Estimation of Reduced Machinery Ownership Costs in Diversified Cropping Systems

Final Report for LNC94-063

Project Type: Research and Education
Funds awarded in 1994: $29,544.00
Projected End Date: 12/31/1997
Matching Federal Funds: $11,990.00
Matching Non-Federal Funds: $12,300.00
Region: North Central
State: Nebraska
Project Coordinator:
Glenn Helmers
Dept of Agricultural Economics, University of Nebraska
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Project Information


The economic benefits of rotational cropping are normally perceived to result from positive yield interactions, reduced inputs, and reduced risk. The objective of this project is to estimate another benefit, that being reduced machine ownership and labor costs when growing crops in combination either in rotations or in simple diversification of continuously grown crops. These benefits have been difficult to quantify previous to recent advancements in securing mixed integer linear programming solutions.

In this project farm returns are maximized for four crop alternatives (corn, soybeans, oats, and alfalfa) or any mix of the four crops. The setting is eastern Nebraska under dryland conditions. In addition to the usual annual cost and returns items, the cost of machine ownership and labor is included in the decision process. While it is recognized that this cost (machine ownership and labor) will vary by cropping system, the quantification of these costs have been difficult to estimate. Here this is accomplished by also including the choice of field machines and labor in the optimizing process and providing a cost for each selected. Omitting machine ownership and labor from consideration in the economics of cropping systems as is commonly done may seriously bias results against diversified and rotational cropping by ignoring system benefits that arise from such crop mixes. The research model of this project includes several field time “windows” during which field operations for any crop must be completed. A large number of field machine alternatives were provided. The benefits of crop diversification arise because smaller machine-labor sets can be used for such multi crop systems compared to larger sets necessary under single crop situations. This occurs because multi crop systems reduce time pressure in the “windows” of field time.

The specific reduced cost results from diversifying crops depend upon farm size and the particular crop mix examined. For example, the highest multi crop benefit was found when soybeans replaced continuous corn on one-half the acreage of a 640 acre farm, with machine ownership, labor, and machine operating costs reduced by 57 dollars per acre (expressed per acre for 640 acres). Machine operating costs were included because these are inseparable from the particular machine set chosen. The reduced cost benefits are less for other crop combinations.

The above benefits were estimated allowing diversified herbicide-tillage methods in combination with diversified cropping. When only diversified cropping under a constant herbicide-tillage system was examined, benefits were reduced but still very significant.

The results were also generalized by crop across a range of rotation systems. This enables machine ownership, labor, and machine operating costs to be estimated for any crop mix from once-estimated relationships. Hence, a model of the detail described above is only needed once to estimate cost relationships and thereafter, cost of machine ownership, labor, and machine operation can be determined for any crop mix.


Cost of machinery ownership and labor for different cropping systems are often termed "fixed" and commonly omitted from budgeted costs for crop systems. However, if these costs are not considered, benefits of diversified farming may be seriously underestimated. The reason is that growing two or more crops together can reduce the necessary machinery and labor compared to growing one crop alone. This can occur because growing only one crop requires high levels of machinery and labor in one or more field time "windows" during which field operations must be completed.

The primary ownership costs under consideration for machinery include depreciation, interest on investment, and repairs. One reason why so little quantification of these costs by crop system has occurred is the difficulty of estimating the most efficient machinery-labor set for any crop or mixes of crops. In recent years, the increased availability of mixed integer linear programming routines allows analysis of such estimates. This model was used in this project.

Project Objectives:

1. Estimate Machinery Ownership Cost Advantages from Rotational Cropping Systems.

2. Develop Rotation Cost Budgets Utilizing Results from Objective 1.


Materials and methods:

Model: Critical Field Time "Windows"

One of the most important components of the model was the critical time period limits to accomplish field tasks. Estimates, using meteorological data on precipitation resulted in average 10-hour days available in 11 time periods. To reduce risk these were reduced by 25 percent such that a higher probability of completing operations in unusual years would occur. The time periods are listed below:

