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A microeconomic evaluation of the impact of Mycoplasma meleagridis infection in turkey production
Preventive Veterinary Medicine, 1 (1982/1983) 289--301
289
Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands
A M I C R O E C O N O M I C E V A L U A T I O N O F T H E I M P A C T OF MYCOPLASMA
M E L E A G R I D I S I N F E C T I O N IN T U R K E Y P R O D U C T I O N
TIM. E. CARPENTER
Department of Epidemiology and Preventive Medicine, School of Veterinary Medicine, University of California, Davis, CA 95616 (U.S.A.) (Accepted 14 June 1983)
ABSTRACT Carpenter, T.E., 1983. A microeconomic evaluation of the impact of Mycoplasma meleagridis infection in turkey production. Prey. Vet. Med., 1 : 289--301. A microeconomic evaluation approach was used to determine the economic impact of
Mycoplasma meleagridis (MM) infection in turkeys. Profit maximization, using the production, cost and profit functions, and prices of inputs and outputs was utilized to determine the economically optimal time birds should be raised as well as the corresponding optimal level of feed input and liveweight meat output. Optimal was defined as that level which maximized profits. Using regression analysis, the predicted weights of MM-infected (MM(+)) males and females were found to be significantly greater, for a given age or level of feed input, than noninfected (MM(--)) cohorts of identical age and parent line. This unusual weight advantage demonstrated by the infected birds may be the result of higher embryo mortality of this group thus reducing the survivability of some of the potentially poor weight gainers in the MM(+) group. By evaluating the profit functions, this weight advantage also translated into a profit advantage of $0.06 per bird associated with raising MM(+) turkeys. Although the weight gain results were obtained from birds raised under environmentally controlled conditions and thus not subjected to typical overcrowding and climatic stress faced under field conditions, they agree with recent results obtained in a field study (Carpenter et ah, 1982a). This apparent profit advantage should be considered when measuring the benefits derived from averting decreased hatchability, leg problems, and other anomalies associated with MM infection. This microeconomic approach should aid producers, veterinarians and administrators in their disease control/eradication decision making. INTRODUCTION I n r e c e n t y e a r s , e c o n o m i c e v a l u a t i o n s o f disease in f o o d p r o d u c t i o n a n i m a l s h a v e f o c u s e d o n t h e p r e s e n c e or a b s e n c e of a s t a t i s t i c a l l y s i g n i f i c a n t diff e r e n c e in f i n a l w e i g h t s o f a n i m a l s in d i f f e r e n t g r o u p s , g e n e r a l l y i n f e c t e d vs n o n i n f e c t e d . All t o o o f t e n s u c h a n a l y s e s h a v e i g n o r e d t h e i n c r e a s e d f e e d req u i r e m e n t ( o r d e c r e a s e d i n s o m e cases w h e r e e f f i c i e n c y was i n c r e a s e d } n e c e s s a r y t o p r o d u c e t h e a d d i t i o n a l w e i g h t . S i m i l a r l y , t h e t i m e r e q u i r e m e n t in-
0167-5877/83/$03.00
© 1983 Elsevier Science Publishers B.V.
290 volved with these changes has often been ignored. Furthermore, when these factors were in fact considered, no attention was given to the fact that with a productivity change there may also be an accompanying change in the most profitable levels of variable inputs used, such as time and feed. Mycoplasma meleagridis (MM) infection in turkeys has been associated with several adverse production effects, from embryo development through growth of the young poult and adult turkey (Rhoades, 1969; Nelson, 1971; Edson et al., 1979; Carpenter et al., 1981). The total economic loss associated with decreased hatchability caused by MM and the cost of a control program have been estimated at $9.4 million/year in the U.S.A. alone (Carpenter et al., 1981). A complete history of MM has been given by Yamamoto (1978). This perceived adverse impact of MM infection on the economics of turkey production has initiated eradication programs to be performed in primary breeder flocks in the United States, Canada and Great Britain. The worldwide impact of these eradication efforts is that multiplier breeders and eventually meat bird producers will soon be supplied birds which are free of MM. Veterinarians and turkey producers throughout the world will soon be faced with evaluating the economic impact of obtaining a flock of birds free from MM and then maintaining this status. One way in which this might be accomplished is through microeconomic evaluation. In economics, there are essentially two levels at which studies may be aimed. The first, microeconomics, deals with the economic actions and behavior of the individual, consumer or producer. Regarding the producer, the focus is on such things as prices of inputs, and outputs, production efficiency and markets. Macroeconomics, on the other hand, focuses on the e c o n o m y as a whole. For example, macroeconomics may be concerned with the effect of a change at the industry, state or national level, while microeconomics is concerned with the effect on the individual producer or consumer. In this study, production, cost and profit functions were evaluated to: (1) introduce the reader to a technique of microeconomics and (2) determine the economic impact of MM infection in turkeys as reflected in the optimal level of (a) production, (b) input utilization, and ultimately (c) profits for a hypothetical turkey producer in the Central Valley of California. The results and conclusions could easily be adapted to other producers throughout the world. MATERIALS AND METHODS
Experimental infection Three hundred seventy-eight poults produced by a flock of MM-free (noninfected) turkeys were divided into two groups. One group had received 0.1 ml of 24-h PPLO-broth culture of MM strain RY-39A (Ghazikhanian and Yamamoto, 1974) on day 9 of incubation. The second group was comprised of a placebo group of poults hatched from eggs inoculated with 0.1 ml of
291 sterile PPLO broth on day 9 of incubation and a control group of poults hatched from eggs left uninoculated. The control and placebo birds were combined because of the apparent lack of adverse impact of the placebo on hatchability of the poults (Carpenter et al., 1981).
Poult placement and data collection A total of 205 female and 173 male poults were raised under environmentally controlled conditions on a Ralston Purina research farm located in St. Louis, MO. The birds were monitored with respect to feed consumption, weight gain, morbidity and mortality. The hens were slaughtered at the end of 17 weeks and the toms at the end of 23 weeks. All variables were recorded for both the hens and toms for a total of 16 weeks (Carpenter et al., 1982b) and these data were used in the present evaluation. Birds were weighed on an individual basis on day 1 for both the hens and toms and on a pen basis on days 28, 53, 77, 98 and 112 for the hens and days 28, 56, 84, and 112 for the toms. Average bird weights were thus used after day 1 weights in the analysis. Feed consumption was also measured on a pen basis on the same date as the pen of birds was weighed.
