An analysis of the marginal value of cropland and nitrogen fertilizer use under alternative farm programs

An analysis of the marginal value of cropland and nitrogen fertilizer use under alternative farm programs Wen-Yuan

Huang and Noel D. Uri

Resources and Technology Division, Economic Research Service, U.S. Department Agriculture, Washington, DC, USA

of

The analysis in this paper is directed at estimating the impact on the marginal value of a crop base acre and on nitrogen fertilizer use of alternative farm programs designed to encourage planting jlexibility in response to changing relative agricultural commodity prices. Four policy alternatives are considered: the current farm program, the Normal Crop Acreage option, the triple-base option, and the Lugar-Leahy (USDA) option. Encouraging planting flexibility via the Lugar-Leahy (USDA) option can be an effective way to reduce the excessive application of nitrogen fertilizer. Additionally, an effective farm policy designed to encourage growing crops besides those used to calculate the base acreage should detach any program deficiency payments from the number of program base acres. For example, the triple-base option would lower the marginal value of a base acre and therefore would increase the likelihood of a farmer adopting some sort of crop rotation scheme (as opposed to continuously planting the same program crop). The accompanying reduction in the excessive nitrogen fertilizer application rate, however, might not be substantial because the triple-base option links dejiciency payments to the number of base acres. The Lugar-Leahy (USDA) option, on the other hand, is an effective way to reduce the excessive nitrogen fertilizer application rate while at the same time inducing farmers to consider the production of alternative crops. Keywords: base acreage, form program analysis, groundwater land, nitrogen fertilizer

Introduction contamination has become an important environmental concern because of the real and suspected risks to human health from exposure to contaminated groundwater. These health risks include methemoglobinemia (blue baby disease), skin, lung and gastric cancer, kidney damage, liver and lung injuries, and respiratory distress. ‘J One of the most visible manifestations of groundwater contamination in many regions of the United States is the high concentrations of nitrates.3 Among the health-related problems associated with exposure to excessive levels of nitrates (i.e., exceeding the maximum concentration level, as suggested by the Environmental Protection Agency, of 10 mg/L for drinking water) are methemoglobinemia, impairment of the nervous system, cancer (stomGroundwater

The views expressed are those of the authors and do not necessarily represent the policies of the Department of Agriculture or the views of other Department of Agriculture staff members. Address reprint requests to Dr. Uri at the CED/SAB (Room 1240), U.S. Department of Agriculture, 1301 New York Ave., NW, Washington, DC 20005, USA. Received

16

23 April

1990; accepted

Appl. Math. Modelling,

19 August

1991

1992, Vol. 16, January

contamination,

marginal value of crop-

ach and lungs), and birth defects. In order to reduce the potential health-related problems associated with exposure to nitrates, nitrate leaching into groundwater must be reduced. One way that has been suggested to mitigate the contamination of groundwater by nitrates is to adopt alternative farming practices to reduce the excessive application of nitrogen fertilizers.2.4.s For example, it has been shown6 that switching from a continuous planting of corn (i.e., planting corn from one year to the next) to an alternating corn-soybean rotation can reduce nitrogen fertilizer loading on cropland (because nitrogen fertilizer is only applied every other year), reduce the nitrogen fertilizer application rate (because nitrogen, which is fixed by soybeans in the rotation, can provide some of the nitrogen needed by corn), and improve the efficiency of nitrogen uptake by the plant. Because of these factors, adoption of the corn-soybean rotation can lead to an overall reduction in the nitrogen fertilizer left in the soil, and therefore it can minimize the potential for nitrogen leaching into the groundwater. Given that these results accurately characterize the benefits of moving to a corn-soybean rotation, is there a mechanism in place, or is there one that is easily implementable, that will facilitate this move? Changing

0 1992 Butterworth-Heinemann

Marginal

value of cropland and N fertilizer use: W.-Y. Huang and N. D. Uri

relative prices (i.e., changing the price of soybeans relative to the price of corn) should be one such device. That is, a priori, one would expect that a corn-soybean producer would increase the number of soybean acres planted by adopting a soybean-intensive crop rotation as the price of soybeans increases relative to the price of corn. This has not, however, been observed in recent years. For example, in spite of a rise in the soybean-corn price ratio over the period 1981-1988 the number of corn acres planted in the Corn Belt rose, while planted soybean acreage changed very little.’ If prices favor soybeans over corn, why do not farmers plant more acres in soybeans and fewer acres in corn? One reason that the ratio of soybean to corn prices has been such a poor indicator of the number of acres planted is that under the current farm programX an increasing share of corn producers’ revenue comes from government deficiency payments. To receive larger payments, farmers need to expand their acreage base. (Deficiency payments are determined on the basis of the number of base acres planted.‘) One way to expand the acreage base is to plant corn continuously. If a farmer plants fewer acres in corn and more in soybeans, he or she relinquishes a portion of the corn base acreage on which future benefits (i.e., deficiency payments) are based. Since the corn program provides peracre net returns that compare favorably with those of soybeans and that are less affected by market price variability, corn producers have become desensitized to the soybean-corn price ratio. For farmers, loss of corn base acreage by leaving the corn program is tantamount to a reduction in future farm income. In recognition of the problem generated by the base acreage formula, Congress has passed several provisions intended to provide producers with greater flexibility in what they plant without eliminating the current system of determining crop base acreage. For example, in the Food Security Act of 1985 (which defines the current farm program), Congress included a “O/92” provision for grains, which allows farmers not to plant their permitted acreage [i.e., the difference between the base acreage and the portion of the base acreage set-aside under the Acreage Reduction Program (ARP)]‘O and still receive 92% of their estimated deficiency payments. Additionally, Congress gave discretionary authority to the Secretary of Agriculture to allow producers to increase individual crop base acreage by up to 10% if they reduced base acreage for other crops by a like amount. * The ad hoc disaster assistance legislation” permitted program crop producers in 1989 to switch between 10% and 25% of their crop base acreage to oilseeds without having their original base acreage reduced the following year. The legislation also permitted producers of any program crop to switch an unlimited number of crop base acres to oats in 1989 and 1990 without affecting their original base acreage.

