zealand. (http://www.nzta.govt.nz/vehicle/index.html)
This implies that only about half the people at this conference own or lease a car. (But are these data accurate? What is a “vehicle”? Are “people” of driving age or total population?)If the number of vehicles in New Zealand and total kilometres of road are compared, two lane roads and one way bridges are adequate (<2 vehicles/minute -but is this a real-time scale?). A little more thought (or experience on NZ roads) shows this calculation is obviously wrong.The NZ average can be refined to regional figures, which then indicate that Auckland needs two lane bridges. Experience and a little more analysis conclude that specific time periods for specific roads are important data.This is because not only does the road system have constraints, but also the time and place where those constraints occur is critical for efficient traffic flows. Each constraint point (Harbour Bridge) and time (5.15pm weekdays) must be recognized for its relative importance to the overall system performance.In order to create an efficient transport system, detail about the system is required. Such data should include the relative cost or income that any change will bring. Is a truck, bus, commercial vehicle, private car or cyclist more valuable as a user of the limited resource? How much of the resource is used up by each user? Is there a non- economic utility from a specific use of that resource? What are other uses for a specified resource? Can we substitute a different resource, or minimise the constraints in another manner.Many would argue for optional transport systems; bus, rail, ferries, and of course the option to spread the use of the resource over longer time periods by spreading or staggering the hours of business, school and local Government throughout the 24 hour, 7 day week cycle.

There is also a need to allow opportunity for more novel solutions such as increasing the speed of travel or replacing traffic lights with roundabouts where every second vehicle entering has right of way.

But these options require an up-skilling of the car “managers” which some may argue is not possible (an argument used about farm managers too.)

Modelling and Production Models

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.

But as the traffic example shows, 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 them 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. This conceptual process proves to be a stumbling block for the more widespread use of LP. This is evidenced by this statement: “After one lecture, a very agitated student complained that “…this modelling is like creative thinking…” (Suriyaarachchi 2001).During the “GSL LP” development these barriers were overcome. Unlike many other models, verification comes from the accuracy of the mathematical figures produced. It is the LP format that ensures the constraints are adhered to and that resources are allocated in a way that achieves the best overall result. The key to feasibility is the method used to define the input functions (establish the equations) organise these (write out the equations) submit to the LP then allow the LP to solve (within constraints and limits) to ensure feasible plans for implementation at farm level.

Farm Systems Economic Modelling

Simplicity brings a dislocation from the reality those farm systems models must retain. Any model must be transparent (Woodward 2008). 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. This has been discussed in a number of papers (Candler 1962; Ferris 1999; Malcolm 2001) but has either been ignored or not understood.

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.

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. (It is this aspect of incorrect application of economics that has led to increasing nutrient loads and the poor return on assets in New Zealand farming).

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 put a resource (and how much) and 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. This 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 resource or input and examining specific use of an input to identify at what time it is most valuable.

Examples would be:

  • Herd or Flock replacement rates (Ridler 2007 Part1).
  • Production and effect on profit (Ridler 2007 Part2)
  • High input vs. low input systems (Ridler 2008)
  • 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 (Ridler and Anderson 2010)
  • Reduction of greenhouse gases. (Anderson 2010).
  • 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 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 are some changes that, due to their very high economic impact on any system, are likely to have industry wide impact however.

In dairy these are:

  • increasing production per cow (MC/MR limits apply). (Anderson 2010)
  • reducing replacement rate
  • improving herd longevity.

[The economic impact of these is so large that they must be removed from any

economic comparison of systems unless being specifically targeted, otherwise any other peripheral change will be confounded.]

Although not immediately obvious without a full understanding of 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 the budget nor the impact of change on the overall system.

The GSL use of 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 algorithm of LP is able to perform multiple analyses using detailed data to identify constraints whilst moving towards a final 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 allowance for 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.

Reading

Baumol WJ. Economic Theory and Operations Analysis. Second Edition. Prentice-Hall international,1965

(Preview at:  http://www.questia.com/PM.qst?a=o&d=59217067 )

Boehlje MD, Eidman VR. Farm Management. John Wiley & Sons, Inc. 806 pp. ISBN 0-

471-04688-4, Ch 10 Farm Planning with Linear Programming, 1984

Dorfman R, Samuelson PA, Solow RM. Linear Programming and Economic Analysis. (2010 edition)

References

Anderson WJ, Ridler BJ. Application of resource allocation optimisation to provide profitable options for dairy production systems. Proceedings of the New Zealand Society of Animal Production 70, 291-5, 2010

Anderson WJ, Ridler BJ. The effect of increasing per cow production and changing herd structure on economic and environmental outcomes within a farm system using optimal resource allocation. Proceedings of the 4th Australasian Dairy Science Symposium 215-20, 2010

Candler W, Sargent D. Farm standards and the theory of production economics.

Australian Journal of Agricultural Economics 15, 282-91, 1962

Ferris 1999: http://www.agrifood.info/perspectives/1999/

Malcolm B. Farm Management Economic Analysis. Section

4.4, www.agrifood.info/perspectives/2001/Malcolm.html, 2001

Ridler, B. Production and Profit Part 1. UKVet Livestock 12, 38-40, 2007

Ridler, B. Production and Profit Part 2. UKVet Livestock 12, 45-6, 2007

Ridler, B. Comparing high-input and low-input dairy systems.

UKVet Livestock 14, 47-9, 2008

Ridler B, Anderson W. An Investigation of the effect of increasing per cow production on cash surplus using home-grown and purchased feeds within a dairy farm system. UKVet Livestock 15, 24-6, 2010

Ridler BJ, Anderson WJ, Fraser P. Milk, money, muck and metrics: inefficient resource allocation on New Zealand dairy farms. New Zealand Agricultural Economics Society (NZARES) conference, Nelson 2010,  http://purl.umn.edu/96492,

Suriyaarachchi R, Dunstall S, Wirth A. emamo: An on-line self learning tool for LP modeling. ASOR National Conference, Adelaide, September 2001, http://people.eng.unimelb.edu.au/wirtha/simondunstallemamo.pdf

Woodward SJR, Romera AJ, Beskow WB, Lovatt SJ. Better simulation modelling to support farming systems innovation: review and synthesis. New Zealand

Journal of Agricultural Research 51, 235-52, 2008

Image 2

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

Image 3

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

Image 41

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

Image 51


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