Production, cost and profit functions Multiple regression (Kleinbaum and Kupper, 1978) was used to develop a model for the production function used in this analysis. A production function refers to the physical relationship between the level of inputs used by a producer and the outputs derived from those inputs. In this study, time will be the input evaluated and allowed to vary while the o u t p u t is liveweight. Furthermore, implicit in time is feed consumed by the birds at a level which will vary with time. Selection of the final production function model was based on agreement of the mathematical model with biologic knowledge and adjusted R-squared value of the model. Total variable costs, those associated with time and feed, and o u t p u t price were chosen to represent the situation for a producer located in the Central Valley of California (California Cooperative Extension, 1981). A cost function (where costs are related to the level of output) and a profit function (where profits are related to the input(s): time in this example) were derived from this information and the economic impact to the producer of MM infection was determined by an evaluation of the profit function.
Sensitivity analysis Sensitivity analysis was performed to measure the impact of price changes on the optimal level of production. In order to facilitate the numerous runs
292 anticipated for the sensitivity analysis, a FORTRAN program was written to calculate the optimal feeding period and hence optimal liveweight, feed consumption and maximum profits for a variety of input--output price combinations. RESULTS Several algebraic forms were analyzed to determine the best production function equation. The following equation was selected:
Y = 0 . 0 9 6 7 2 + 0.01248(T) + 2 . 3 0 3 . 1 0 - 3 ( T ) 2- 1 . 0 6 0 . 1 0 - 5 ( T ) 3 (2.11)
(1.95)
(15.11)
(-11.63)
+ 2 . 0 1 6 . 1 0 -3 (MM) (T) + 4 . 0 8 4 . 1 0 -2 (S) (T) (2.00) (42.46) where Y -- liveweight of the turkey; T = age of the bird; S = a d u m m y variable denoting sex (0 = female, 1 = male); MM = a d u m m y variable for MM-infection status (0 = MM(--), 1 = MM(+)). Adjusted R-squared = 0.996. Note, the t-values appear in parentheses below their respective coefficients and all of the coefficients are significant at P < 0.0005 with the exceptions of the intercept, P = 0.036, the (MM) (T) interaction term, significant at P = 0.046, and the linear time term (T), P = 0.053. In interpreting the above equation, it may be clearer to think of it as four equations rather than a single equation. The four equations predict the weight gain for (1) MM(+) males, (2) MM(--) males, (3) MM(+) females, and (4) MM(--) females. They may be written asfollows: 0.09672 + 5.5336.10-2(T) + 2 . 3 0 3 , 1 0 - 3 ( T ) :
- 1.060*10-S(T) 3,
0.09672 + 5.3320.10-2(T) + 2 . 3 0 3 , 1 0 -3(T) 2 -
(1)
1 . 0 6 0 . 1 0 -s (T) 3,
(2)
0.09672 + 1 . 4 4 9 6 . 1 0 - 2 ( T ) + 2 . 3 0 3 , 1 0 -3(T) 2 - 1 . 0 6 0 . 1 0 -5(T) 3,
(3)
0.09672 + 1.2480.10-2(T) + 2 . 3 0 3 , 1 0 -3(T) 2 -
(4)
1 . 0 6 0 . 1 0 -s (T) 3.
With these four regression equations, weight gains for each of the groups could be predicted according to length of time fed. The results of a sample of calculations for the four groups considering the time period of 100--160 days appear in Table I and Fig. 1. From the production schedule results, the m a x i m u m predicted weights of the MM(+), 24:53 lb, and MM(--), 24.22 lb, males appear at approximately 155 days. The m a x i m u m weight for the females appears 5 days earlier with the MM(+), hens at 18.31 lb and the MM(--) hens at 18.01 lb. In a statistical analysis of the impact of MM, it might be concluded here that MM(+) toms and hens exhibit a 0.31 lb weight advantage over their noninfected comparisons. This difference would then be tested for statistical significance. Being significantly different, the difference would then be multiplied by the price of meat and concluded to be the "economic impact due to
293 TABLE I Liveweight over 100--160 days for Mycoplasma meleagridis-infected (MM(+)) and noninfected (MM(-)) male and female turkeys Time (days)
Liveweight (lb)
100 105 110 115 120 125 130 135 140 145 150 155 160
MM(+) males
MM(-) males
MM(+) females
MM(-) females
18.06 19.03 19.97 20.80 21.58 22.30 22.92 23.46 23.90 24.23 24.44 24.53 24.49
17.86 18.82 19.72 20.56 21.34 20.04 22.66 23.19 23.61 23.93 24.14 24.22 24.17
13.98 14.74 15.45 16.10 16.68 17.19 17.61 17.95 18.18 18.30 18.31 18.20 17.96
13.77 14.53 15.23 15.87 16.44 16.94 17.35 17.67 17.90 18.01 18.01 17.89 17.63
25
MM(+/moles
2 4 1 2 3~
MM(-)meles
1 9 iB I 20
~- LLJ
~
"'"'~MM~I+ f...... -I feme/es
17 16 15 14 13 I00
I
i1~0
J
i
120
A G E (doys) I
I
130
i
L
140
I
I
i50
I
I
160
Fig. 1. Regression equations (production functions) for four groups of turkeys: Mycoplasma meleagridis-infected (MM(+)) males and females, and M. meleagridis-noninfected (MM(-)) males and females, from 100 to 160 days of age. MM infection". Such a conclusion would, however, ignore the producer profit motive and be potentially erroneous. Hence the need to proceed further, beyond a statistical evaluation, and evaluate the producer's profit funct i o n . T h a t is, t h e p r o d u c e r d o e s n o t a c t so as t o p r o d u c e a n a n i m a l w i t h a
294 m a x i m u m weight. I n s t e a d he is a t t e m p t i n g to p r o d u c e an a n i m a l at a level w h i c h m a x i m i z e s his profits. This level is n o t o n l y r e s p o n s i v e to the p r e s e n c e or a b s e n c e o f an i n f e c t i o n , such as MM, it is also d e p e n d e n t u p o n f a c t o r s such as i n p u t and o u t p u t prices. Prior to evaluating the p r o f i t f u n c t i o n , it is n e c e s s a r y t o k n o w t h e variable c o s t involved w i t h the p r o d u c t i o n process. T h e r e f o r e a c o s t f u n c t i o n was fitted t o the g r o w t h d a t a . T h e variable costs c o n s i d e r e d i n c l u d e d feed costs, h e a t i n g e x p e n s e s , m e d i c a t i o n and o t h e r v e t e r i n a r y costs, l a b o r costs, i n t e r e s t charges, and a n y o t h e r costs i n c u r r e d as a result o f retaining t h e t u r k e y s . B e f o r e s p e c i f y i n g the variable c o s t f u n c t i o n , it was n e c e s s a r y to d e t e r m i n e t h e r e l a t i o n s h i p b e t w e e n feed c o n s u m p t i o n and age o f t h e birds w h i c h w e r e fed ad l i b i t u m . T h e s a m e criteria were used t o specify this r e l a t i o n s h i p as was used w i t h the p r o d u c t i o n f u n c t i o n : F=-0.01099(-0.11)
