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Efficiency Gains in Broiler Production Through Contract Parameter Fine Tuning1
Efficiency Gains in Broiler Production Through Contract Parameter Fine Tuning1 TOMISLAV VUKINA and WILLIAM E. FOSTER2 Department of Agricultural and Resource Economics, North Carolina State University, Campus Box 8109, Raleigh, North Carolina 27695 contract parameter values. The foci of the analysis are three contract parameters: base payment, bonus factor, and the utilities cost allocation factor. In the first two cases, the simulation generated ambiguous results. In the third case, results seem to indicate that switching part of the electricity cost from the grower's cost into the settlement cost may result in a mutual welfare gain.
(Key words: economic optimization, broiler production, contracts, growers' payments) 1996 Poultry Science 75:1351-1358
INTRODUCTION The U.S. broiler industry is almost entirely vertically coordinated by production contracts. Judged by their prevalence, contracts have proven to be a successful mode of organizing broiler production. They have benefitted farmers by offering opportunities to earn income with relatively low capital requirements, by alleviating cash flow problems typically plaguing small farms, and by allowing enterprise diversification on the farm. The major efficiency gain from contracts probably is the reallocation of risk from the farmers to integrators, who have the means to act upon uncertain outcomes (Knoeber and Thurman, 1995). Broiler contracts also have their critics, largely originating from the growers' own ranks, who complain about gains from contract arrangements being largely appropriated by integrators, whereas growers receive only small or even negative returns from contract production. The existing controversy can be reduced to a standard principal-agent type problem. Production contracts are designed to provide growers with appropriate incentives to manage their broiler farms in a way that will maximize integrator's returns, and at the same time be significantly rewarding to growers to keep the existing
Received for publication March 29, 1996. Accepted for publication June 17, 1996. !An earlier version of this paper entitled "Grower Response to Broiler Production Contract Design" was presented at the NE-165 Conference Vertical Coordination in the Food System in Washington, DC, June 5-6, 1995. 2 Currently on sabbatical leave at Pontificia Universidad Catolica de Chile in Santiago, Chile.
growers in business and attract new ones. Growers then attempt to maximize their net returns within the constraints of the contract. Assuming a perfect incentives mechanism or costless monitoring and enforcement, profit maximizing growers would also maximize the integrator's profit. To the extent that the two outcomes differ, room for welfare improvement potentially exists either through rearrangement of incentives (i.e., contract redesign) or t h r o u g h m o r e efficient monitoring and enforcement. The disparity between grower management practices and management practices prescribed by the integrator has long been recognized by agricultural engineers and poultry scientists. The divergence between the strategy that maximizes returns to the grower and the one that maximizes returns to the integrator was first identified by Timmons and Gates (1986) and Gates and Timmons (1986). Using a simulation approach, they found that the contractual arrangement between grower and integrator influences the optimal housing environment and may in fact decrease economic returns for one party at the expense of the other. In subsequent work, Aho and Timmons (1988) found that, depending on the contract specifications, chicken house temperature settings that maximize returns to the grower can be greatly different from those that maximize returns to the integrator. They also found that fine tuning contract specifications can result in temperatures selected by the grower that more closely approximate the integrator optimum. The objective of this paper is to model the grower's decision making process and to gauge the sensitivity of the decision rules to changes in the contract parameters. The underlying hypothesis is that prudent manipulation
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ABSTRACT This paper reports on an analysis of existing broiler production contracts, with an attempt to establish the degree of efficiency gains possible from contract alteration. With the use of settlement cost and farm level data, an assessment is made of optimal grower input decisions given contract specifications. Using this analytical framework, alternative contract designs are simulated by searching over possible
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VUKINA AND FOSTER
of production contract parameters may result in efficiency gains. By efficiency improvement (gain) we mean the scenario where modification of the contract generates a situation in which 1) both parties benefit (win-win criterion), or 2) one party wins and the other party loses, but aggregate gains are larger than aggregate losses so that gainers can, at least in theory, compensate losers (compensation criterion). Econometric estimations of the cost functions and behavioral relationships are done using the combination of settlement cost and farm level data from one broiler contract growout farm in North Carolina. The results seem to suggest that switching part of the utility costs from the grower to the integrator may result in a mutual welfare gain.
Formulation of the Problem Production contracts are legal agreements between an integrator company and a producer (farmer) that bind the producer to specific production practices. Broiler contracts vary from company to company, but all of them have two common features. One is the division of responsibility for providing inputs and the other is the method used to determine grower's compensation (Knoeber, 1989). Both features have been subject to modifications over time, and are still undergoing changes. Typically, the grower provides land and housing facilities, utilities (electricity and water), and labor. Operating expenses, such as repairs and maintenance, chicken house clean-up costs, and manure and dead bird disposal are generally the responsibility of the grower also. The integrator company provides chicks, feed, medication, and services of field personnel. Most of the broiler contracts have a fairly similar structure characterized by the performance-based farmers' remuneration schemes. The performance payment is based on the fixed base payment per pound of live meat delivered, and the variable bonus payment is based on the grower's relative performance (sometimes called the prime cost rating). The bonus payment is determined as a percentage of the difference between average settlement costs of all growers that belong to the integrator's particular profit center whose flocks were harvested in the same week period and a producer's individual settlement costs. Settlement costs are obtained by adding chick, feed, medication, and other customary flock costs divided by total pounds of live poultry delivered. For below-average settlement costs (above-average performance), the grower receives a positive bonus and for the above-average settlement costs, he receives a negative bonus. The total revenue (R) to the grower is the sum of the base and bonus payments multiplied by the net delivered live pounds of poultry: Rit = (b t + Bit) qit
[1]
B it = /3 n
jti %
%
>£*-%
%
n
,j = l,2,...,n [2]
where n represents the total number of growers within the profit center; Cit/q;t is the per pound settlement cost previously defined; and /3 is a bonus factor (usually 50 or 75%). Expressions [1] and [2] can be combined to give the performance payment-based revenue function of the i t h grower's t * flock:
Rit
b t + /3
A? -
n -
1
c
it
qit
[3]
where A t is the t t h flock average settlement cost for the entire group of growers excluding the individual settlement cost of the grower under consideration. The most important cost of broiler production is feed, accounting for approximately two thirds of the live weight costs. Ownership of feed is retained by the integrator and all contracts provide some type of feed efficiency bonus or penalty to motivate efficiency and prevent pilferage. Feed constitutes the single largest component of the integrator's cost. Other components of the so-called chargeable flock costs (i.e., settlement costs) are the costs of chicks and medication. The bulk of grower's operating cost are labor and utilities (electricity and fuel). Smaller items include repairs and maintenance costs, and manure and mortality disposal costs. If the grower decides to expend more labor input by taking better care of the chickens, this should, ceteris paribus, increase the total pounds of live meat produced and also positively impact his relative performance and consequently increase the payment per pound. Another control variable at the grower's disposal is the selection of appropriate broiler house temperature throughout the life of the broilers. Setting the in-house temperatures should respond to the dynamic environmental requirements of birds growing to the market weight under a wide range of climatic conditions and variety of housing types. Because both inputs are scarce, whatever the grower perceives as the optimal use of labor and utilities will depend on their respective opportunity costs determined, among other things, by the farm enterprise portfolio, grower's socioeconomic characteristics, and specific contract design (i.e., the distribution! of production costs responsibilities). Using the performance payment formula [3], with subscripts suppressed for convenience, the grower's static
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MATERIALS AND METHODS
where i denotes the i * grower; t denotes t t h flock; b t denotes the base payment per live pound; Bit is the bonus payment per live pound; and qi t is the number of pounds of live poultry delivered. The current broiler production technology typically allows for growout of six flocks per year. Algebraically, the bonus payment to the i * grower for the t t h flock can be expressed as a fraction of his prime cost rating:
EFFICIENCY GAINS THROUGH CONTRACT FINE TUNING
profit maximization problem can be formulated follows: Max 7r q,u
b + a A
as
c(q,u) + Xpuu
g(q,u,w) - (1 - X)puu
[4]
The necessary conditions for profit maximization in [4] are: 3
*
_ = 3x 3u
=
U a. b
_ ^ u ) du
flA-
* 8c (q' U >
dg(q^w)
+ PA - 0 - ^ _ 3g(q^w) _ 3u
^— = 0 pu[X(/3
_
1}
+
a]
the profit maximizing model. However, one has to keep in mind that changes in prices and contract parameters will also affect other growers within the group whose average settlement costs are represented by A". One way to address this problem is to assume that a change in a contract parameter affects all growers competing for the bonus payment within the same group equally, so that the relative position of an individual grower vis a vis the entire group before and after the change remains the same. Analytically, the above assumption reduces to augmenting the system [7] by a third equation maintaining the relationship between the individual grower's settlement costs and the average settlement cost of the remaining growers in the group fixed. The new system to be solved for the optimal values of q, u, and A has the following form: q* = q(b,/3,X,w,pu) u* = u(b,/3,X,w,pu) ^ = <5A* q
[8]
where 5 measures an average settlement cost differential between an individual grower and the group. If the performance of the individual grower (averaged over certain number of flocks) is below the group average (i.e., the settlement cost per unit of output is above the group average), 8 will be greater than one, and vice versa. Rather than evaluating signs of the comparative statics, the grower's response to changes in contract specifications will be simulated by solving the system of equations in [7] and [8] for different values of contract parameters.