* The U.S. Department provision,

however.

of Agriculture

has never

implemented

this

While these provisions have had some impact on which crops have been planted, they have not led to the flexibility that would be expected in the absence of the distortions introduced by the deficiency payments program. As farm legislation is scheduled for renewal in 1990, both the House and Senate agricultural committees have begun to debate whether to modify the formulation of the crop base acreage calculation under the current (existing) farm program to remove the unintended market distortions of the type discussed above. For example, Senators Lugar (R-IN) and Leahy (DVT) have introduced the Agricultural Competitiveness and Planting Flexibility Act of 1990 (ACPF) in which farmers would be free to determine their own mix of crop plantings within the established normal crop base acreage. The normal crop base acreage consists of the S-year moving average of planted acreage of program crops* plus some oilseed crops. The U.S. Department of Agriculture (USDA) has also recommended a planting flexibility proposal for the 1990 farm bi11.12This proposal suggests using the normal crop acreage concept,** which is similar to the normal crop base acreage notion found in the Lugar-Leahy proposal, to define substitutable crops and their permitted acres (i.e., the number of acres that can be planted in these substitutable crops), to authorize crop-specific acreage reduction programs, and to provide authority to plant acres idled under the program provisions in exchange for giving up a specified amount in deficiency payments. Will the implementation of a planting flexibility option result in a more market-oriented production of agricultural commodities in the United States (where relative price changes lead to the expected supply response) than has been the case under the current farm program? Will it result in a crop production mix that will lead to a reduction in nitrogen fertilizer use (if the relative prices of the various commodities so dictate) such that any excessive application of nitrogen fertilizer will be minimized? To address these questions, in what follows, the estimation and comparison of the economic value of the corn base acreage among several different flexibility options is considered. If the value of keeping corn base acreage under a flexibility option is high relative to the other options, farmers have less of an incentive to switch to other crops in response to changes in relative market prices. On the other hand, if the value of the corn base acreage is low (relative to other crops’ base acreage), farmers should switch to other crops in response to changing relative market prices.

* Technically, the average program yield is computed by averaging the yield on the program crop over the preceding five years. excluding the years with the highest and lowest yield. ** Specifically, normal crop acreage (NCA) is defined as the sum of a farm’s acreage bases of program crops (wheat, feed grains, upland and extra-long staple cotton, and rice), plus historical plantings of oilseeds (soybeans, sunflowers, and rapeseed, including canala)

Appl.

Math.

Modelling,

1992,

Vol. 16, January

17

Marginal

value of cropland and N fertilizer uses: W.- Y Huang and N. D. Uri

Will the implementation of a planting flexibility option result in a reduction in the nitrogen fertilizer application rate? To answer this question, it is necessary to estimate the marginal return of nitrogen fertilizer under the various options. If it is assumed that farmers will endeavor to maximize net farm income, then they will apply the proper amount of fertilizer. This means that farmers, in making their input use decisions, will equate the marginal physical product of nitrogen fertilizer (MPP) with the ratio of the price of nitrogen fertilizer to the commodity price. An estimation of the marginal physical product of nitrogen fertilizer under each option and a comparison of this value across options are needed. In order to evaluate the efficacy of the various policy options in affecting crop selection (and hence nitrogen fertilizer use) this paper will estimate the marginal value of the corn base acreage under alternative planting flexibility policy options, and it will compute the associated nitrogen fertilizer application rate for corn production. Corn is selected because it has a relatively high nitrogen fertilizer application rate and it is a very inefficient user of nitrogen fertilizer if corn is produced on a continuous basis. In what follows, the policy options for planting flexibility will be delineated, the methodology for computing the value of the base acreage and the fertilizer application rate will be detailed, and this methodology will be implemented. Policy options for planting flexibility Four policy options will be analyzed: the current farm program (which, as noted above, has little explicit provision for crop production flexibility), the normal crop acreage program, the triple-base plan (discussed below), and the Lugar-Leahy (USDA) program. These are the options currently receiving the most attention. Their relevant components for the consideration at hand are briefly highlighted below. The current farm program

A farmer participating in the current farm program maintains a base acreage for a crop which is used to compute deficiency payments. The crop acreage base is a 5-year moving average of the number of acres planted in the program crop (as qualified in the previous section). The program yields for the base acreage are frozen at their historical levels. A participating farmer has to set aside a certain percentage of the base acres. These acres are part of what is nominally referred to as the Acreage Reduction Program. (The set-aside varies based on the crop.) Under the program, if a corn or wheat farmer, for example, were to plant another crop, he or she would have a lower corn or wheat crop acreage base, and therefore future deficiency payments would be reduced. Normal Crop Acreage

option

The concept of normal crop acreage is not new. It was used in 1978 and 1979.i2 Under this option a farmer