1. Spring preplant for corn, oats, and soybeans and planting corn and oats. April 15 - May 8.

2. Spring preplant and plant for soybeans. May 9 - June 1.

3. Alfalfa harvesting imbedded window of 2 above. May 15 - June 1.

4. Rotary hoeing of corn and soybeans. June 1-9.

5. Cultivation 1 (low chemical and convention corn and soybeans). June 10-22.

6. Cultivation 2 (low chemical corn and soybeans) and alfalfa harvesting 2. June 23 - July 7.

7. Combine oats. July 10-28.

8. Alfalfa harvesting 3. Aug. 1-15.

9. Soybean combining 1. Oct. 7-21.

10. Soybean combining 2 and corn combining 1. Oct. 22-30.

11. Combine corn. Nov. 1-21.

Also, if desired the model could choose to plant soybeans in the second spring period with preplant operations completed in the first period. Hand weeding requirements took place in period 7 and 8.

Intensity Based vs. Assumed Hour Based Costs For Depreciable Assets

In optimization models where the cost for an input changes as the input use changes, a problem can occur unless a process exists to correctly specify the linkage of the cost to use. If not, the resultant input use may vary considerably from that use originally assumed in developing the cost. In such a case the process if unstable and inaccurate and little confidence can be placed in the optimization process.

In this model there are three aspects of machine ownership costs which require attention to maintain a bias-free model. These are (1) depreciation, (2) repairs, and (3) interest on investment. Depreciation was costed on a per hour of use basis. Similarly, capital costs are dependent upon use in that greater use per year reduced per acre capital costs. A procedure was developed to linearize this relationship. This process is necessary to avoid the logical difficulty of having an assumed use per year used in calculating cost yet allowing use per year to be variable.

Research results and discussion:

Cropping Systems and Herbicide-Tillage Diversification (Part 1)

In one component of the project directed at Objective 1 an analysis was made of the reduced cost benefits of crop diversification, herbicide-tillage diversification, and a combination of both (Appendix 1b).

Four crops (corn, soybeans, oats, and alfalfa) were used in forming six crop rotations. These were corn-soybeans (C-SB), corn-soybeans-soybeans (C-SB-SB), corn-corn-soybeans (C-C-SB), corn-oats-alfalfa-alfalfa (C-O-A-A). corn-soybeans-oats-alfalfa (C-SB-O-A), and corn-soybeans-corn-oats-alfalfa (C-SB-C-O-A). These six along with continuous corn (C) and continuous soybeans (SB) provided the eight cropping systems analyzed. Here an 800 acre farm was analyzed and yield interactions for rotations included in the net return analysis.

Three herbicide-tillage systems were studied. A conventional (CV) system for corn and soybeans employs broadcasted herbicides and one cultivation along with preplant tillage. For the low chemical option (L) a rotary hoe and two cultivation operations are used for post plant tillage along with banded herbicides. For no-till, preplant tillage does not occur and no cultivations or rotary hoeing occurs, however a "burndown" operation using additional herbicides beyond that used in the conventional option is included. Some hand weeding occurs with all three operations and this varies across the three alternatives wit the greatest hand labor requirement under the low chemical option.

The effect of herbicide-tillage mixing is summarized in Table 1. For each crop system, optimum returns were determined 1) by allowing only one H-T alternative, 2) by allowing a mix of H-T but each crop of each system is required to have the same H-T alternative, and 3) allowing a full mix of crop systems as well as H-T alternatives so that each crop of each crop system could employ a different H-T choice.

Overall, for single H-T systems, the low chemical and no-till systems dominate the conventional H-T system. Cropping systems involving oats and alfalfa performed very poorly under the study assumptions. Yet systems involving high proportions of corn also performed poorly demonstrating the high resource requirements of corn in particular "windows."

When mixing of H-T systems is allowed, returns are significantly enhanced for continuous corn, corn-soybeans, and corn-corn-soybeans. For the three cropping systems involving oats and alfalfa, a single H-T remains dominate over potential mixed H-T systems. It can be seen that in every case, mixing of systems involved low chemical and no-till systems.

Only slight increases are found when the last step is allowed (mixed H-T per crop of the rotation). Thus, advantages of mixed herbicide-tillage systems are nearly all realized in full rotation sequences where for each rotation system, H-T practices are the same.

Crop Mixes

Holding herbicide-systems constant, the effect of crop mixing is demonstrated in Table 2. For each of the three H-T systems, optimum solutions were obtained for 1) single crops, 2) the two single crop systems and six multi-crop systems, and 3) cropping system mixes. For the latter two only the optimal solutions are presented.