[5] =
Q
[6]
and the sufficient conditions would require the matrix of second derivatives of the profit function to be negative definite. The first order conditions can be solved for the choice functions in terms of prices and contract specification parameters:
Estimation of the Grower's Profit Maximization Model The model parameters are obtained by estimating the system of four equations; two cost functions of the CobbDouglas 3 form (settlement cost and grower's own cost), and two first order conditions for profit maximization [5] and [6] rewritten in elasticity forms: log c = log a 0 + « q log q + a u log (") + a t log t + et
q* = q(A ,b,/3,X,w,pu) u* = u(A",b,j6,X,w,pu)
log g = log 70 + Tqlog q + Tulog (") + 7w log w + 7t log t + €2
[7]
Assuming that it is possible to solve the system [7] for q* and u*, it becomes meaningful to evaluate signs of the partial derivatives comprising the comparative statics of
^Allowing the flexibility of functional form, cost functions were originally estimated as translog functions of their arguments and estimated separately using ordinary least squares. In both cases, all crossand higher-order terms were jointly not significantly different from zero. With all cross- and higher-order terms insignificantly different from zero, the translog specification reduces to Cobb-Douglas functional form.
Pq g PuU
0c Tq
4
e
£3
= au + 7 U ^ + e4
[9] where: P = (b + /3A); a q = (9c/3q)(q/c) is the output elasticity of the settlement cost; a u = (3c/3u)(u/c) is the utilities elasticity of the settlement cost; y„ = (9g/3q)(q/g) is the output elasticity of the grower's cost; yu = (3g/ 3u)(u/g) is the utilities elasticity of the grower's cost; t is a time variable sequentially numbering flocks; T is the
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where c(q,u) is the integrator's cost associated with an individual grower (i.e., settlement cost); g(q,u,w) is the grower's cost; u and p u are utilities input and price; and w is the wage rate. The number of growers contracting with one integrator is assumed fairly large so that (n - l ) / n term from expression [3] is assumed to be close to unity. Settlement cost is determined by the level of output and grower's inputs and is obtained by summing up feed and other chargeable flock costs (chicks and medication) delivered to the grower's farm. Grower's cost is a function of output, utilities, and the prevailing wage rate, and is obtained by summing up small operating expenses (repairs and maintenance) and labor expenses, where number of hours worked is assumed constant for a given capacity. The specification of the grower's profit function in [4] allows for the portion (X) of the utility cost to be a part of the settlement cost. For example, if X = 0, the entire electricity bill is borne by the grower (the current typical case), if X = 1, the electricity cost becomes a part of the settlement costs.
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V U K I N A A N D FOSTER TABLE 1. 3SLS Estimates of the grower's model parameters Coefficient
Estimate
t
log a0 o:q au at log 7 0 7
-3.5787 1.2166 -0.013773 -0.11693 -1.51 0.61628
-11.25 64.47 -5.504 -3.376 -0.4674 2.413
-0.078557 0.32666
-2.623 1.298
0.4454
2.699
7u
7W 7t
multiplying the number of occupancy days by 8 and by the wage rate. The only other piece of information used is the average monthly temperature measured at the meteorological station closest to the farm under consideration. Using the number of occupancy days in different months, the monthly temperature averages are transformed into average temperatures for each of the 36 flocks. The average temperatures for 36 flocks were then averaged again, and the absolute temperature deviations from that historical mean are calculated for each flock.
RESULTS AND DISCUSSION The estimated parameters of the cost functions from the restricted model are presented in Table 1. Almost all parameters are highly significant and have expected signs. Both settlement and grower's own costs are increasing functions of production volume and decreasing functions of electricity consumption. From the grower's perspective, the increase in bonus payment and the decrease in other own costs can be achieved with increased electricity expenditures. It is important to note the different sign of the time variable in settlement cost (a t ) and grower's own cost function (7 t ). The results indicate that as the number of flocks grown increases, the total settlement cost decreases and the grower's own cost increases. Both results seem to be intuitively correct. With more flocks grown, the grower becomes more skilled and the feed conversion ratio of his birds is improving. Contrary to that, with the progression of time, the facilities deteriorate which increases the cost of repair and maintenance.
Simulation Results Having an analytical framework based on observed behavior of how growers make decisions conditional upon contract stipulations allows simulation of alternative designs. Given the estimated technical production relationships and the associated optimal grower decision rules, an optimal contract design could be determined by searching over possible contract parameter values. The foci of our analysis are the three contract parameters: the base payment b; the bonus factor /3, and the utilities cost
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absolute deviation from the average temperature; e are normally distributed error terms; and other variables are previously defined. The cost functions (first two equations) represent technological relationships, whereas the system of first order conditions (the last two equations) represents a set of behavioral relationships. Total settlement cost (obtained by summing up chicks, feed, medication, and other customary flock costs) is specified as a function of output (pounds of live poultry moved from the grower's farm) and utilities (normalized electricity usage). The electricity consumption is normalized by the absolute temperature deviations so that the variable represents kilowatt-hours of electricity used per degree Fahrenheit deviation from the historical mean temperature. Grower's own cost (calculated as a sum of small operating expenses and labor expenses) is specified as a function of output, utilities, and the wage rate. The first order conditions were used to impose the profit maximizing behavior on the system. The model was estimated using 3-Stage-Least-Squares (3SLS) procedure imposing cross-equation restrictions on parameters (e.g., a q from the first equation in [9] has to be equal to a q from the third equation, etc.). The empirical analysis based on the presented analytical model is performed using the combination of settlement cost and farm level data from one broiler contract growout farm in North Carolina. The data set reflects a representative North Carolina broiler contract growing enterprise. The farmer has four chicken houses with the total average capacity of 104,000 birds and grows chickens for one of the biggest companies in the country. Aside from broilers, there are other enterprises on the farm such as corn, soybeans, tobacco, and sweet potatoes. The data set covers the period between January 1,1988 and April 6, 1994. In that period the farmer grew 36 broiler blocks. The settlement cost, the electricity consumption and costs, and the repair, maintenance and other small operating costs data are available for the entire period. Electricity is used for lights and ventilation and is the grower's single largest operating cash expense related to the broiler business. Fuel cost is part of the settlement cost. Monthly electricity bills are converted into electricity consumption and cost per flock using the number of occupancy days for each flock. A similar approach is used to convert monthly figures for repair, maintenance, and other operating expenses into per flock dollar amounts. Observations on labor input were not available. Data points are constructed by assuming a constant 2 h / d per chicken house labor requirement considered to be an industry average by most integrators. Because our grower has four chicken houses, the labor requirements translates into 8 h / d for each occupancy day during the life of the flock. The price of labor is obtained from the Employment Security Commission of North Carolina. The quarterly statewide data on average weekly wage per employee in the Agricultural Production-Livestock sector (SIC Code 02) is converted into average hourly wage rate based on the 40-h working week. Total labor expenses are obtained by
EFFICIENCY GAINS THROUGH CONTRACT FINE TUNING -
1
|
1
!