2.876.10-2(T) (-2.02)
+ 4 . 2 6 1 . 1 0 .3 (T) 2 (12.58)
8.339.10-6(T) 3 (-4.12)
+ 6 . 5 3 6 . 1 0 .2 ( S ) ( T ) + 2 . 7 4 1 . 1 0 .3 (MM) (T), (30.58) (1.23) A d j u s t e d R - s q u a r e d = 0.996. T h e regression c o e f f i c i e n t s w e r e again highly significant, P < 0 . 0 0 0 5 , w i t h the e x c e p t i o n s of the i n t e r c e p t , P = 0.914, the (MM) (T) i n t e r a c t i o n t e r m , P = 0.22 and the linear t i m e t e r m , P = 0.045. As w i t h the p r o d u c t i o n f u n c t i o n , t h e f e e d - t i m e r e l a t i o n s h i p m a y be expressed as f o u r s e p a r a t e e q u a t i o n s , o n e f o r each o f t h e g r o u p s w i t h feed as the d e p e n d e n t variable: (1) MM(+) males, (2) MM(--) males, (3) MM(+) females, and (4) MM(--) f e m a l e s : -0.01099
+ 3.9341.10 -2(T) + 4.261.10 -3(T) 2 -
8.339.10 -3(T) 3
(1)
-0.01099
+ 3.6600.10-2(T)
+ 4.261.10-3(T) 2 -
8.339.10-3(T) 3
(2)
-0.01099
-
2 . 6 0 1 9 . 1 0 .2 (T) + 4 . 2 6 1 . 1 0 - 3 ( T ) 2 -
8.339.10 -3(T) 3
(3)
-0.01099
-
2 . 8 7 6 0 . 1 0 - 2 ( T ) + 4 . 2 6 1 . 1 0 .3 (T) 2 -
8 . 3 3 9 . 1 0 - 3 ( T ) 3.
(4)
T h e d i f f e r e n c e s in t h e f o u r e q u a t i o n s are in t h e p r e s e n c e or a b s e n c e o f the MM-status a n d / o r sex i n t e r a c t i o n t e r m s . Given t h e prices o f the variable inp u t s , t h e t o t a l daily c o s t o f raising t h e t u r k e y s m a y be c a l c u l a t e d :
PD = P F ( F ) + P T ( T ) w h e r e PD = t o t a l daily c o s t ( c e n t s / d a y ) ; PF = price of feed ( c e n t s / l b ) ; F = f(T), the level o f feed c o n s u m e d (lb) m e a s u r e d as a f u n c t i o n o f t i m e ; T = t i m e ( d a y s ) ; and PT = daily costs m i n u s feed e x p e n s e ( c e n t s / d a y ) . Given the a b o v e e q u a t i o n s , t h e t o t a l variable costs, r e v e n u e s and p r o f i t s m a y be c a l c u l a t e d f o r each o f the f o u r g r o u p s o f t u r k e y s . An e x a m p l e using the MM(+) and M M ( - ) males a p p e a r s in T a b l e II.
295 TABLE II Days fed, total variable costs, revenues and profits (US $) for Mycoplasma meleagrides-infected (MM(+)) and non-infected (MM(-)) male turkeys raised from 100--160 days Days fed
100 105 110 115 120 125 130 135 140 145 150 155 160
Variable costs
Revenues
Profits
MM(+)
MM(-)
MM(-~)
MM(-)
MM(+)
MM(-)
4.44 4.78 5.14 5.49 5.85 6.22 6.59 6.97 7.35 7.74 8.13 8.52 8.91
4.41 4.75 5.10 5.46 5.82 6.19 6.56 6.94 7.32 7.70 8.09 8.48 8.87
7.22 7.61 7.99 8.32 8.63 8.92 9.17 9.38 9.56 9.69 9.78 9.81 9.80
7.14 7.53 7.89 8.23 8.54 8.82 9.06 9.27 9.45 9.57 9.65 9.69 9.67
2.78 2.83 2.85 2.83 2.78 2.70 2.58 2.41 2.21 1.95 1.65 1.29 0.89
2.73 2.78 2.79 2.77 2.72 2.63 2.50 2.33 2.t3 1.87 1.56 1.21 0.80
T h e results p r e s e n t e d in T a b l e II m a y also be r e f e r r e d to as the variable c o s t , r e v e n u e and p r o f i t schedules. T h e variable costs are a f u n c t i o n o f t i m e as well as feed c o n s u m p t i o n . With r e s p e c t to t i m e , t h e y increase in a linear t r e n d (Fig. 2). With r e s p e c t to feed, h o w e v e r , t h e y increase at an increasing r a t e for a given p e r i o d o f t i m e . This changing variable cost m a y m o s t easily be viewed b y observing the rate of change for a single g r o u p , e.g. either the MM(+) or MM(--) males. In e i t h e r case, the change in variable cost over the initial 5-day p e r i o d is a p p r o x i m a t e l y $0.33. This rate o f c h a n g e increases and reaches a m a x i m u m o f $ 0 . 3 9 t o w a r d the later p a r t o f t h e feeding regime. T h e r e v e n u e s for these t w o g r o u p s r e a c t quite d i f f e r e n t l y t h a n the costs as the age o f the birds increases (Fig. 2). F o r e x a m p l e , f r o m d a y 100 to 105, the c h a n g e in r e v e n u e is $ 0 . 3 9 for b o t h t h e MM(+) and M M ( - ) t o m s . T h e increase in r e v e n u e increases at a faster rate t h a n t h e costs until 115 d a y s w h e r e the cost increase was $ 0 . 3 5 and r e v e n u e increase was $0.33 for the MM(+) males and $ 0 . 0 1 m o r e for the M M ( - ) males in b o t h categories. Cont i n u e d feed o f t h e m a l e s results n o t o n l y in an increased daily cost, it also results in daily r e v e n u e increasing at a decreasing rate. In fact, in the final p e r i o d , 1 5 5 - - 1 6 0 days, the t o t a l r e v e n u e decreases f r o m w h a t it was in the previous p e r i o d . This results f r o m t h e birds reaching a m a x i m u m weight and t h e n losing w e i g h t w i t h the a m o u n t o f feed t h e y c o n s u m e in this final period. T h e i m p o r t a n t f e a t u r e o f T a b l e II is the p r o f i t level for each o f the t i m e periods. F r o m T a b l e II and Fig. 3, it m a y be seen t h a t the p r o f i t s f o r b o t h the MM(+) a n d M M ( - ) birds reach t h e i r m a x i m u m at a p p r o x i m a t e l y 110
296 --
tO
TR
9 Z
uJ
8
~-
7
2k . -
6
~
4
~
3
~
2
rVC (feed + t,me)
VC (feed)
VC (hme)
I
ilo
I
I00
l
I I I I 120 150 140 AGE (days) i
160
150
Fig. 2. Variable c o s t s for t i m e (VC ( t i m e ) ) , feed (VC (feed)) and total (TVC (feed + t i m e ) ) and total r e v e n u e ( T R ) for Mycoplasma meleagridis-infected male t u r k e y s f r o m ] 0 0 to 1 6 0 days o f age. 3oo F
25
i
0
~
00i rSO
F0
I00 \ " MM (+) moles MM {-] males
rr
13.