For single crop, single H-T systems the no-till systems always performed poorly. Also, except for soybeans grown conventionally or in a low chemical manner the remainder of the single crop, single H-T systems performed poorly.

When one rotation was allowed, the no-till H-T system "reversed" itself by outperforming the conventional and low chemical alternatives ($47,591 vs. $34,977 and $39,155 respectively). This was accomplished in a corn-soybean-soybean crop mix. For the conventional H-T choice, crop mixes did not result in any advantage. For the low chemical option, only a very slight advantage ($39,155 vs. $39,070) was realized by a corn-soybean-soybean rotation vs. the continuous soybean option.

When mixes in rotations were allowed, significant and roughly equal increases in returns were realized for each H-T alternative. The optimum levels of crops in such cases involved high proportions of soybeans compared to corn.

Specific and General Crop Diversification Relationships (Part 2)

This part if directed at both Objectives 1 and 2. In this analysis (Appendix 4) crops are first added to other crops in a proportional way and the impact on machine ownership, labor, and machine operating costs observed (termed MOLMO). Further the sequencing of the inclusion of the crop is important. Thus, "branches" resembling a decision tree occur. The results of those branches for each of three initial crops are presented in Table 3. A 640 acre farm was assumed.

The three basic crops (corn, soybeans, and oats) are each analyzed as initial crops and other crops added in different sequences. Alfalfa cannot be used as an initial crop because it requires a "nurse" crop oats for establishment.

When replacing 320 of the 640 acres of corn with soybeans, for example, a benefit of $57.42 per acre is achieved for all 640 acres. Thus, for the 640 acres, MOLMO costs are $36,751 less for 320 corn - 320 soybeans compared to 640 acres of corn. When oats is then added to corn-soybeans resulting in 213.3 acres of each, another $3.15 per acre benefit for all 640 acres is secured. Finally, when alfalfa is added resulting in 160 acres of all four crops, a $33.06 loss per acre occurs. Another view of this is that compared to 640 acres of corn, an equal mix of corn, soybeans, oats and alfalfa result in a decreased cost of $27.51 per acre (57.42 + 3.15 - 33.06). The addition of soybeans to corn generalizing across all additions has mixed (positive and negative) results. Oats is always positive and alfalfa is always negative.

When soybeans is the initial crop, the addition of corn results in mixed effects. Oats has positive benefits, and alfalfa is always negative. Starting with oats, the impact resulting from the addition of corn is mixed, soybean impacts are always positive and alfalfa impacts always negative.

Summarizing across all initial crops, the addition of oats always results in positive benefits with alfalfa having negative benefits. For corn and soybeans the results are mixed depending on particular settings. These results it must be noted are for specific initial crops and for specific proportional changes.

To develop Objective 2 of the project sixty five combinations of corn, soybeans, oats, and alfalfa were constructed to examine the general effect on MOLMO costs for various cropping systems (Appendix 1d). Because alfalfa can't be grown without the presence of oats, the 65 systems do not involve equal proportions of all crops. The proportions of crops covered includes zero, 20, 33.3, 40, 50, 60, 66.7, 75, 80, and 100.

All 65 systems were analyzed related to alfalfa. Alfalfa has had a long history associated with crop diversification. However, the results in Figure 1 demonstrate that while estimated MOLMO costs for alfalfa at 20 percent are not dramatically higher compared to other crops, these costs increase very dramatically thereafter.

For accurate estimates of other crops only the 37 systems not involving alfalfa were examined. This is because oats is tied to alfalfa establishment hence its estimate is biased relative to corn and soybeans using 65 systems because alfalfa has such high costs. For corn, costs increase as the proportion of corn increases. The opposite occurs for soybeans. Hence, combinations of corn and soybeans of one-third and two-thirds respectively would be predicted to be quite efficient relative to the opposite mix. For oats, a small decrease occurs over the 20-50 percent range but generally oat costs are generally stable and relatively low.