! |
1 |
1 |
I i
I
/
/
/
J
1
\
/ l
! -•-Profit(l)
-B-Proffl(2)
-*-Cost(1)
-*-Cost(2)
O 0.4 *
1
j
1
1
0.035
1 0.0355
o
1!
i i !
i i i
! !
j
|
1
i
I
_ _.
_. L
_
j
._!_.
0.8 •
r* L .."
..!
ii
i
! 1 1
i j
i
j
i
i
!
1
1 i i
i i i
I i i
|
!
! i
! 1
:
i
!
i i
i s
i _ . _ j — j —
i i i _ i -
—•— Proflt(1)
-»-Profit(2)
-*-Cost(1)
-*-Cost(2)
i
i - -|
i
i
:
i
!
!
! —Ti
Ti
j
!
— i
i •
!
[
|
I
!
1 1
i j
i
1 1
i - i
i i
' —
0
i
1 0.036
i 0.0365
i 0.037
0.0375
0.038
Bonus Factor
Base Payment in $/Lb
Figure 2. Bonus factor simulation results. Figure 1. Base payment simulation results.
allocation factor A. The results are summarized in Tables 2 to 4, and Figures 1 to 3. Given the cost functions estimates, the solution to the system of first order conditions for profit maximization [5] and [6] is analytically intractable. The individual first order conditions include the sums of two Cobb-Douglas functions for which a closed form solution does not exist. Therefore, the system is solved With the Gauss-Newton method using "fsolve" routine available in the MATLAB Optimization Toolbox software. Using parameter estimates from Table 1, we explore two scenarios. In the first scenario the value of the group average settlement cost A~ is fixed at the sample mean and the system of equations [7] is solved for optimal choices of u and q. The maximum profit of $10,180.94 is obtained by selecting q* = 458,388 lb of net live weight, and u* = 16,061 kWh of electricity. In the second scenario we allow the group average settlement cost to vary freely fixing the relative position of the individual grower vis-a-vis the entire group. Historically (36 flocks average), the performance of our grower is below the group average performance, i.e., his settlement costs are above the group average by approximately 2% (5 = 1.021). The system of equation [8] is solved for optimal choice of q, u, and A and the following set of results was
4 The mean values of profit and decision variables (with standard deviations in parentheses) are: 7r = 10,227 (2,096); q = 458,287 (30,976); u = 15,883 (3,044); and A = $0.26 (0.02).
obtained: ir* = $9,464.53; q* = 434,470 lb; u* = 15,224 kWh; and A* = $0.26/lb. In both cases, the optimal values are within one standard deviation from the sample mean values. 4 In the analysis that follows, the welfare position of a grower is represented by his profit function as specified in [4]. Since all elements necessary to describe the profit function of an integrator were not available, we have to resort to an approximation of the integrator's ultimate objectives. Being part of the completely vertically integrated industry, aside from broiler grow-out enterprise, broiler companies also own and operate broiler breeder flocks, hatcheries, feed mills, processing facilities, and transportation and marketing departments. The only observable segment of the vertically integrated chain of activities comprising broiler production was the one where integrator's activities intersect grower's actions and decisions. Therefore, we describe the integrator's objective as one of minimizing the settlement cost (i.e., chicks, feed, medication and other customary flock costs per pound of live poultry produced). Alternatively, an integrator's objective may be defined as minimizing the sum of settlement costs and payments made out to growers for their services rendered per pound of poultry produced. Whereas pursuing the first goal is almost entirely technologically determined, the second goal may involve constraints such as nourishing good relationship with growers and maintaining a positive image with the community at large.
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I l
•
1 1
:-
integrator tost in $/L
l
I
1
i
i
i
1355
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VUKINA AND FOSTER TABLE 2. Base payment comparative statics simulation
b
u*
q*
cVq*
A*
Base Payment Searching over possible values for the base payment parameter b shows that increasing base payment creates larger profits for the grower but also larger per pound integrators costs. Allowing for the group response generates more rapid response as one moves away from the mean observed value of b (3.66c/lb) compared to the scenario with the individual grower's response only. Looking at the rates of change indicates that the change in
e=r
Int. cost
($/lb)
Profit ($)
0.2638 0.2647 0.2656 0.2665 0.2674 0.2683 0.2692
0.0349 0.0350 0.0350 0.0351 0.0351 0.0352 0.0352
0.2987 0.2997 0.3006 0.3016 0.3025 0.3035 0.3044
9,482.05 9,700.56 9,922.79 10,148.77 10,378.56 10,612.21 10,849.75
0.2449 0.2666 0.2666 0.2666 0.2707 0.2784 0.2856
0.0336 0.0340 0.0345 0.0350 0.0353 0.0357 0.0362
0.2785 0.3006 0.3011 0.3016 0.3060 0.3141 0.3218
5,584.73 9,690.29 9,919.43 10,148.57 11,255.75 13,522.40 15,976.34
the base payment generates more rapid response in grower's profit than in integrators per unit cost. However, this can be misleading because of the relative magnitudes of the integrator's total costs and grower's profit. For example, allowing all growers to adapt to changes simultaneously, the increase in the base payment from 3.65<£/lb to 3.70 <2/lb increases profit to our grower by $1,107, whereas total costs to the integrator increase by $13,020. On the other hand, the integrator gained close to 36,000 live lb of chicken meat. Because the total revenue obtained for these broilers is unknown as are the other components of the integrator's costs, the conclusion as to whether an increase in the base payment can qualify as a contract improving design remains ambiguous. Simulation also seems to indicate that decreasing the base payment away from its actual value has an offsetting effect on the welfare position of the two parties. The decline in grower's profit almost exactly matches the decline in integrator's total cost, with almost no change in the production volume.
Bonus Factor
I
—
-1
-0.8
-0.6
-0.4
-0.2
-*-Profit(1)
-»-Prom(2)
-*-Cost(1)
-K-COSt(2)
I
i
0.6
0.8
1 1
L
1
0
0.2
L
r
0.4
1
Utilities Allocation Factor
Figure 3. Utilities allocation factor simulation results.
Experimenting with different values of the bonus factor generated results presented in Table 3 and Figure 2. Only a fairly narrow range of fi values was searched over. Moving further away from the actual value of |S = 0.5 generates optimal values for q and u outside the technologically feasible region, and in case of full adjustment scenario caused serious numerical problems. The results seem to indicate that increasing the bonus factor away from its actual value of 0.5 has almost no effect on either party's welfare position. Adjusting 0 downwards would increase profits to the grower but also increase integrator's per unit costs. Both tendencies are more pronounced with full adjustment (Case 2). Whether decreasing 0 can be considered as a contract improvement would depend on whether the losses to the integrator exceed the gains to the grower. However, to successfully
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(lb) ($/lb) (kWh) Case 1: Allowing for the grower's response only 0.0350 434,817 15,237 0.0355 442,221 15,495 0.0360 449,719 15,757 0.0365 457,310 16,023 0.0370 464,996 16,293 0.0375 472,776 16,566 0.0380 480,654 16,843 Case 2: Allowing for the group response 0.0350 301,654 10,655 0.2420 0.0355 458,287 15,883 0.2636 0.0360 15,883 0.2636 458,287 0.0365 458,287 15,883 0.2636 0.0370 494,244 17,322 0.2673 0.0375 567,415 19,923 0.2749 0.0380 644,049 22,685 0.2820
R/lb
EFFICIENCY GAINS THROUGH CONTRACT FINE TUNING
1357
TABLE 3. Bonus factor comparative statics simulation
0
q*
u*
A*
implement compensation criterion, in this case as in the previous case, the knowledge of the integrator's profit function is needed.