~
050
ioo to5 Jr Ji izo m5 p3o ~35 f4o 145 tS0
t55 i60
AGE (days) Fig. 3. S h o r t - r u n p r o f i t s f o r Mycoplasma m e l e a g r i d i s - i n f e e t e d ( M M ( - ) ) males f r o m 1 0 0 to ] 6 0 days o f age.
( M M ( + ) ) and - n o n i n f e e t e d
days, $2.83 and $2.77, respectively. Prior to this age, profits were increasing at an decreasing rate, initially at $0.05 per 5-day period and $0.02 for the 1 0 5 - - 1 1 0 day period, for the MM(+} males. After maximum profits were realized (day 110), extension beyond this date resulted in the profits decreasing at an increasing rate, i.e. - $ 0 . 0 2 for days 110--115; - $ 0 . 0 5 for days 115--120, and - $ 0 . 4 0 for the final period of 155--160 days, for the MM(+)
297 males. This p a t t e r n is similar to that shown for the MM(-) males. From Table II, it may be concluded t hat given this econom i c information, the p r o d u c e r would raise male turkeys for approxi m at el y 110 days in order to maximize his profits at $2.85 for MM(+) t om s and $2.79 for MM(-) toms. Thus the MM(+) birds would yield a relative profit of $0.06 per male. The short-run profit function directly produces the expected profits for a given age as well as the optimal profit. It is derived by considering the shortrun costs of the variable inputs and the price received for the o u t p u t . In this example, we assumed variable costs of $0.01 per day to retain the birds and $0.09 per p o u n d of feed cons um ed by the turkeys. F u r t h e r m o r e the price o f t u r k e y was set at $0.40 per pound, measured on a liveweight basis. The profit f u n c t i o n m a y be written as follows: Pr = P Y ( Y ) - ( E X i P X i )
where Pr = profit (US $ per bird); P Y = price of t urkey (US $ per p o u n d ) ; Y = liveweight of the t u r k e y , determined from the p r o d u c t i o n function presented above; X i = level of input i (time and feed) used; and P X i = price of input i (time and feed). Thus in the above equation it may be seen t h a t the profit is calculated as the difference between the total revenue ( P Y ( Y ) ) a n d the total costs ( E X i P X i ) . To find the optimal time and corresponding level of feed given to the turkeys, the derivative of the profit function with respect to time (MPr) was determined. The o p t i m u m , or m a x i m u m , profit occurs when the MPr is equal to zero. In order to insure t hat this level corresponds to a local maxim u m and n o t minimum, it is necessary to also look at the second derivative. If the second derivative is less than zero, then we have a p r o d u c t i o n level which maximizes profit. If the value of the second derivative at the given level o f the input is greater than zero, the o u t p u t will minimize the profit. Thus it is i m p o r t a n t to determine the value of the second derivative as well as the first. The first derivative of profit, with respect to time, or the marginal profit (MPr), is written as dPr
= P Y * ( 5 . 5 3 3 6 . 1 0 -2 + 4 . 6 0 6 . 1 0 -3 (T) - 3 . 1 8 0 . 1 0 -s (T) 2 ) - P T
MPr =--
dT
+ P F * ( 3 . 9 4 3 1 . 1 0 -2 + 8 . 5 2 2 . 1 0 - 3 ( T ) - 2 . 5 0 2 . 1 0 -s (T)2).
The second derivative of profit, with respect to time is written as d2Pr -
P Y * ( 4 . 6 0 6 . 1 0 -3 - 6 . 3 6 0 . 1 0 -s (T)) + P F * ( 8 . 5 2 2 . 1 0 - 3 - 5 . 0 0 4 . 1 0 -s
dT 2 -
5 . 0 0 4 " 1 0 -s (T)).