The costs of machine ownership, labor, and machine operation for systems of the specific analysis previously discussed can be derived from the general results shown in Figure 1. For example, a corn, soybean, oats, alfalfa system would involve the average of the costs for all four crops in Figure 1 each examined at 25 percent. That cost for machine ownership, labor, and machine operation could be compared to other crop systems evaluated in the same way. This derivation process enables crop budgets for crop systems to be easily derived from the general analysis of estimated relationships by crop. The accuracy of this method is strong. For example, the estimated actual cost of machine ownership, labor, and machine operation for a corn-soybeans-oats cropping system is $105.81 per acre. Using the general results from Figure 1 which were derived from the large number of system estimations, the estimated average cost of the corn-soybeans-oats system is $108.33 per acre. The difference is only approximately $2.50 per acre. Hence, these averages (such as $108.33) can be placed in budgets of cropping systems to cover costs that previously were generally not included. As a context, these average costs can be compared to that of the average of the three crops grown on the entire acreage (Figure 1 - 640 acres). These are $166.38, $108.03, and $115.08 for corn, soybeans, and oats respectively. The average of these is $129.83 per acre. This can be noted as significantly in error relative to $105.81 seriously underestimating system benefits for this three-crop system.

Appendix 1c is also included demonstrating that system benefits derived from the model can be imposed in budgets. The only limitation to this process is that the overall optimal solution cannot be reached using imposed costs.

Research conclusions:

a) System Benefits

The system benefits of crop diversification estimated in this analysis are useful to producers contemplating crop organization changes. While most of the system benefits are exhausted with two crops, this study is important to producers who are considering specializing in only one crop. These benefits are realized for corn and soybeans, corn and oats, and soybeans and oats and are approximately 30-50 dollars per acre (all crop acres).

b) Machinery Replacement.

Closely related to (a) is the issue of replacing machinery in concert with future cropping changes. The results of this project demonstrate that maintaining crop mixes along with the machinery optimum for that mix yields substantial economic advantage over specialized cropping with machinery dedicated to only one crop. This is important to producers who are considering either rapid or gradual changes in their machinery set.

c) Risk Analysis.

Conventional risk analysis commonly examines risk-return tradeoffs using crop combinations including only net returns above operating cost. This analysis provides support for a broader return context involving differences in ownership costs for different crop mix portfolios. Thus, crop diversification appears to be a more dominant characteristic both in terms of returns as well as risk than previously thought.

d) Herbicide-Tillage Diversification.

As reported, crop diversification is most efficient when practiced in association with herbicide-tillage diversification. This is a practice commonly reported by producers. However, it is sometimes thought that herbicide-tillage diversification is only a transition between methods rather than a long term strategy. This project has shown that herbicide-tillage diversification deserves additional attention as a long-term strategy.

e) Part Time Farming.

Increasingly farm organization tends to revolve around integer units of labor such as one-half, one, one and one-half, etc. person units. The optimum crop mix and machinery mix for such situations may be considerably different from those where hourly labor is hired. This research demonstrates these relationships and is useful in advising part time farmers, in particular, about optimum adjustments.

Economic Analysis

The economic benefits of mixed cropping in terms of reduced machine ownership, labor, and machine operating costs have been discussed in the results section (Part 2). In addition, the impacts of reduced inputs and yield interactions arising from multi cropping are included in the results section (Part 1).

Farmer Adoption

Farmers tend to practice the results found in this research. This behavioral validation is extremely important to the confidence that can be placed in the research model. However, much media attention tends to be directed toward specialized cropping and larger machinery. Also, currently it is commonly suggested that past commodity programs have required multi cropping due to base restrictions and without these cropping will move toward greater specialization. This research indicates that producers should generally continue their present cropping and machinery mixes. The recommendations of this study will be directed to farmers in this general sense.

Involvement of Other Audiences.

Extension educators have expressed interest in this research and plans are being made to release parts of this work in the coming year through Extension audiences.

Participation Summary

Project Outcomes


Areas needing additional study

This research needs to be completed in other regions with the results incorporated into cost budgets by crop system. Currently crop budgets are generally directed only to crop specific enterprises.

The research needs to be expanded to include livestock. For many farms particular livestock enterprises may mesh very well with the results described in this study. Further, the inclusion of livestock may result in still greater advantages of multi cropping beyond those described in this project.

Information Products

Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the U.S. Department of Agriculture or SARE.