Utilities Allocation Factor The utilities allocation factor impact was simulated for values of X between -1 and 1. Specifying the negative values for X reallocates part of the existing settlement cost
R/lb
c*/q* —
Int. cost
($/lb)
Profit
—
($)
0.2695 0.2689 0.2683 0.2677 0.2672 0.2666 0.2661 0.2656 0.2651 0.2646
0.0338 0.0341 0.0343 0.0346 0.0348 0.0351 0.0353 0.0356 0.0358 0.0361
0.3033 0.3029 0.3026 0.3023 0.3020 0.3017 0.3014 0.3011 0.3009 0.3006
10,230.27 10,217.49 10,206.23 10,196.42 10,188.01 10,180.94 10,175.16 10,170.62 10,167.27 10,165.07
0.2884 0.2835 0.2786 0.2736 0.2687 0.2637 0.2666 0.2666 0.2666 0.2666
0.0348 0.0349 0.0349 0.0349 0.0349 0.0349 0.0350 0.0350 0.0350 0.0350
0.3232 0.3183 0.3134 0.3085 0.3036 0.2986 0.3017 0.3017 0.3017 0.3016
15,956.63 14,461.73 13,071.50 11,777.19 10,570.54 9,464.53 10,173.96 10,167.05 10,160.13 10,153.21
from integrator to grower, and positive values for X reallocates part of the utilities bill from the grower to the integrator. Both scenarios are meaningful due to the fact that fuel cost is a part of the settlement cost born by the integrator and the electricity bill is a part of the grower's expenses. For the particular contract under consideration, the actual value of X is zero. Under both full adjustment and partial adjustment scenarios, increasing utilities allocation factor increases profit to grower. The larger the
TABLE 4. Utilities allocation factor comparative statics simulation A
q*
u*
A*
(lb) (kWh) Case 1: Allowing for the grower's response only 442,177 10,468 -1.0 444,909 11,259 -0.8 -0.6 447,855 12,175 451,052 13,249 -0.4 -0.2 454,543 14,523 458,388 16,061 0.0 0.2 462,663 17,951 467,472 20,328 0.4 0.6 472,964 23,406 479,358 27,544 0.8 1.0 486,994 33,393 Case 2: Allowing for the group response 382,351 9,069 0.2551 -1.0 -0.8 391,264 9,915 0.2561 400,745 10,905 -0.6 0.2571 -0.4 410,891 12,007 0.2581 13,482 -0.2 421,824 0.2592 0.0 15,224 0.2604 434,470 446,716 17,332 0.2 0.2615 0.4 20,053 461,159 0.2628 23,628 0.6 477,415 0.2642 0.8 496,056 28,514 0.2657 517,972 35,549 1.0 0.2674
c*/q*
R/lb
Profit
Int. cost
($/lb)
—
($)
0.2661 0.2662 0.2663 0.2664 0.2665 0.2666 0.2667 0.2669 0.2670 0.2672 0.2674
0.0362 0.0360 0.0359 0.0356 0.0354 0.0351 0.0347 0.0343 0.0337 0.0330 0.0321
0.3023 0.3022 0.3021 0.3020 0.3019 0.3017 0.3015 0.3012 0.3008 0.3003 0.2995
9,697.54 9,779.03 9,866.90 9,962.23 10,066.33 10,180.94 10,308.35 10,451.67 10,615.29 10,805.70 11,033.04
0.2584 0.2593 0.2604 0.2614 0.2625 0.2637 0.2649 0.2661 0.2675 0.2691 0.2708
0.0358 0.0357 0.0355 0.0354 0.0352 0.0349 0.0346 0.0342 0.0338 0.0331 0.0323
0.2942 0.2950 0.2959 0.2968 0.2976 0.2986 0.2995 0.3004 0.3013 0.3022 0.3031
7,950.67 8,206.95 8,480.97 8,775.73 9,095.00 9,464.53 9,828.14 10,257.16 10,743.02 11,303.82 11,967.75
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(lb) (kWh) Case 1: Allowing for the grower's response only 0.475 481,850 16,311 0.480 476,868 16,256 0.485 472,037 16,207 0.490 467,351 16,154 0.495 462,803 16,106 0.500 458,388 16,061 0.505 454,100 16,018 0.510 449,934 15,976 0.515 445,885 15,937 0.520 441,948 15,899 Case 2: Allowing for the group response 0.475 673,360 22,890 0.2847 0.480 619,108 21,160 0.2799 0.485 568,304 19,534 0.2750 0.490 520,654 18,005 0.2702 16,562 0.495 475,876 0.2653 0.500 15,224 0.2604 434,470 458,287 0.505 15,883 0.2636 0.510 458,287 15,883 0.2636 0.515 458,287 15,883 0.2636 0.520 15,883 458,287 0.2636
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VUKINA AND FOSTER
5
This number is obtained as the sample mean of the average settlement cost for the entire group ($0.26/lb) plus the sample mean of the per pound payment to the grower ($0.04/lb).
econometric estimation of the cost functions and behavioral relationships requires a combination of settlement costs and farm level data. With the settlement cost and farm level inputs records, optimal grower input decisions can be estimated and alternative contract designs can be simulated by searching over possible contract parameter values. However, industry-wide analysis of this kind is yet precluded because the farm level cost data for sufficient number of farms is difficult to assemble. Further research in this area will focus on close collaboration with the industry to start the process of monitoring and recording of the farm level cost data.
REFERENCES Aho, P. W., and M. B. Timmons, 1988. Disparate grower and integrator optimum growout temperatures. Poultry Sci. 67: 534-537. Gates, R. S., and M. B. Timmons, 1986. Real-Time Economic Optimization of Broiler Production. Paper No. 86-4552,1986 Winter Meeting American Society of Agricultural Engineers, Chicago, IL, December 16-19. Knoeber, C. R., 1989. A real game of chicken: Contracts, tournaments, and the production of broilers. J. Law Econ. Organization 5(2):271-292. Knoeber, C. R., and W. N. Thurman, 1995. "Don't count your chickens...": risk and risk shifting in the broiler industry. Am. J. Agric. Econ. 77:486^96. Timmons, M. B., and R. S. Gates, 1986. Economic optimization of broiler production. Trans. ASAE 29:1373-1378, 1384.