In order to find the a m o u n t of time necessary to raise the MM(+) males to the weight which would maximize profits, the two necessary conditions which must be m et are t hat MPr = 0 and d 2 P r / d T 2 < O. The first condition is approached by setting M P r = 0 and then solving for T. Results of the
298 TABLE III Liveweights, levels of feed, time, cost and revenue associated with short-run profit maximization for Mycoplasma meleagridis-infected (MM(+)) and noninfected (MM(--)) male and female turkeys Sex
MM status (+]-)
Weight (lb)
Time (days)
Feed (lb)
Variable cost (US $)
Revenue (US $)
Profits (US $)
Male Male
+ -
19.97 19.67
110.2 109.7
44.91 44.30
5.14 5.08
7.99 7.87
2.84 2.78
Female Female
+ -
14.13 13.84
101.0 100.4
32.23 31.63
3.91 3.85
5.65 5.54
1.74 1.68
TABLE IV A sensitivity analysis for the predicted time (days) requirement, final liveweight (lb), and profits (US S/bird) from male turkeys according to MM status, assuming various input and output prices (US $) Prices of inputs and outputs
Optimal time
Optimal weight
Profits
Feed
Time
Meat
MM(+)
MM(-)
MM(+)
MM(-)
MM(+)
MM(-)
0.09 0.09 0.09 0.09
0.005 0.010 0.015 0.020
0.40 0.40 0.40 0.40
114.1 110.2 106.0 101.4
113.7 109.7 105.5 100.9
20.65 19.97 19.21 18.34
20.35 19.67 18.90 18.03
3.41 2.85 2.31 1.79
3.34 2.78 2.25 1.73
0.06 0.12 0.15
0.010 0.010 0.010
0.40 0.40 0.40
125.6 92.6 72.5
125.2 92.1 72.0
22.37 16.55 12.17
22.06 16.26 11.91
4.36 1.67 0.84
4.28 1.62 0.81
0.09 0.09 0.09 0.09 0.09 0.09 0.09
0.010 0.010 0.010 0.010 0.010 0.010 0.010
0.30 0.35 0.40 0.45 0.50 0.55 0.60
89.1 101.6 110.2 116.4 121.1 124.8 127.8
88.5 101.2 109.7 115.9 120.7 124.4 127.4
15.81 18.38 19.97 21.02 21.75 22.27 22.66
15.52 18.09 19.67 20.72 21.44 21.96 22.35
1.02 1.88 2.85 3.87 4.94 6.04 7.17
0.99 ] .84 2.78 3.80 4.85 5.94 7.04
0.12 0.12 0.12 0.12
0.015 0.015 0.015 0.010
0.40 0.45 0.50 0.50
87.2 97.6 105.1 108.5
86.7 97.1 104.7 108.1
15.41 17.57 19.05 19.68
15.11 17.27 18.75 19.38
1.22 2.05 2.96 3.50
1.18 1.99 2.89 3.43
FORTRAN program provided not only the optimal time and hence feed cons u m p t i o n a n d w e i g h t f o r t h e i n i t i a l p r i c e s ( T a b l e I I I ) , b u t also v a l u e s f o r a v a r i e t y o f p r i c e c o m b i n a t i o n s in a s e n s i t i v i t y a n a l y s i s ( T a b l e I V ) . T h e o p t i m a l w e i g h t f o r t h e M M ( + ) b i r d s w a s a p p r o x i m a t e l y 0 .3 lb h e a v i e r
299 than their MM(-) cohorts. Also, the additional feed (0.61 and 0.59 lb) necessary to produce these weights and the time (0.5 and 0.6 days) requirement were greater for the MM(+) toms and hens respectively (Table III). It may be seen from Table III t h a t both the MM(+) toms and hens were predicted to yield a profit greater by $0.06 per bird than their MM(-) cohorts, assuming PT = $0.01, P F = $0.09 and P Y = $0.40. However, upon evaluation of the results from the profit function (Table III) rather than the schedule presented in Table II, a less accurate measure, the optimal period required to raise the MM(+) birds is greater than that of the MM(-) cohorts, 0.5 days for the males and 0.6 days for the females. In reality, it is more probable t h a t the birds will be raised an identical period of time with the final weights being different. This would not change the profit advantage demonstrated by the MM(+) birds. In order to evaluate the impact of MM infection when faced with prices other than the initial prices, several simulation runs were performed and the optimum weight-time-feed for each calculated. Results obtained from a sample of runs for the males are presented in Table IV. In the sensitivity analysis the price of feed was allowed to vary from a low of $0.06/lb up to a high of $0.15/lb. The variable price of time ranged from $0.005 up to $0.02/day. The impact of a price change on turkey meat was evaluated over a range of $0.30 to $0.60/lb liveweight. Results showed that for all prices considered, the profits from MM(+) birds were superior to those from MM(-) birds at each price combination. The impact of the sensitivity analysis demonstrated that while this advantage remains at varying price levels, there is a change in the relative advantage. That is the profit advantage varied from $0.03 to $0.13/bird depending on the prices assumed. The importance of this will be addressed in the discussion section. DISCUSSION In this paper, the liveweight prices of both males and females were set at $0.40 per pound. While there will most likely be a different price for hens and toms, a single price was assumed for ease of analysis. Any problems which might have been created by the simplification should have been obviated in the sensitivity analysis and by not comparing the results of the toms and the hens. This analysis was conducted for a short-run problem. If it were being considered over a long-run period, e.g. more than 6 months, all of the costs involved in raising the turkeys, i.e. the fixed as well as the variable costs would have been considered as being variable. In such a situation, the conclusions reached in this paper m a y have been different. However, it is felt that the effect would not be significant and the results would be similar to those presented in this short-run evaluation. In the short run, the size of the fixed costs will not affect the optimal production level and may therefore be ignored in the short-run profit evaluation.
300 The conclusions regarding the economic advantage associated with MM(+) birds in this study should not be construed to imply t h a t MM infection is economically beneficial. As stated earlier in this paper, the results presented were obtained from a trial in which birds were raised under environmentally controlled conditions. In considering the overall economic impact of MM infection, there is much debate concerning its true clinical impact. For example, if there is truly a 5% increase in the number of salable poults produced by MM(-) turkeys (Carpenter et al., 1981), this must be taken into consideration when evaluating the apparent $0.06 per bird profit advantage associated with MM(+) turkeys. That is, the advantage (increased salable poults) of MM(-) stock must be compared with the disadvantages, i.e. cost of producing and maintaining MM(-) birds in addition to a potential weight gain advantage of MM(+) birds. One m e t h o d in which this might be accomplished is by a break-even point analysis (Carpenter et al., 1979) where the added revenue received by raising MM(+) birds may be equated to the potential benefit from improved poult production. When this point is found, the prices yielding a break-even point should be considered as to their likelihood of occurring before a decision may be made on the economics of the infection and its control. In animal health economics, the most frequently used tool for evaluating the "economic impact" of a disease, or its associated control/eradication program has been benefit--cost analysis. In its correct form, benefit--cost analysis takes into consideration the effect on consumer surplus, producer surplus and the distribution impact of the project being analyzed. However, to date due to the dearth of sound data concerning the impact of a disease on the productivity of an individual animal and the profit-maximizing approach which the livestock producer might take, the underlying assumptions upon which such analyses are based are questionable. Hence, subsequent evaluations based on such assumptions are subject to error from the start. By using microeconomics, the true impact of how diseases actually affect the producer may be more accurately estimated. With this improved estimate, the veterinarian, producer or other decision maker, may then make a more informed recommendation to the producer and thus effect more cost-effective disease control programs.