18

Appl. Math. Modelling,

1992, Vol. 16, January

who wishes to participate in the farm program would be required to indicate the total number of acres he or she intended to plant in all program crops and then retire a specified percentage of this intended planted acreage from use. The farmer would be free to allocate the available cropland to program crops without constraint. Deficiency payments would be based on an adjustment in the number of acres actually planted in the various program crops. This adjustment would be made by an allocation factor, which is the ratio of the national aggregate program acreage planted in the specific crop to the estimated total number of harvested acres. The program yields applied to the base acres are the estimated harvested yields in the current period and not a historical average. Triple-base

option

Under this option, I3first introduced by Rep. Charles Stenholm (D-TX) in 1985, a farmer participating in the deficiency payments program would have three categories of “base” acres. (The total number of base acres would be determined on the basis of historical plantings.) The farmer would agree to take a certain percentage of land out of production, as under the ARP. This would constitute the first base. But the government would make deficiency payments only on a specified percentage of the base acres-the second base. On the remainder of the base acres-the third basethe farmer would be free to produce any crop to sell in the market but would receive no payments on crops produced on this portion of the land. Thus for instance, under a 10/80/10 triple-base plan, a farmer with 100 wheat base acres would be required to idle 10 acres under the ARP and would have his or her deficiency payments based on 80 acres rather than the 90 remaining acres. The farmer would grow the program crop on the 80 acres. The program yields would be estimated actual (not historical) yields. The farmer would be permitted to grow any crop on the remaining IO acres. Lugar-Leahy

(USDA)

option

Under the Lugar-Leahy (USDA) option a farmer participating in the current (existing) farm program would have to maintain an NCA base, using a 5-year moving average of the number of acres planted in program crops plus the number of acres planted in oilseeds and industrial crops. The farmer would be free to determine his or her own mix of crop plantings within the NCA base. Any government payments would be made on the basis of the farmer’s historical planting patterns. The crop base acreage and the program crop yields would be frozen for the duration of the 1990 farm bill. Because the U.S. Department of Agriculture’s planting flexibility proposal for the 1990 farm bill in general was similar to the provisions of the Lugar-Leahy plan, the option will be referred to as the Lugar-Leahy (USDA) option. A farm-level model to evaluate the policy options In order to evaluate the various policy options a farmlevel model is formulated that will allow for the esti-

Marginal

value of cropland and N fertilizer use: W.-Y. Huang and N. D. Uri

mation of the economic value of the base acres for the various crops. The model assumes that a farmer seeks to maximize the net farm income received both from the government program (in the form of deficiency payments) and in the marketplace. The model determines the optimal mix of crops that will maximize net farm income. Throughout the following analysis it is assumed that DPi = 0 if crop i is not a program crop and MPi > LR; (i.e., the market price of crop i is assumed to always exceed its loan rate).

A farmer operating in an environment detined by the current farm program should determine the optimal mix of crops by maximizing net farm income, NR. This translates into the following problem: Maximize X,.N, NR = 2 [ MRi(N;) + DP<]X; 1 Subject to

7 (X;l( 1 - Ai)) I L

for for

iEp

(14

all i

(lb)

Unless otherwise indicated, the index i ranges over the total number of crops that can be produced by a farmer. k, where k is the number of Thatis,i= 1,2 ,..., crops that can be produced. Note that the control variables are Xi and N,. That is, the farmer has control over the number of acres planted in crop i and the nitrogen application rate on that crop. The Lagrange multiplier Vi will be associated with constraint (la), and the Lagrange multiplier W will be associated with constraint (lb). Thus Vi is the imputed value of a base acre of crop i and indicates how much net farm income will be changed if the base acreage is changed by 1 acre. Solving aNRiIdXB; = 0 for Vi will give the marginal value of a base acre when net farm income is maximized. W is the imputed value of an additional acre of cropland available for agricultural production and indicates by how much the net farm income will change if the total number of cropland acres is changed by 1 acre. The optimal nitrogen fertilizer application rate, NT (where the asterisk is used to indicate the optimal value of the relevant variable), is computed by solving the following first-order condition for Ni: aYi(NJlaNi = rIMPi

Maximize X,.Ni NR = C [MRi(Ni)X; + (Yi(Ni)/PYi)DPiXiSi] i Subject to 7 (X;l( 1 - Ai)) 5 NCA

Current farm program

X,/(1 - Ai) sXB,

NCA option A farmer operating in an environment where the normal crop acreage (as originally defined in the 1970s) program is in effect would use the following model to determine his or her optimal mix of crops:

for

all i

(2)

7 (X,/(1 - Ai)) I L

for

for

iEp

all i

(da) (4b)

where S; is the allocation factor, defined as the total number of program acres planted in crop i divided by the total number of harvested acres of crop i. (Note that it is necessary to introduce the term PYi into the objective function because of the way the deficiency payments variable is originally defined.) NCA is the number of normal crop acres, which is equal to the sum of the number of acres planted in program crops plus the number of acres historically planted in oilseeds. The nitrogen fertilizer application rate for crop i is computed by solving the following first-order condition for Ni: aYi(Ni)IaNi = rI(MPi + (DPiIPYi)Si)

(5)

The marginal value of a base acre, VT, is given as V* = (MR,*(N;) + Yi(Ni)DPi)(l - A;) - W* for all i

(6)

By solving equation (5) for the optimal value of N and substituting it into equation (6) the marginal value of an additional crop base acre can be obtained. Triple-base option

A farmer operating in an environment where the triple-base option defines the policy with regard to deficiency payments would use the following model to maximize his or her net farm income: Maximize X,.N, NR = 2 [MRi(Ni)Xi] + C [DP;Xy] i I Subject to Xyl(l -AJ(l

- BJ =XBi

for

iEp

(74

The marginal value of a base acre, Vi*, is given as VT = (MRT(N;) + DPi)(l - Ai) - W* for

all i

(3)

where W* is the marginal value (i.e., shadow price) of the total number of acres available for production. This value (i.e., W*) is greater than or equal to zero.