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portion of the utilities costs switched over from the grower's cost into the settlement cost, the larger the profits for the grower. The impact of a change in X on the integrator's per unit cost depends on the type of adjustment scenario. Under partial adjustment scenario, the increase in X results in decreasing integrator's unit cost. Under full adjustment scenario, the increase in X increases integrator costs. The obtained results seem to indicate that increasing X, i.e., switching part of the electricity cost from the grower's cost into the settlement cost may be a candidate for the contract redesign. There are two arguments to support this claim. First, the partial adjustment model unambiguously signals an efficiency improvement (grower's profits are increasing while integrator's per unit cost is decreasing). Second, in the full adjustment model, increasing X from 0 to 0.2 increases grower's profit by $364, whereas the total integrator's costs increase by $4,058 with the gain in the volume of production of 12,246 lb. If we value these additional pounds only at variable costs necessary to produce them (30(f/lb),5 the benefits to the grower would approximately equal the costs to the integrator. The main emphasis of this paper is on methodological issues and less on specific estimation and simulation results. The presented analysis was done using one contract growout farm data only, and therefore the results may not be representative of the entire industry and all geographical and climatic regions. As seen in the paper,
(Key words: economic optimization, broiler production, contracts, growers' payments) 1996 Poultry Science 75:1351-1358
INTRODUCTION The U.S. broiler industry is almost entirely vertically coordinated by production contracts. Judged by their prevalence, contracts have proven to be a successful mode of organizing broiler production. They have benefitted farmers by offering opportunities to earn income with relatively low capital requirements, by alleviating cash flow problems typically plaguing small farms, and by allowing enterprise diversification on the farm. The major efficiency gain from contracts probably is the reallocation of risk from the farmers to integrators, who have the means to act upon uncertain outcomes (Knoeber and Thurman, 1995). Broiler contracts also have their critics, largely originating from the growers' own ranks, who complain about gains from contract arrangements being largely appropriated by integrators, whereas growers receive only small or even negative returns from contract production. The existing controversy can be reduced to a standard principal-agent type problem. Production contracts are designed to provide growers with appropriate incentives to manage their broiler farms in a way that will maximize integrator's returns, and at the same time be significantly rewarding to growers to keep the existing
Received for publication March 29, 1996. Accepted for publication June 17, 1996. !An earlier version of this paper entitled "Grower Response to Broiler Production Contract Design" was presented at the NE-165 Conference Vertical Coordination in the Food System in Washington, DC, June 5-6, 1995. 2 Currently on sabbatical leave at Pontificia Universidad Catolica de Chile in Santiago, Chile.
growers in business and attract new ones. Growers then attempt to maximize their net returns within the constraints of the contract. Assuming a perfect incentives mechanism or costless monitoring and enforcement, profit maximizing growers would also maximize the integrator's profit. To the extent that the two outcomes differ, room for welfare improvement potentially exists either through rearrangement of incentives (i.e., contract redesign) or t h r o u g h m o r e efficient monitoring and enforcement. The disparity between grower management practices and management practices prescribed by the integrator has long been recognized by agricultural engineers and poultry scientists. The divergence between the strategy that maximizes returns to the grower and the one that maximizes returns to the integrator was first identified by Timmons and Gates (1986) and Gates and Timmons (1986). Using a simulation approach, they found that the contractual arrangement between grower and integrator influences the optimal housing environment and may in fact decrease economic returns for one party at the expense of the other. In subsequent work, Aho and Timmons (1988) found that, depending on the contract specifications, chicken house temperature settings that maximize returns to the grower can be greatly different from those that maximize returns to the integrator. They also found that fine tuning contract specifications can result in temperatures selected by the grower that more closely approximate the integrator optimum. The objective of this paper is to model the grower's decision making process and to gauge the sensitivity of the decision rules to changes in the contract parameters. The underlying hypothesis is that prudent manipulation
1351
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ABSTRACT This paper reports on an analysis of existing broiler production contracts, with an attempt to establish the degree of efficiency gains possible from contract alteration. With the use of settlement cost and farm level data, an assessment is made of optimal grower input decisions given contract specifications. Using this analytical framework, alternative contract designs are simulated by searching over possible
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VUKINA AND FOSTER
of production contract parameters may result in efficiency gains. By efficiency improvement (gain) we mean the scenario where modification of the contract generates a situation in which 1) both parties benefit (win-win criterion), or 2) one party wins and the other party loses, but aggregate gains are larger than aggregate losses so that gainers can, at least in theory, compensate losers (compensation criterion). Econometric estimations of the cost functions and behavioral relationships are done using the combination of settlement cost and farm level data from one broiler contract growout farm in North Carolina. The results seem to suggest that switching part of the utility costs from the grower to the integrator may result in a mutual welfare gain.
Formulation of the Problem Production contracts are legal agreements between an integrator company and a producer (farmer) that bind the producer to specific production practices. Broiler contracts vary from company to company, but all of them have two common features. One is the division of responsibility for providing inputs and the other is the method used to determine grower's compensation (Knoeber, 1989). Both features have been subject to modifications over time, and are still undergoing changes. Typically, the grower provides land and housing facilities, utilities (electricity and water), and labor. Operating expenses, such as repairs and maintenance, chicken house clean-up costs, and manure and dead bird disposal are generally the responsibility of the grower also. The integrator company provides chicks, feed, medication, and services of field personnel. Most of the broiler contracts have a fairly similar structure characterized by the performance-based farmers' remuneration schemes. The performance payment is based on the fixed base payment per pound of live meat delivered, and the variable bonus payment is based on the grower's relative performance (sometimes called the prime cost rating). The bonus payment is determined as a percentage of the difference between average settlement costs of all growers that belong to the integrator's particular profit center whose flocks were harvested in the same week period and a producer's individual settlement costs. Settlement costs are obtained by adding chick, feed, medication, and other customary flock costs divided by total pounds of live poultry delivered. For below-average settlement costs (above-average performance), the grower receives a positive bonus and for the above-average settlement costs, he receives a negative bonus. The total revenue (R) to the grower is the sum of the base and bonus payments multiplied by the net delivered live pounds of poultry: Rit = (b t + Bit) qit
[1]
B it = /3 n
jti %
%
>£*-%
%
n
,j = l,2,...,n [2]
where n represents the total number of growers within the profit center; Cit/q;t is the per pound settlement cost previously defined; and /3 is a bonus factor (usually 50 or 75%). Expressions [1] and [2] can be combined to give the performance payment-based revenue function of the i t h grower's t * flock:
Rit
b t + /3
A? -
n -
1
c
it
qit
[3]
where A t is the t t h flock average settlement cost for the entire group of growers excluding the individual settlement cost of the grower under consideration. The most important cost of broiler production is feed, accounting for approximately two thirds of the live weight costs. Ownership of feed is retained by the integrator and all contracts provide some type of feed efficiency bonus or penalty to motivate efficiency and prevent pilferage. Feed constitutes the single largest component of the integrator's cost. Other components of the so-called chargeable flock costs (i.e., settlement costs) are the costs of chicks and medication. The bulk of grower's operating cost are labor and utilities (electricity and fuel). Smaller items include repairs and maintenance costs, and manure and mortality disposal costs. If the grower decides to expend more labor input by taking better care of the chickens, this should, ceteris paribus, increase the total pounds of live meat produced and also positively impact his relative performance and consequently increase the payment per pound. Another control variable at the grower's disposal is the selection of appropriate broiler house temperature throughout the life of the broilers. Setting the in-house temperatures should respond to the dynamic environmental requirements of birds growing to the market weight under a wide range of climatic conditions and variety of housing types. Because both inputs are scarce, whatever the grower perceives as the optimal use of labor and utilities will depend on their respective opportunity costs determined, among other things, by the farm enterprise portfolio, grower's socioeconomic characteristics, and specific contract design (i.e., the distribution! of production costs responsibilities). Using the performance payment formula [3], with subscripts suppressed for convenience, the grower's static
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MATERIALS AND METHODS
where i denotes the i * grower; t denotes t t h flock; b t denotes the base payment per live pound; Bit is the bonus payment per live pound; and qi t is the number of pounds of live poultry delivered. The current broiler production technology typically allows for growout of six flocks per year. Algebraically, the bonus payment to the i * grower for the t t h flock can be expressed as a fraction of his prime cost rating:
EFFICIENCY GAINS THROUGH CONTRACT FINE TUNING
profit maximization problem can be formulated follows: Max 7r q,u
b + a A
as
c(q,u) + Xpuu
g(q,u,w) - (1 - X)puu
[4]
The necessary conditions for profit maximization in [4] are: 3
*
_ = 3x 3u
=
U a. b
_ ^ u ) du
flA-
* 8c (q' U >
dg(q^w)
+ PA - 0 - ^ _ 3g(q^w) _ 3u
^— = 0 pu[X(/3
_
1}
+
a]
the profit maximizing model. However, one has to keep in mind that changes in prices and contract parameters will also affect other growers within the group whose average settlement costs are represented by A". One way to address this problem is to assume that a change in a contract parameter affects all growers competing for the bonus payment within the same group equally, so that the relative position of an individual grower vis a vis the entire group before and after the change remains the same. Analytically, the above assumption reduces to augmenting the system [7] by a third equation maintaining the relationship between the individual grower's settlement costs and the average settlement cost of the remaining growers in the group fixed. The new system to be solved for the optimal values of q, u, and A has the following form: q* = q(b,/3,X,w,pu) u* = u(b,/3,X,w,pu) ^ = <5A* q
[8]
where 5 measures an average settlement cost differential between an individual grower and the group. If the performance of the individual grower (averaged over certain number of flocks) is below the group average (i.e., the settlement cost per unit of output is above the group average), 8 will be greater than one, and vice versa. Rather than evaluating signs of the comparative statics, the grower's response to changes in contract specifications will be simulated by solving the system of equations in [7] and [8] for different values of contract parameters.