REFERENCES
Carpenter, T.E., Miller, K.F., Gentry, R.F., Schwartz, L.D. and Mallinson, E.T., 1979. Control of Mycoplasma gallisepticum in commercial laying chickens using artificial exposure to Connecticut F strain Mycoplasma gallisepticum. Proc. 83rd U.S.A.H.A. Meet., San Diego, CA, pp. 364--370. Carpenter, T.E., Edson, R.K. and Yamamoto, R., 1981. Decreased hatchability of turkey eggs caused by experimental infection with Mycoplasma meleagridis. Avian Dis., 25: 151--156.
301 Carpenter, T.E., Riemann, H.P. and Franti, C.E., 1982a. The effect of Mycoplasma meleagridis infection and egg dipping on the weight-gain performance of turkey poults. Avian Dis., 26: 272--278. Carpenter, T.E., Riemann, H.P. and McCapes, R.H., 1982b. The effect of experimental turkey embryo infection with Mycoplasma meleagridis on weight, weight gain, feed consumption, and conversion. Avian Dis., 26: 689--695. California Cooperative Extension, 1981. The Budget Generator: Turkey production in Central California. Cooperative Extension, University of California, Davis, CA, No. 406, 6 pp. Edson, R.K., Yamamoto, R., Ortmayer, H.B. and Massay, D.E., 1979. The effect of Mycoplasma meleagridis on hatchability of turkey eggs. Proc. 28th West. Poult. Dis. Conf. and 13th Poult. Health Symp., Davis, CA., pp. 24--29. Ghazikhanian, G. and Yamamoto, R., 1974. Characterization of pathogenic and nonpathogenic strains of Mycoplasma meleagridis: In vivo and in vitro studies. Am. J. Vet. Res., 35: 425--430. Kleinbaum, D.G. and Kupper, L.L., 1978. Applied Regression Analysis and Other Multivariable Methods. Duxbury Press, North Scituate, MA, 556 pp. Nelson, R.C., 1971. Evaluation of egg dipping (1967--1970). In: Proc. Symp. on Leg Weakness in Turkeys. Iowa State Univ., Ames, IA, pp. 13--21. Rhoades, K.R., 1971. Mycoplasma meleagridis infection: development of lesions and distribution of infection in turkey embryos. Avian Dis., 1 5 : 7 6 2 - - 7 7 4 . Thompson Jr., A.A., 1981. Economics of the Firm. Prentice-Hall, Englewood, Cliffs, NJ, 635 pp. Yamamoto, R., 1978. Mycoplasma meleagridis infection. In: M.S. Hofstad, B.W. Calnek, W.M. Hemboldt, W.M. Reid and H.W. Yoder, Jr. (Editors), Diseases of Poultry. Iowa State Univ. Press, Ames, IA, 7th ed., pp. 250--270.
289
Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands
A M I C R O E C O N O M I C E V A L U A T I O N O F T H E I M P A C T OF MYCOPLASMA
M E L E A G R I D I S I N F E C T I O N IN T U R K E Y P R O D U C T I O N
TIM. E. CARPENTER
Department of Epidemiology and Preventive Medicine, School of Veterinary Medicine, University of California, Davis, CA 95616 (U.S.A.) (Accepted 14 June 1983)
ABSTRACT Carpenter, T.E., 1983. A microeconomic evaluation of the impact of Mycoplasma meleagridis infection in turkey production. Prey. Vet. Med., 1 : 289--301. A microeconomic evaluation approach was used to determine the economic impact of
Mycoplasma meleagridis (MM) infection in turkeys. Profit maximization, using the production, cost and profit functions, and prices of inputs and outputs was utilized to determine the economically optimal time birds should be raised as well as the corresponding optimal level of feed input and liveweight meat output. Optimal was defined as that level which maximized profits. Using regression analysis, the predicted weights of MM-infected (MM(+)) males and females were found to be significantly greater, for a given age or level of feed input, than noninfected (MM(--)) cohorts of identical age and parent line. This unusual weight advantage demonstrated by the infected birds may be the result of higher embryo mortality of this group thus reducing the survivability of some of the potentially poor weight gainers in the MM(+) group. By evaluating the profit functions, this weight advantage also translated into a profit advantage of $0.06 per bird associated with raising MM(+) turkeys. Although the weight gain results were obtained from birds raised under environmentally controlled conditions and thus not subjected to typical overcrowding and climatic stress faced under field conditions, they agree with recent results obtained in a field study (Carpenter et ah, 1982a). This apparent profit advantage should be considered when measuring the benefits derived from averting decreased hatchability, leg problems, and other anomalies associated with MM infection. This microeconomic approach should aid producers, veterinarians and administrators in their disease control/eradication decision making. INTRODUCTION I n r e c e n t y e a r s , e c o n o m i c e v a l u a t i o n s o f disease in f o o d p r o d u c t i o n a n i m a l s h a v e f o c u s e d o n t h e p r e s e n c e or a b s e n c e of a s t a t i s t i c a l l y s i g n i f i c a n t diff e r e n c e in f i n a l w e i g h t s o f a n i m a l s in d i f f e r e n t g r o u p s , g e n e r a l l y i n f e c t e d vs n o n i n f e c t e d . All t o o o f t e n s u c h a n a l y s e s h a v e i g n o r e d t h e i n c r e a s e d f e e d req u i r e m e n t ( o r d e c r e a s e d i n s o m e cases w h e r e e f f i c i e n c y was i n c r e a s e d } n e c e s s a r y t o p r o d u c e t h e a d d i t i o n a l w e i g h t . S i m i l a r l y , t h e t i m e r e q u i r e m e n t in-
0167-5877/83/$03.00
© 1983 Elsevier Science Publishers B.V.