Xi - X~ ~ C (XBi(1 - Ai) - X~)

U’b)

F (Xjl( 1 - ai)) I L

(7c)

for

all i

where Bi is the percentage of the base acres that will not receive deficiency payments. Bi = 0 if i is a non-

Appl. Math. Modelling,

1992, Vol. 16, January

19

Marginal

value of cropland and N fertilizer uses: W.-Y. Huang and N. D. Uri

program crop. XT is the number of acres planted in program crops receiving deficiency payments. The nitrogen fertilizer application rate for program crops is determined by solving the following relationship for N;: for

d Y;(N;)/dN; = rIMP;

all i

(8)

The marginal value of a base acre, Vi*, is given as VT = DP;(l Lugar-Leahy

- A;)(1 - B;)

(USDA)

for

all i

(9)

option

With the Lugar-Leahy (USDA) option in effect a farmer would use the following model to maximize his or her net farm income: Maximize Xi,N, NR = x (MR;(N;)X;) I

+ z

(DP;XB;(l

- A;))

1

Subject to for

C (X;l( 1 - A;)) 5 NCA 2 (Xi/( 1 - A;)) 5 L

for

iEp

(104

all i

(lob)

the Acreage Reduction Program, the neoclassical production technology, and the program yields are likewise assumed to be the same. Finally, in order to simplify the notation the crop subscript will be omitted, since corn is implicitly the focus of attention. NCA option

versus

the current farm program

With regard to the nitrogen fertilizer application rate a comparison of relationship (2) with relationship (5) suggests that the nitrogen application rate will be greater than the NCA option, since the expression [(DPIPY)(S)] is positive. (As a consequence the effect on corn yield attributable to a one-unit (i.e., 1 lb.) increase in the nitrogen fertilizer application rate will be smaller.) That is, more nitrogen fertilizer will be applied under the NCA option. The assumption that the same neoclassical production technology (i.e., one characterized by diminishing marginal returns) is being used under the alternative programs is significant in reaching this conclusion. Assuming that not all of the available cropland is used under the two alternatives (this assumption simplifies the discussion), the difference in the value of a corn base acre, Dncalcp, under the two alternatives is given as

I

D

The optimal nitrogen fertilizer application rate for program crops can be calculated from the following relation: aY;(N;)/aN; = rIMP;

for

all i

(11)

The marginal value of a base acre, VT, is given as V* = MRT(N;)(l

- A;) - W*

for

alli

(12)

By solving equation (11) for N and substituting this value into equation (12) the optimal values V* and W* are obtained.

Comparison of policy options As noted above, the focus of the empirical work will be on corn. The optimal nitrogen fertilizer application rate for corn associated with the current farm program will be compared to that associated with each of the alternative planting flexibility policy options previously discussed. Also, a comparison will be made between the marginal value of corn base acres under the current farm program and the value under the various planting flexibility policy options. In interpreting the results it should be kept in mind that a relatively high marginal value of a corn base acre under a particular option indicates that a farmer would have less of an economic incentive to switch from corn to the production of another crop in response to a change in the relative market prices of the crops. Additionally, throughout the subsequent analysis the target prices and the loan rates associated with individual crops are assumed to be identical across each of the policy alternatives. Other factors such as the number of corn base acres, the cropland available for production, the percentage of the cropland set-aside under

20

Appl. Math. Modelling,

1992, Vol. 16, January

IlGikp

= [(MRtN)

- [(M&V

+ (Y(N)IYP)DP)(l

+ DP)(l - A)],,

-

A)l,,, (13)

The first bracketed term on the right-hand side of this expression is the marginal value of a base acre under the NCA option, while the second bracketed term is the marginal value of a base acre under the current farm program. If it is assumed that the corn yield under the NCA option exceeds the historical (program) yield and if the net return from selling corn is the same under the two options, then this difference is positive. Alternatively, if the actual yield is approximately equal to the historical yield and if the net return from the NCA option exceeds the net return under the current farm program, the difference will also be positive. Next, if the actual yield is equal to the historical yield and if the net return from the NCA option equals the net return under the current farm program, the difference will be zero. If the actual yield approximately equals the historical (program) yield and if the net return under the NCA option is less than that under the current farm program (because more nitrogen fertilizer is used under the NCA option), the difference will be negative. Finally, if the actual yield exceeds the historical yield and if the net return from the NCA option is less than that under the current farm program, the sign of the difference will depend on the relative magnitudes of the differences in the two factors (i.e., yield and net return). A positive value of the difference Dncalcpimplies that a switch to the NCA option would lead to an increase in the marginal value of a corn base acre, while a negative sign means that there would be a decrease in the marginal value of a corn base acre. A priori, without knowledge of the relative magnitudes of the yields and