[5] =
Q
[6]
and the sufficient conditions would require the matrix of second derivatives of the profit function to be negative definite. The first order conditions can be solved for the choice functions in terms of prices and contract specification parameters:
Estimation of the Grower's Profit Maximization Model The model parameters are obtained by estimating the system of four equations; two cost functions of the CobbDouglas 3 form (settlement cost and grower's own cost), and two first order conditions for profit maximization [5] and [6] rewritten in elasticity forms: log c = log a 0 + « q log q + a u log (") + a t log t + et
q* = q(A ,b,/3,X,w,pu) u* = u(A",b,j6,X,w,pu)
log g = log 70 + Tqlog q + Tulog (") + 7w log w + 7t log t + €2
[7]
Assuming that it is possible to solve the system [7] for q* and u*, it becomes meaningful to evaluate signs of the partial derivatives comprising the comparative statics of
^Allowing the flexibility of functional form, cost functions were originally estimated as translog functions of their arguments and estimated separately using ordinary least squares. In both cases, all crossand higher-order terms were jointly not significantly different from zero. With all cross- and higher-order terms insignificantly different from zero, the translog specification reduces to Cobb-Douglas functional form.
Pq g PuU
0c Tq
4
e
£3
= au + 7 U ^ + e4
[9] where: P = (b + /3A); a q = (9c/3q)(q/c) is the output elasticity of the settlement cost; a u = (3c/3u)(u/c) is the utilities elasticity of the settlement cost; y„ = (9g/3q)(q/g) is the output elasticity of the grower's cost; yu = (3g/ 3u)(u/g) is the utilities elasticity of the grower's cost; t is a time variable sequentially numbering flocks; T is the
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where c(q,u) is the integrator's cost associated with an individual grower (i.e., settlement cost); g(q,u,w) is the grower's cost; u and p u are utilities input and price; and w is the wage rate. The number of growers contracting with one integrator is assumed fairly large so that (n - l ) / n term from expression [3] is assumed to be close to unity. Settlement cost is determined by the level of output and grower's inputs and is obtained by summing up feed and other chargeable flock costs (chicks and medication) delivered to the grower's farm. Grower's cost is a function of output, utilities, and the prevailing wage rate, and is obtained by summing up small operating expenses (repairs and maintenance) and labor expenses, where number of hours worked is assumed constant for a given capacity. The specification of the grower's profit function in [4] allows for the portion (X) of the utility cost to be a part of the settlement cost. For example, if X = 0, the entire electricity bill is borne by the grower (the current typical case), if X = 1, the electricity cost becomes a part of the settlement costs.
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V U K I N A A N D FOSTER TABLE 1. 3SLS Estimates of the grower's model parameters Coefficient
Estimate
t
log a0 o:q au at log 7 0 7
-3.5787 1.2166 -0.013773 -0.11693 -1.51 0.61628
-11.25 64.47 -5.504 -3.376 -0.4674 2.413
-0.078557 0.32666
-2.623 1.298
0.4454
2.699
7u
7W 7t
multiplying the number of occupancy days by 8 and by the wage rate. The only other piece of information used is the average monthly temperature measured at the meteorological station closest to the farm under consideration. Using the number of occupancy days in different months, the monthly temperature averages are transformed into average temperatures for each of the 36 flocks. The average temperatures for 36 flocks were then averaged again, and the absolute temperature deviations from that historical mean are calculated for each flock.
RESULTS AND DISCUSSION The estimated parameters of the cost functions from the restricted model are presented in Table 1. Almost all parameters are highly significant and have expected signs. Both settlement and grower's own costs are increasing functions of production volume and decreasing functions of electricity consumption. From the grower's perspective, the increase in bonus payment and the decrease in other own costs can be achieved with increased electricity expenditures. It is important to note the different sign of the time variable in settlement cost (a t ) and grower's own cost function (7 t ). The results indicate that as the number of flocks grown increases, the total settlement cost decreases and the grower's own cost increases. Both results seem to be intuitively correct. With more flocks grown, the grower becomes more skilled and the feed conversion ratio of his birds is improving. Contrary to that, with the progression of time, the facilities deteriorate which increases the cost of repair and maintenance.
Simulation Results Having an analytical framework based on observed behavior of how growers make decisions conditional upon contract stipulations allows simulation of alternative designs. Given the estimated technical production relationships and the associated optimal grower decision rules, an optimal contract design could be determined by searching over possible contract parameter values. The foci of our analysis are the three contract parameters: the base payment b; the bonus factor /3, and the utilities cost
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absolute deviation from the average temperature; e are normally distributed error terms; and other variables are previously defined. The cost functions (first two equations) represent technological relationships, whereas the system of first order conditions (the last two equations) represents a set of behavioral relationships. Total settlement cost (obtained by summing up chicks, feed, medication, and other customary flock costs) is specified as a function of output (pounds of live poultry moved from the grower's farm) and utilities (normalized electricity usage). The electricity consumption is normalized by the absolute temperature deviations so that the variable represents kilowatt-hours of electricity used per degree Fahrenheit deviation from the historical mean temperature. Grower's own cost (calculated as a sum of small operating expenses and labor expenses) is specified as a function of output, utilities, and the wage rate. The first order conditions were used to impose the profit maximizing behavior on the system. The model was estimated using 3-Stage-Least-Squares (3SLS) procedure imposing cross-equation restrictions on parameters (e.g., a q from the first equation in [9] has to be equal to a q from the third equation, etc.). The empirical analysis based on the presented analytical model is performed using the combination of settlement cost and farm level data from one broiler contract growout farm in North Carolina. The data set reflects a representative North Carolina broiler contract growing enterprise. The farmer has four chicken houses with the total average capacity of 104,000 birds and grows chickens for one of the biggest companies in the country. Aside from broilers, there are other enterprises on the farm such as corn, soybeans, tobacco, and sweet potatoes. The data set covers the period between January 1,1988 and April 6, 1994. In that period the farmer grew 36 broiler blocks. The settlement cost, the electricity consumption and costs, and the repair, maintenance and other small operating costs data are available for the entire period. Electricity is used for lights and ventilation and is the grower's single largest operating cash expense related to the broiler business. Fuel cost is part of the settlement cost. Monthly electricity bills are converted into electricity consumption and cost per flock using the number of occupancy days for each flock. A similar approach is used to convert monthly figures for repair, maintenance, and other operating expenses into per flock dollar amounts. Observations on labor input were not available. Data points are constructed by assuming a constant 2 h / d per chicken house labor requirement considered to be an industry average by most integrators. Because our grower has four chicken houses, the labor requirements translates into 8 h / d for each occupancy day during the life of the flock. The price of labor is obtained from the Employment Security Commission of North Carolina. The quarterly statewide data on average weekly wage per employee in the Agricultural Production-Livestock sector (SIC Code 02) is converted into average hourly wage rate based on the 40-h working week. Total labor expenses are obtained by
EFFICIENCY GAINS THROUGH CONTRACT FINE TUNING -
1
|
1
!