290 volved with these changes has often been ignored. Furthermore, when these factors were in fact considered, no attention was given to the fact that with a productivity change there may also be an accompanying change in the most profitable levels of variable inputs used, such as time and feed. Mycoplasma meleagridis (MM) infection in turkeys has been associated with several adverse production effects, from embryo development through growth of the young poult and adult turkey (Rhoades, 1969; Nelson, 1971; Edson et al., 1979; Carpenter et al., 1981). The total economic loss associated with decreased hatchability caused by MM and the cost of a control program have been estimated at $9.4 million/year in the U.S.A. alone (Carpenter et al., 1981). A complete history of MM has been given by Yamamoto (1978). This perceived adverse impact of MM infection on the economics of turkey production has initiated eradication programs to be performed in primary breeder flocks in the United States, Canada and Great Britain. The worldwide impact of these eradication efforts is that multiplier breeders and eventually meat bird producers will soon be supplied birds which are free of MM. Veterinarians and turkey producers throughout the world will soon be faced with evaluating the economic impact of obtaining a flock of birds free from MM and then maintaining this status. One way in which this might be accomplished is through microeconomic evaluation. In economics, there are essentially two levels at which studies may be aimed. The first, microeconomics, deals with the economic actions and behavior of the individual, consumer or producer. Regarding the producer, the focus is on such things as prices of inputs, and outputs, production efficiency and markets. Macroeconomics, on the other hand, focuses on the e c o n o m y as a whole. For example, macroeconomics may be concerned with the effect of a change at the industry, state or national level, while microeconomics is concerned with the effect on the individual producer or consumer. In this study, production, cost and profit functions were evaluated to: (1) introduce the reader to a technique of microeconomics and (2) determine the economic impact of MM infection in turkeys as reflected in the optimal level of (a) production, (b) input utilization, and ultimately (c) profits for a hypothetical turkey producer in the Central Valley of California. The results and conclusions could easily be adapted to other producers throughout the world. MATERIALS AND METHODS
Experimental infection Three hundred seventy-eight poults produced by a flock of MM-free (noninfected) turkeys were divided into two groups. One group had received 0.1 ml of 24-h PPLO-broth culture of MM strain RY-39A (Ghazikhanian and Yamamoto, 1974) on day 9 of incubation. The second group was comprised of a placebo group of poults hatched from eggs inoculated with 0.1 ml of
291 sterile PPLO broth on day 9 of incubation and a control group of poults hatched from eggs left uninoculated. The control and placebo birds were combined because of the apparent lack of adverse impact of the placebo on hatchability of the poults (Carpenter et al., 1981).
Poult placement and data collection A total of 205 female and 173 male poults were raised under environmentally controlled conditions on a Ralston Purina research farm located in St. Louis, MO. The birds were monitored with respect to feed consumption, weight gain, morbidity and mortality. The hens were slaughtered at the end of 17 weeks and the toms at the end of 23 weeks. All variables were recorded for both the hens and toms for a total of 16 weeks (Carpenter et al., 1982b) and these data were used in the present evaluation. Birds were weighed on an individual basis on day 1 for both the hens and toms and on a pen basis on days 28, 53, 77, 98 and 112 for the hens and days 28, 56, 84, and 112 for the toms. Average bird weights were thus used after day 1 weights in the analysis. Feed consumption was also measured on a pen basis on the same date as the pen of birds was weighed.
Production, cost and profit functions Multiple regression (Kleinbaum and Kupper, 1978) was used to develop a model for the production function used in this analysis. A production function refers to the physical relationship between the level of inputs used by a producer and the outputs derived from those inputs. In this study, time will be the input evaluated and allowed to vary while the o u t p u t is liveweight. Furthermore, implicit in time is feed consumed by the birds at a level which will vary with time. Selection of the final production function model was based on agreement of the mathematical model with biologic knowledge and adjusted R-squared value of the model. Total variable costs, those associated with time and feed, and o u t p u t price were chosen to represent the situation for a producer located in the Central Valley of California (California Cooperative Extension, 1981). A cost function (where costs are related to the level of output) and a profit function (where profits are related to the input(s): time in this example) were derived from this information and the economic impact to the producer of MM infection was determined by an evaluation of the profit function.
Sensitivity analysis Sensitivity analysis was performed to measure the impact of price changes on the optimal level of production. In order to facilitate the numerous runs
292 anticipated for the sensitivity analysis, a FORTRAN program was written to calculate the optimal feeding period and hence optimal liveweight, feed consumption and maximum profits for a variety of input--output price combinations. RESULTS Several algebraic forms were analyzed to determine the best production function equation. The following equation was selected:
Y = 0 . 0 9 6 7 2 + 0.01248(T) + 2 . 3 0 3 . 1 0 - 3 ( T ) 2- 1 . 0 6 0 . 1 0 - 5 ( T ) 3 (2.11)
(1.95)
(15.11)
(-11.63)
+ 2 . 0 1 6 . 1 0 -3 (MM) (T) + 4 . 0 8 4 . 1 0 -2 (S) (T) (2.00) (42.46) where Y -- liveweight of the turkey; T = age of the bird; S = a d u m m y variable denoting sex (0 = female, 1 = male); MM = a d u m m y variable for MM-infection status (0 = MM(--), 1 = MM(+)). Adjusted R-squared = 0.996. Note, the t-values appear in parentheses below their respective coefficients and all of the coefficients are significant at P < 0.0005 with the exceptions of the intercept, P = 0.036, the (MM) (T) interaction term, significant at P = 0.046, and the linear time term (T), P = 0.053. In interpreting the above equation, it may be clearer to think of it as four equations rather than a single equation. The four equations predict the weight gain for (1) MM(+) males, (2) MM(--) males, (3) MM(+) females, and (4) MM(--) females. They may be written asfollows: 0.09672 + 5.5336.10-2(T) + 2 . 3 0 3 , 1 0 - 3 ( T ) :
- 1.060*10-S(T) 3,
0.09672 + 5.3320.10-2(T) + 2 . 3 0 3 , 1 0 -3(T) 2 -
(1)
1 . 0 6 0 . 1 0 -s (T) 3,
(2)
0.09672 + 1 . 4 4 9 6 . 1 0 - 2 ( T ) + 2 . 3 0 3 , 1 0 -3(T) 2 - 1 . 0 6 0 . 1 0 -5(T) 3,
(3)
0.09672 + 1.2480.10-2(T) + 2 . 3 0 3 , 1 0 -3(T) 2 -
(4)
1 . 0 6 0 . 1 0 -s (T) 3.