Marginal

value of cropland and N fertilizer use: W.-Y. Huang and N. D. Uri

the marginal revenues under the two policy options, what would happen to the marginal value of a base acre in response to a change in the farm program is indeterminate. Triple-base

option versus the current farm program

The nitrogen fertilizer application rates under these two programs will be approximately the same, because the marginal physical product under each alternative will be equated to the ratio of the price of nitrogen fertilizer to the market price of corn. This is seen by comparing relationship (2) to relationship (8). There would be minimal variation in both of these prices under the alternatives. The difference in the value of a corn base acre, D tb,cp, under the two alternatives is given as D tb/cp

=

[Dp(l

-

A)(1

-

[(MWV)

-

B)ltb +

DP)(l

-

A)lc, (14)

Since the value of the first bracketed term on the right-hand side in expression (14) is less than the value of the second bracketed term and assuming W is zero (i.e., not all available cropland is being used), the value of Dtblcp is negative. This implies that the marginal value of a corn base acre will fall (relative to the value under the current farm program) if the triple-base option is adopted. Lugar-Leahy (USDA) current farm program

option versus the

The nitrogen fertilizer application rate under these two alternatives will be the same because the marginal physical product under each alternative will be equated to the ratio of the price of nitrogen fertilizer to the market price of corn. This is determined by comparing relationship (2) with relationship (11). There would be minimal variation in both of these prices under the alternatives. The difference in the value of a corn base acre, Dlllcp under the two alternatives is given as D u/cP= [~N’O(l

- 4111 - [WNV + DP)( 1 - A)l,,

(15)

Since the value of the first bracketed term on the right-hand side in expression (15) is less than the value of the second bracketed term (because the marginal return from selling the corn will be approximately the same) and assuming W is zero, the value of DlllCPis negative. This implies that the marginal value of a corn base acre will fall (relative to the value under the current farm program) if the Lugar-Leahy (USDA) option is adopted. In sum, the nitrogen fertilizer application rates under the alternatives considered are ordered such that the nitrogen fertilizer application rate under the NCA option is greater than that under the current farm program. The nitrogen fertilizer application rates under the current farm program, the triple-base option, and the Lugar-Leahy (USDA) option are approximately equal.

If the total number of acres available for agricultural production is greater than the sum of acreage included in program crops (that is, if W = O), then the marginal values of a corn base acreage under the options considered will be ordered such that marginal value of an acre under the current farm program is greater than that under the triple-base option, which, in turn, exceeds that under the Lugar-Leahy (USDA) option. The placement of the NCA option in the ranking depends on the assumptions with regard to changes in the marginal revenue from selling corn and the ratio of the current yield to its historical level and the allocation factor S. The marginal value of a base acre under the Lugar-Leahy (USDA) option is less than the value under the triple-base option because the Lugar-Leahy (USDA) option places less of a restriction on farmers when they make their crop selection. A decline in the marginal value of a base acre resulting from the switch from the current farm program to the Lugar-Leahy (USDA) option or the triple-base option implies that farmers may be less reticent about moving from continuously planting the same crop (i.e., corn) to an alternating rotation. Analyzing

the policy alternatives

In this section the marginal values of a corn base acre, the nitrogen fertilizer application rates, and the extent of excessive nitrogen fertilizer application are estimated under the current farm program, the NCA option, the triple-base option, and the Lugar-Leahy (USDA) option. The objective functions previously discussed are optimized subject to the relevant (i.e., as previously delineated) constraints. The production function is assumed to be nonlinear, whereby crop yield, Yi(Ni), is specified for each crop sequence to be a quadratic function of the nitrogen fertilizer application rate, Ni, and a constant term.6 As a consequence of this assumption the models are mixed-integer, nonlinear mathematical programming models and are solved using the generalized algebraic modeling system (GAMS).i4 To implement the models characterizing the policy alternatives, various data sources were used. The market price and target price data were obtained from the USDA Baseline Projections.15 They represent 1989 actual prices and are assumed to remain the same across the various alternatives. Program yield (at 130 BuJacre) also were taken from this source. The nitrogen price was that prevailing in December 1989 (at $O.E/lb.). Both the program yield and the nitrogen price are likewise assumed to remain constant across alternatives. The ARP is assumed to be 10% of the base acreage. The data on the cost of production are for the state of Iowa and were taken from Iowa State University.i6 In order to illustrate the impact of cropland availability on the marginal value of land, two alternatives are considered. In the first the amount of cropland available for agricultural production is limited to 120 acres; in the second there is no limit on the available number of cropland acres, but there is a limit on the