! |
1 |
1 |
I i
I
/
/
/
J
1
\
/ l
! -•-Profit(l)
-B-Proffl(2)
-*-Cost(1)
-*-Cost(2)
O 0.4 *
1
j
1
1
0.035
1 0.0355
o
1!
i i !
i i i
! !
j
|
1
i
I
_ _.
_. L
_
j
._!_.
0.8 •
r* L .."
..!
ii
i
! 1 1
i j
i
j
i
i
!
1
1 i i
i i i
I i i
|
!
! i
! 1
:
i
!
i i
i s
i _ . _ j — j —
i i i _ i -
—•— Proflt(1)
-»-Profit(2)
-*-Cost(1)
-*-Cost(2)
i
i - -|
i
i
:
i
!
!
! —Ti
Ti
j
!
— i
i •
!
[
|
I
!
1 1
i j
i
1 1
i - i
i i
' —
0
i
1 0.036
i 0.0365
i 0.037
0.0375
0.038
Bonus Factor
Base Payment in $/Lb
Figure 2. Bonus factor simulation results. Figure 1. Base payment simulation results.
allocation factor A. The results are summarized in Tables 2 to 4, and Figures 1 to 3. Given the cost functions estimates, the solution to the system of first order conditions for profit maximization [5] and [6] is analytically intractable. The individual first order conditions include the sums of two Cobb-Douglas functions for which a closed form solution does not exist. Therefore, the system is solved With the Gauss-Newton method using "fsolve" routine available in the MATLAB Optimization Toolbox software. Using parameter estimates from Table 1, we explore two scenarios. In the first scenario the value of the group average settlement cost A~ is fixed at the sample mean and the system of equations [7] is solved for optimal choices of u and q. The maximum profit of $10,180.94 is obtained by selecting q* = 458,388 lb of net live weight, and u* = 16,061 kWh of electricity. In the second scenario we allow the group average settlement cost to vary freely fixing the relative position of the individual grower vis-a-vis the entire group. Historically (36 flocks average), the performance of our grower is below the group average performance, i.e., his settlement costs are above the group average by approximately 2% (5 = 1.021). The system of equation [8] is solved for optimal choice of q, u, and A and the following set of results was
4 The mean values of profit and decision variables (with standard deviations in parentheses) are: 7r = 10,227 (2,096); q = 458,287 (30,976); u = 15,883 (3,044); and A = $0.26 (0.02).
obtained: ir* = $9,464.53; q* = 434,470 lb; u* = 15,224 kWh; and A* = $0.26/lb. In both cases, the optimal values are within one standard deviation from the sample mean values. 4 In the analysis that follows, the welfare position of a grower is represented by his profit function as specified in [4]. Since all elements necessary to describe the profit function of an integrator were not available, we have to resort to an approximation of the integrator's ultimate objectives. Being part of the completely vertically integrated industry, aside from broiler grow-out enterprise, broiler companies also own and operate broiler breeder flocks, hatcheries, feed mills, processing facilities, and transportation and marketing departments. The only observable segment of the vertically integrated chain of activities comprising broiler production was the one where integrator's activities intersect grower's actions and decisions. Therefore, we describe the integrator's objective as one of minimizing the settlement cost (i.e., chicks, feed, medication and other customary flock costs per pound of live poultry produced). Alternatively, an integrator's objective may be defined as minimizing the sum of settlement costs and payments made out to growers for their services rendered per pound of poultry produced. Whereas pursuing the first goal is almost entirely technologically determined, the second goal may involve constraints such as nourishing good relationship with growers and maintaining a positive image with the community at large.
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I l
•
1 1
:-
integrator tost in $/L
l
I
1
i
i
i
1355
1356
VUKINA AND FOSTER TABLE 2. Base payment comparative statics simulation
b
u*
q*
cVq*
A*
Base Payment Searching over possible values for the base payment parameter b shows that increasing base payment creates larger profits for the grower but also larger per pound integrators costs. Allowing for the group response generates more rapid response as one moves away from the mean observed value of b (3.66c/lb) compared to the scenario with the individual grower's response only. Looking at the rates of change indicates that the change in
e=r
Int. cost
($/lb)
Profit ($)
0.2638 0.2647 0.2656 0.2665 0.2674 0.2683 0.2692
0.0349 0.0350 0.0350 0.0351 0.0351 0.0352 0.0352
0.2987 0.2997 0.3006 0.3016 0.3025 0.3035 0.3044
9,482.05 9,700.56 9,922.79 10,148.77 10,378.56 10,612.21 10,849.75
0.2449 0.2666 0.2666 0.2666 0.2707 0.2784 0.2856
0.0336 0.0340 0.0345 0.0350 0.0353 0.0357 0.0362
0.2785 0.3006 0.3011 0.3016 0.3060 0.3141 0.3218
5,584.73 9,690.29 9,919.43 10,148.57 11,255.75 13,522.40 15,976.34
the base payment generates more rapid response in grower's profit than in integrators per unit cost. However, this can be misleading because of the relative magnitudes of the integrator's total costs and grower's profit. For example, allowing all growers to adapt to changes simultaneously, the increase in the base payment from 3.65<£/lb to 3.70 <2/lb increases profit to our grower by $1,107, whereas total costs to the integrator increase by $13,020. On the other hand, the integrator gained close to 36,000 live lb of chicken meat. Because the total revenue obtained for these broilers is unknown as are the other components of the integrator's costs, the conclusion as to whether an increase in the base payment can qualify as a contract improving design remains ambiguous. Simulation also seems to indicate that decreasing the base payment away from its actual value has an offsetting effect on the welfare position of the two parties. The decline in grower's profit almost exactly matches the decline in integrator's total cost, with almost no change in the production volume.
Bonus Factor
I
—
-1
-0.8
-0.6
-0.4
-0.2
-*-Profit(1)
-»-Prom(2)
-*-Cost(1)
-K-COSt(2)
I
i
0.6
0.8
1 1
L
1
0
0.2
L
r
0.4
1
Utilities Allocation Factor
Figure 3. Utilities allocation factor simulation results.
Experimenting with different values of the bonus factor generated results presented in Table 3 and Figure 2. Only a fairly narrow range of fi values was searched over. Moving further away from the actual value of |S = 0.5 generates optimal values for q and u outside the technologically feasible region, and in case of full adjustment scenario caused serious numerical problems. The results seem to indicate that increasing the bonus factor away from its actual value of 0.5 has almost no effect on either party's welfare position. Adjusting 0 downwards would increase profits to the grower but also increase integrator's per unit costs. Both tendencies are more pronounced with full adjustment (Case 2). Whether decreasing 0 can be considered as a contract improvement would depend on whether the losses to the integrator exceed the gains to the grower. However, to successfully
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(lb) ($/lb) (kWh) Case 1: Allowing for the grower's response only 0.0350 434,817 15,237 0.0355 442,221 15,495 0.0360 449,719 15,757 0.0365 457,310 16,023 0.0370 464,996 16,293 0.0375 472,776 16,566 0.0380 480,654 16,843 Case 2: Allowing for the group response 0.0350 301,654 10,655 0.2420 0.0355 458,287 15,883 0.2636 0.0360 15,883 0.2636 458,287 0.0365 458,287 15,883 0.2636 0.0370 494,244 17,322 0.2673 0.0375 567,415 19,923 0.2749 0.0380 644,049 22,685 0.2820
R/lb
EFFICIENCY GAINS THROUGH CONTRACT FINE TUNING
1357
TABLE 3. Bonus factor comparative statics simulation
0
q*
u*
A*
implement compensation criterion, in this case as in the previous case, the knowledge of the integrator's profit function is needed.