Appl. Math. Modelling,

1992, Vol. 16, January

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Marginal

value of cropland and N fertilizer uses: W.- Y. Huang and N. D. U-i

number of program base acres. (The choice of 120 acres of cropland available for agricultural production is arbitrary. The number of cropland acres selected does not affect the results of the analysis.) The data on yields and nitrogen fertilizer use are from field experiments conducted at the Iowa State University research farm at Kanawha, Iowa.” These experiments were specifically concerned with estimating the impact of the rate of nitrogen fertilizer use on yields under different crop rotation sequences, and hence other factors that could potentially affect yields (irrigation, pesticide use, etc.) were held constant across the experiments. (This implies that the impact of these other factors on yields will be adequately captured in the constant term.) Consequently, the quadratic yield function, estimated on the basis of these field experiment data, can be used without fear that systematic bias has been introduced due to an improper functional specification (i.e., omitting relevant explanatory variables from the production function specification). In order to determine how farmers might respond under the alternative agricultural policies, two scenarios are considered. The first assumes that farmers currently are continuously growing corn and plan to continue doing so. The second scenario assumes that farmers currently are optimally rotating their crops in such a way as to maximize their net farm income. Thus not only are farmers looking at the revenue considerations associated with continuously planting corn and trying to maximize net revenue subject to the costs associated with a given set of factor inputs (which, in this exercise, are assumed to remain unchanged across policy alternatives) required to produce corn, but they are also explicitly looking at the revenue and costs (including the nitrogen fertilizer cost) associated with producing alternative crops on a rotating basis with corn. Under the continuous corn rotation the number of base acres is set equal to 120. This corresponds to the total number of cropland acres available when the amount of cropland is limited. The continuous corn planting and the optimal corn rotation (which consists

Table

1.

flexibility

of a corn-soybean rotation)* provide two entirely different sets of estimates-one set based on no flexibility in the choice of the crop to be planted and another where there is considerable flexibility in this choice. Table 1 displays the estimated marginal values of a corn base acre under the different farm programs. The results show that under the normal crop acreage option a corn base acre has the highest marginal value when the total amount of available cropland is not a limiting factor, while under the Lugar-Leahy (USDA) option a corn base acre has the lowest marginal value. The value of the other alternatives are in between. Thus for example, under the normal crop acreage option for a continuous corn rotation a corn base acre has a marginal value of $162, implying that if an additional acre of cropland were available, a farmer could increase his or her net farm income by $162 if corn were planted on that additional acre. For the optimal crop rotation (where the number of base acres is a binding con* A variety of rotations were considered where corn and soybeans were alternated following different planting patterns. For example, in a corn-soybean rotation the patterns were defined such that one half of the available cropland was planted in corn and the other half was planted in soybeans. The actual acres planted in soybeans change from one year to the next. This approach was used to simplify the analysis. Thus with an ARP of 10%. approximately 57 of the available 120 acres will be planted in soybeans in any one year, while approximately 63 acres will be allocated to the corn base. With 10% of the 63 acres withdrawn from production an equal number of acres will be planted in corn and soybeans. Soybean yield functions were estimated for each crop sequence in a fashion analogous to the corn yield functions based on the same Iowa State University field experiment data noted above. Thus the soybean specification was quadratic, etc. A 6-year crop rotation cycle was used. Longer rotation cycles did not yield significantly different results from those obtained with the 6-year cycle. Actual 1989 price data and cost data for soybeans and corn were used. A large number of different rotation patterns were considered in the context of the alternative farm programs that have been considered in the foregoing discussion. It was determined that a corn-soybean-corn-soybean-corn-soybean rotation was optimal except under the Lugar-Leahy (USDA) option, where a corn-soybean-corn-soybean-soybean-soybean rotation was optimal. Complete details of the analysis are available from the authors upon request.

Marginal values of corn base (in dollars/acre) policy options Continuous

Policy ootions* Current farm program NCA Triple base Lugar-Leahy (USDA)

acres under alternative

corn rotation

Appl.

Math. Modelling,

Optimal crop rotation

Cropland unlimited (L 2 0 %B = 120)

Cropland limited (L 5 120 XB = 63)

Cropland unlimited (L 2 0 XB = 63)

61

152

-11

157

86 42 -36

162 134 56

-17 -29 -53

170 148 92

Cropland limited (L 5 120 XB = 1201**

l The various policy options are defined in the text. ** L denotes the total number of acres available for production and XB denotes the number of corn base acres available.

22

planting

1992, Vol. 16, January

of agricultural

commodities,

Marginal

value of cropland and N fertilizer use: W.-Y. Huang and N. D. U-i

straint), under the normal crop acreage option the associated marginal value is $170. Under the Lugar-Leahy option, on the other hand, for a continuous corn rotation a corn base acre has a marginal value of $56, while for the optimal crop rotation it has a value of $92. Corresponding marginal values for the current farm program and the triple-base option for continuously growing corn are $152 and $134, respectively, and for the optimal crop rotation, $157 and $148, respectively. These results are consistent with the comparison made above. When the amount of cropland available for agricultural production is limited, the marginal value of a corn base acre will be less because the marginal value of total cropland will be positive.* That is, there is a nonzero opportunity cost associated with use of cropland for producing corn which is not present when the amount of cropland is unlimited. The ordering of the effect of the various policy alternatives on the marginal value of a base acre when there is a limited amount of cropland is analogous to that when there is no such constraint. Thus for example, the results (given in Table 1) show that under the normal crop acreage option a corn base acre has the highest marginal value when the total amount of available cropland is a limiting factor, while under the Lugar-Leahy (USDA) option a corn base acre has the lowest marginal value. The values of the other alternatives, as before, are in between. Hence under the NCA option for a continuous corn rotation a corn base acre has a marginal value of $86 [which indicates the increase in net farm income if an additional acre of cropland is available and implies that additional acre is included in the number of base acres (such that it is used to produce corn)], while for the optimal crop rotation (where the number of base acres is a binding constraint) the associated marginal value is - $17. Under the Lugar-Leahy option, on the other hand, for a continuous corn rotation a corn base acre has a marginal value of -$36, while for the optimal crop rotation it has a marginal value of - $53. The negative values obtained for the marginal value of a base acre arise from the loss of income associated with the set-aside under the Acreage Reduction Program, the foregone income from engaging in soybean production (as opposed to corn production), the fact that government deficiency payments are not tied to program base acreage in the case of the continuous corn rotation, and the Acreage Reduction Program and the limited amount of base acreage in the case of the optimal crop rotation. With these negative values, farmers have a strong incentive to select an alternative strategy (i.e., choose different crops to grow) that will result in a positive marginal value for the base acres. The strategy would obviously depend on the specific policy alternative implemented.

* An examination of the relationships defining the marginal value of a base acre will illustrate this point. Thus for example, from relationship (2), when W* is positive (implying that constraint (lb) is binding), V* will be smaller than when it is equal to zero.

The conclusion arising from these results is selfevident. The structure of the farm program does have an impact on the marginal value of a corn base acre. This in turn implies that a farmer’s incentive to switch to an alternative crop when the relative market prices of agricultural commodities change is de facto affected by the nature of the farm program under which he or she is operating. The Lugar-Leahy (USDA) option results in the strongest incentive for switching, while the normal crop acreage option yields the weakest incentive. Finally, with regard to the marginal value of a base acre, it should be noted that under the current farm program the difference in the marginal value of a base acre when continuously growing corn and when the optimal rotation is being followed is only about $5 ($157 - $152). This is not very large, and it may explain why a considerable number of farmers continue to grow corn on a continuous basis even though they could gain by switching to an optimal corn-soybean crop rotation. Ix The nitrogen fertilizer application rates associated with the various policy alternatives are given in Table 2. There are no large differences in the application rates between the various alternatives under either the continuous planting of corn or the optimal crop rotation. For instance, under the continuous planting of corn the difference between the NCA option and the other alternatives is only 6 lb./acre. (This represents about 3% of the nitrogen applied.) This result is attributable to the assumption that the nitrogen fertilizer price and the market price of corn are constant across policy alternatives. The difference in the estimates between the continuous corn rotation and the optimal crop rotation under each policy alternative is between 5 and 7 lb./acre. This means that moving to an optimal crop rotation would result in approximately a 3-4% reduction in the nitrogen fertilizer application rate as the nitrogen-fixing characteristic of soybeans comes into play. Corn yields vary little across the alternative policy options. This is mainly a function of the nature of the production function and the minimal impact of the various policy alternatives on nitrogen fertilizer use. This

Table 2. Nitrogen fertilizer application rates and crop yields under alternative planting flexibility policy options Continuous corn rotation

Policy options* Current farm program NCA Triple base Lugar-Leahy (USDA)

Optimal crop rotation

Nitrogen application (lb./acre)

Corn yield (Bu./acre)

Nitrogen application (lb./acre)

Corn yield (BuJacre)

194

143

187

162

200 194 194

144 143 143

195 187 187

163 162 162

* The various policy options are defined in the text.

Appl.

Math.

Modelling,

1992, Vol.

16, January

23

Marginal

value of cropland and N fertilizer uses: W.-Y. Huang and N. D. U-i

Table 3. Excessive nitrogen fertilizer application rates (in pounds) under alternative planting flexibility policy options Continuous corn rotation Policy options* Current farm program NCA Triple base Lugar-Leahy (USDA)

Optimal crop rotation

Per acre

Per rotation (6 vears)

Per acre

Per rotation (6 vears)

65

390

41

124

71 65 65

426 390 390

49 41 41

147 124 82

* The various policy options are defined in the text.

result holds for both the continuous planting of corn and the optimal crop rotation. Excessive nitrogen fertilizer application rates under the different policy alternatives are given in Table 3. There are only small differences in the application rates among the various policy alternatives, and these result in but small differences in the excessive application rate of nitrogen fertilizer. This observation holds for both the continuous planting of corn and the optimal crop rotation scenarios. However, switching from the continuous planting of corn to the optimal crop rotation reduces by a relatively large amount the excessive nitrogen fertilizer application rates. For example, moving from the continuous planting of corn to the optimal crop rotation reduces by between 22 and 24 lb./acre the nitrogen fertilizer application rate under the alternative farm programs. Moreover, over the 6-year rotation cycle there is a significant reduction in the excessive application of nitrogen fertilizer under the LugarLeahy (USDA) option. Under this option, only about 82 lb./acre of excessive nitrogen fertilizer will be applied. This reduction is the result of relying on the nitrogen-fixing characteristic of soybeans. Compared to the other alternatives, this represents a significant reduction in nitrogen fertilizer use.

The foregoing analysis has been directed at estimating the impact on the marginal value of a crop base acre and on nitrogen fertilizer use of alternative farm programs designed to encourage planting flexibility in response to changing relative agricultural commodity prices. Encouraging planting flexibility via the LugarLeahy (USDA) option can be an effective way to reduce the excessive nitrogen fertilizer application rate. Additionally, an effective farm policy designed to encourage growing crops besides those used to calculate the base acreage should detach any program deficiency payments from the number of program base acres. For example, the triple-base option would lower the marginal value of a base acre and therefore would increase the likelihood of a farmer adopting some sort of crop rotation scheme (as opposed to continuously planting the same program crop). The accompanying reduction in the excessive application of nitrogen fertilizer ap-

Appl.