Utilities Allocation Factor The utilities allocation factor impact was simulated for values of X between -1 and 1. Specifying the negative values for X reallocates part of the existing settlement cost
R/lb
c*/q* —
Int. cost
($/lb)
Profit
—
($)
0.2695 0.2689 0.2683 0.2677 0.2672 0.2666 0.2661 0.2656 0.2651 0.2646
0.0338 0.0341 0.0343 0.0346 0.0348 0.0351 0.0353 0.0356 0.0358 0.0361
0.3033 0.3029 0.3026 0.3023 0.3020 0.3017 0.3014 0.3011 0.3009 0.3006
10,230.27 10,217.49 10,206.23 10,196.42 10,188.01 10,180.94 10,175.16 10,170.62 10,167.27 10,165.07
0.2884 0.2835 0.2786 0.2736 0.2687 0.2637 0.2666 0.2666 0.2666 0.2666
0.0348 0.0349 0.0349 0.0349 0.0349 0.0349 0.0350 0.0350 0.0350 0.0350
0.3232 0.3183 0.3134 0.3085 0.3036 0.2986 0.3017 0.3017 0.3017 0.3016
15,956.63 14,461.73 13,071.50 11,777.19 10,570.54 9,464.53 10,173.96 10,167.05 10,160.13 10,153.21
from integrator to grower, and positive values for X reallocates part of the utilities bill from the grower to the integrator. Both scenarios are meaningful due to the fact that fuel cost is a part of the settlement cost born by the integrator and the electricity bill is a part of the grower's expenses. For the particular contract under consideration, the actual value of X is zero. Under both full adjustment and partial adjustment scenarios, increasing utilities allocation factor increases profit to grower. The larger the
TABLE 4. Utilities allocation factor comparative statics simulation A
q*
u*
A*
(lb) (kWh) Case 1: Allowing for the grower's response only 442,177 10,468 -1.0 444,909 11,259 -0.8 -0.6 447,855 12,175 451,052 13,249 -0.4 -0.2 454,543 14,523 458,388 16,061 0.0 0.2 462,663 17,951 467,472 20,328 0.4 0.6 472,964 23,406 479,358 27,544 0.8 1.0 486,994 33,393 Case 2: Allowing for the group response 382,351 9,069 0.2551 -1.0 -0.8 391,264 9,915 0.2561 400,745 10,905 -0.6 0.2571 -0.4 410,891 12,007 0.2581 13,482 -0.2 421,824 0.2592 0.0 15,224 0.2604 434,470 446,716 17,332 0.2 0.2615 0.4 20,053 461,159 0.2628 23,628 0.6 477,415 0.2642 0.8 496,056 28,514 0.2657 517,972 35,549 1.0 0.2674
c*/q*
R/lb
Profit
Int. cost
($/lb)
—
($)
0.2661 0.2662 0.2663 0.2664 0.2665 0.2666 0.2667 0.2669 0.2670 0.2672 0.2674
0.0362 0.0360 0.0359 0.0356 0.0354 0.0351 0.0347 0.0343 0.0337 0.0330 0.0321
0.3023 0.3022 0.3021 0.3020 0.3019 0.3017 0.3015 0.3012 0.3008 0.3003 0.2995
9,697.54 9,779.03 9,866.90 9,962.23 10,066.33 10,180.94 10,308.35 10,451.67 10,615.29 10,805.70 11,033.04
0.2584 0.2593 0.2604 0.2614 0.2625 0.2637 0.2649 0.2661 0.2675 0.2691 0.2708
0.0358 0.0357 0.0355 0.0354 0.0352 0.0349 0.0346 0.0342 0.0338 0.0331 0.0323
0.2942 0.2950 0.2959 0.2968 0.2976 0.2986 0.2995 0.3004 0.3013 0.3022 0.3031
7,950.67 8,206.95 8,480.97 8,775.73 9,095.00 9,464.53 9,828.14 10,257.16 10,743.02 11,303.82 11,967.75
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(lb) (kWh) Case 1: Allowing for the grower's response only 0.475 481,850 16,311 0.480 476,868 16,256 0.485 472,037 16,207 0.490 467,351 16,154 0.495 462,803 16,106 0.500 458,388 16,061 0.505 454,100 16,018 0.510 449,934 15,976 0.515 445,885 15,937 0.520 441,948 15,899 Case 2: Allowing for the group response 0.475 673,360 22,890 0.2847 0.480 619,108 21,160 0.2799 0.485 568,304 19,534 0.2750 0.490 520,654 18,005 0.2702 16,562 0.495 475,876 0.2653 0.500 15,224 0.2604 434,470 458,287 0.505 15,883 0.2636 0.510 458,287 15,883 0.2636 0.515 458,287 15,883 0.2636 0.520 15,883 458,287 0.2636
1358
VUKINA AND FOSTER
5
This number is obtained as the sample mean of the average settlement cost for the entire group ($0.26/lb) plus the sample mean of the per pound payment to the grower ($0.04/lb).
econometric estimation of the cost functions and behavioral relationships requires a combination of settlement costs and farm level data. With the settlement cost and farm level inputs records, optimal grower input decisions can be estimated and alternative contract designs can be simulated by searching over possible contract parameter values. However, industry-wide analysis of this kind is yet precluded because the farm level cost data for sufficient number of farms is difficult to assemble. Further research in this area will focus on close collaboration with the industry to start the process of monitoring and recording of the farm level cost data.
REFERENCES Aho, P. W., and M. B. Timmons, 1988. Disparate grower and integrator optimum growout temperatures. Poultry Sci. 67: 534-537. Gates, R. S., and M. B. Timmons, 1986. Real-Time Economic Optimization of Broiler Production. Paper No. 86-4552,1986 Winter Meeting American Society of Agricultural Engineers, Chicago, IL, December 16-19. Knoeber, C. R., 1989. A real game of chicken: Contracts, tournaments, and the production of broilers. J. Law Econ. Organization 5(2):271-292. Knoeber, C. R., and W. N. Thurman, 1995. "Don't count your chickens...": risk and risk shifting in the broiler industry. Am. J. Agric. Econ. 77:486^96. Timmons, M. B., and R. S. Gates, 1986. Economic optimization of broiler production. Trans. ASAE 29:1373-1378, 1384.
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portion of the utilities costs switched over from the grower's cost into the settlement cost, the larger the profits for the grower. The impact of a change in X on the integrator's per unit cost depends on the type of adjustment scenario. Under partial adjustment scenario, the increase in X results in decreasing integrator's unit cost. Under full adjustment scenario, the increase in X increases integrator costs. The obtained results seem to indicate that increasing X, i.e., switching part of the electricity cost from the grower's cost into the settlement cost may be a candidate for the contract redesign. There are two arguments to support this claim. First, the partial adjustment model unambiguously signals an efficiency improvement (grower's profits are increasing while integrator's per unit cost is decreasing). Second, in the full adjustment model, increasing X from 0 to 0.2 increases grower's profit by $364, whereas the total integrator's costs increase by $4,058 with the gain in the volume of production of 12,246 lb. If we value these additional pounds only at variable costs necessary to produce them (30(f/lb),5 the benefits to the grower would approximately equal the costs to the integrator. The main emphasis of this paper is on methodological issues and less on specific estimation and simulation results. The presented analysis was done using one contract growout farm data only, and therefore the results may not be representative of the entire industry and all geographical and climatic regions. As seen in the paper,