Notation MPi TPi xi Ci Ni Yi(Ni) LRi PY; ;i

XB, P

Conclusion

24

plication, however, might not be substantial, because the triple-base option links deficiency payments to the number of base acres. The Lugar-Leahy (USDA) option, on the other hand, is an effective option to reduce the excessive nitrogen fertilizer application rate while at the same time inducing farmers to consider the production of alternative crops. Finally, what do the results of the analysis portend for groundwater quality? There is little in these policy alternatives to suggest that significant reductions in the nitrogen fertilizer application rate will be realized if they are continued (in the case of the current farm program) or implemented (in the case of the remaining options). There is, however, a significant reduction possible in the excessive application of nitrogen fertilizer under the Lugar-Leahy (USDA) option over a 6-year rotation cycle if farmers who are currently growing corn on a continuous basis (accounting for 26% of all acres planted in 1988)19were to switch to an optimal crop rotation sequence. Such a switch would be expected to lead directly to an improvement in groundwater quality.

Math. Modelling,

1992, Vol. 16, January

L MRi(Ni)

per-unit (e.g., bushel or cwt.) market price for crop i per-unit target price for crop i number of acres of crop i planted per-unit production cost for crop i (excluding fertilizer costs) per-acre nitrogen fertilizer application rate for crop i per-acre yield for crop i expressed as a function of nitrogen fertilizer use per-unit loan rate for crop i per-acre program yield for crop i nitrogen fertilizer price percentage of base acres in the Acreage Reduction Program (ARP) for crop i. Ai is zero for nonprogram crops number of base acres for crop i set of program crops (i.e., p = (1, 2, . . . , p}) where there are a total of p program crops total number of acres of cropland available for agricultural production net return from selling crop i in the market; that is, MRi(Ni) = MPiYi(Ni) C; - rNi

DPi

NR

EXi

total deficiency payments for crop i; that is, DPi = [TPi - Max(LRi, MPi)]PYf for i E p. For nonprogram crops, DPi = 0 net farm income from crop production including the benefits received from the farm program per-acre excessive nitrogen fertilizer application rate for crop i; that is, EXi = Ni - Yi(Ni)F where F is the amount (in pounds) of nitrogen fertilizer used in producing one unit of crop i

Marginal

value of cropland and N fertilizer use: W.-Y. Huang and N. D. Uri

References Protecting the Nation’s Groundwaterfrom Contamination, Office of Technology Assessment, Washington, DC, 1984 Groundwater Protection, The Conservation Foundation, Washington, DC, 1987 Lee, L. and Nielsen, E. Farm chemicals and groundwater contamination. Agriculture and Ground Water Quality, ed. J. Nelson and E. McTernan, Okla. State Univ., Stillwater, OK, 1989

4 5 6

I 8 9 10

Water Quality and Agriculture: An International Perspective on Policies, The Agriculture, Resource, and Environmental

Policy Research Consortium, Washington, DC, April 1989 Feliciano. Improving Groundwater Quality. Water Resources Research, ed. T. Napiel. Soil Conservation Society of America, Ankeng, Iowa, 1986 Huang, W. and Lantin, R. An analysis of policy options for adopting alternative farming practices to reduce nitrate leaching. Draft Rept., Econ. Res. Serv., U.S. Dept. Agric., March, Washington, DC, 1990 Glauber, J. Why aren’t corn farmers moving to soybeans? Agricultural Outlook. Economic Research Service, U.S. Department of Agriculture, Washington, DC, June 1988 Glaser, L. Provisions of the Food Security Act of 1985. AIB Rept. No. 498, Econ. Res. Serv., U.S. Dept. of Agric., Washington, DC, 1986 Uri, N. D. Target prices, market prices, and economic efficiency in agriculture in the United States. J. of Consum. Policy 1989, 12, l-12 The basic mechanism of U.S. farm policy. Part one: Target,

loan and deficiency. Misc. Publ. No. 1470, Econ. Res. Serv., U.S. Dept. of Agric., Washington, DC, May 1989 11 U.S. Congress. Disaster Assistance Act of 1989, Public Law 101-82, 1989; Congressional Record--Senate, 135(163). Nov. 19, 1989 12 1990 Farm Bill: Proposal of the Administration, U.S. Department of Agriculture, Washington, DC. Feb. 1990 13 Ek, C. Normal Crop Acreage. CRS Rept. No. 89-467 ENR, Congr. Res. Serv., Libr. of Congr., Washington, DC, Aug. 14, 1989 14 Ek, C. The Triple Base Plan. CRS Rept. No. 89-381 ENR, Congr. Res. Serv., Libr. of Congr., Washington, DC, June 26, 1989 1.5 Kendrick, D. and Meeraus, A. CAMS: An introduction. Development Research Department, World Bank, Washington, DC, 1985 USDA Baseline Projections, Economic Research Service, U.S. Department of Agriculture, Washington, DC, Jan. 1990 Estimated costs of crop production-1989. Publ. No. FM-1712, Iowa State Univ. Ext., Ames, IA, Dec. 1989 Iowa State Experiment Station at Kanawha. Exp. Stn. Rept. No. ORC87-14, 22, Iowa State Univ., Ames, IA, 1989 Duffy, M. and Chase, C. Impacts of the 1985 Food Security Act on crop rotations and fertilizer use. Unpublished manuscript, Dept. of Econ., Iowa State Univ., Ames, IA, 1989 20 Agricultural resources: Inputs, situation and output. Rept. No. AR-15, Econ. Res. Serv., U.S. Dept. of Agric., Washington, DC, Aug. 1989

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1992, Vol. 16, January

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