With these four regression equations, weight gains for each of the groups could be predicted according to length of time fed. The results of a sample of calculations for the four groups considering the time period of 100--160 days appear in Table I and Fig. 1. From the production schedule results, the m a x i m u m predicted weights of the MM(+), 24:53 lb, and MM(--), 24.22 lb, males appear at approximately 155 days. The m a x i m u m weight for the females appears 5 days earlier with the MM(+), hens at 18.31 lb and the MM(--) hens at 18.01 lb. In a statistical analysis of the impact of MM, it might be concluded here that MM(+) toms and hens exhibit a 0.31 lb weight advantage over their noninfected comparisons. This difference would then be tested for statistical significance. Being significantly different, the difference would then be multiplied by the price of meat and concluded to be the "economic impact due to
293 TABLE I Liveweight over 100--160 days for Mycoplasma meleagridis-infected (MM(+)) and noninfected (MM(-)) male and female turkeys Time (days)
Liveweight (lb)
100 105 110 115 120 125 130 135 140 145 150 155 160
MM(+) males
MM(-) males
MM(+) females
MM(-) females
18.06 19.03 19.97 20.80 21.58 22.30 22.92 23.46 23.90 24.23 24.44 24.53 24.49
17.86 18.82 19.72 20.56 21.34 20.04 22.66 23.19 23.61 23.93 24.14 24.22 24.17
13.98 14.74 15.45 16.10 16.68 17.19 17.61 17.95 18.18 18.30 18.31 18.20 17.96
13.77 14.53 15.23 15.87 16.44 16.94 17.35 17.67 17.90 18.01 18.01 17.89 17.63
25
MM(+/moles
2 4 1 2 3~
MM(-)meles
1 9 iB I 20
~- LLJ
~
"'"'~MM~I+ f...... -I feme/es
17 16 15 14 13 I00
I
i1~0
J
i
120
A G E (doys) I
I
130
i
L
140
I
I
i50
I
I
160
Fig. 1. Regression equations (production functions) for four groups of turkeys: Mycoplasma meleagridis-infected (MM(+)) males and females, and M. meleagridis-noninfected (MM(-)) males and females, from 100 to 160 days of age. MM infection". Such a conclusion would, however, ignore the producer profit motive and be potentially erroneous. Hence the need to proceed further, beyond a statistical evaluation, and evaluate the producer's profit funct i o n . T h a t is, t h e p r o d u c e r d o e s n o t a c t so as t o p r o d u c e a n a n i m a l w i t h a
294 m a x i m u m weight. I n s t e a d he is a t t e m p t i n g to p r o d u c e an a n i m a l at a level w h i c h m a x i m i z e s his profits. This level is n o t o n l y r e s p o n s i v e to the p r e s e n c e or a b s e n c e o f an i n f e c t i o n , such as MM, it is also d e p e n d e n t u p o n f a c t o r s such as i n p u t and o u t p u t prices. Prior to evaluating the p r o f i t f u n c t i o n , it is n e c e s s a r y t o k n o w t h e variable c o s t involved w i t h the p r o d u c t i o n process. T h e r e f o r e a c o s t f u n c t i o n was fitted t o the g r o w t h d a t a . T h e variable costs c o n s i d e r e d i n c l u d e d feed costs, h e a t i n g e x p e n s e s , m e d i c a t i o n and o t h e r v e t e r i n a r y costs, l a b o r costs, i n t e r e s t charges, and a n y o t h e r costs i n c u r r e d as a result o f retaining t h e t u r k e y s . B e f o r e s p e c i f y i n g the variable c o s t f u n c t i o n , it was n e c e s s a r y to d e t e r m i n e t h e r e l a t i o n s h i p b e t w e e n feed c o n s u m p t i o n and age o f t h e birds w h i c h w e r e fed ad l i b i t u m . T h e s a m e criteria were used t o specify this r e l a t i o n s h i p as was used w i t h the p r o d u c t i o n f u n c t i o n : F=-0.01099(-0.11)
2.876.10-2(T) (-2.02)
+ 4 . 2 6 1 . 1 0 .3 (T) 2 (12.58)
8.339.10-6(T) 3 (-4.12)
+ 6 . 5 3 6 . 1 0 .2 ( S ) ( T ) + 2 . 7 4 1 . 1 0 .3 (MM) (T), (30.58) (1.23) A d j u s t e d R - s q u a r e d = 0.996. T h e regression c o e f f i c i e n t s w e r e again highly significant, P < 0 . 0 0 0 5 , w i t h the e x c e p t i o n s of the i n t e r c e p t , P = 0.914, the (MM) (T) i n t e r a c t i o n t e r m , P = 0.22 and the linear t i m e t e r m , P = 0.045. As w i t h the p r o d u c t i o n f u n c t i o n , t h e f e e d - t i m e r e l a t i o n s h i p m a y be expressed as f o u r s e p a r a t e e q u a t i o n s , o n e f o r each o f t h e g r o u p s w i t h feed as the d e p e n d e n t variable: (1) MM(+) males, (2) MM(--) males, (3) MM(+) females, and (4) MM(--) f e m a l e s : -0.01099
+ 3.9341.10 -2(T) + 4.261.10 -3(T) 2 -
8.339.10 -3(T) 3
(1)
-0.01099
+ 3.6600.10-2(T)
+ 4.261.10-3(T) 2 -
8.339.10-3(T) 3
(2)
-0.01099
-
2 . 6 0 1 9 . 1 0 .2 (T) + 4 . 2 6 1 . 1 0 - 3 ( T ) 2 -
8.339.10 -3(T) 3
(3)
-0.01099
-
2 . 8 7 6 0 . 1 0 - 2 ( T ) + 4 . 2 6 1 . 1 0 .3 (T) 2 -
8 . 3 3 9 . 1 0 - 3 ( T ) 3.
(4)
T h e d i f f e r e n c e s in t h e f o u r e q u a t i o n s are in t h e p r e s e n c e or a b s e n c e o f the MM-status a n d / o r sex i n t e r a c t i o n t e r m s . Given t h e prices o f the variable inp u t s , t h e t o t a l daily c o s t o f raising t h e t u r k e y s m a y be c a l c u l a t e d :
PD = P F ( F ) + P T ( T ) w h e r e PD = t o t a l daily c o s t ( c e n t s / d a y ) ; PF = price of feed ( c e n t s / l b ) ; F = f(T), the level o f feed c o n s u m e d (lb) m e a s u r e d as a f u n c t i o n o f t i m e ; T = t i m e ( d a y s ) ; and PT = daily costs m i n u s feed e x p e n s e ( c e n t s / d a y ) . Given the a b o v e e q u a t i o n s , t h e t o t a l variable costs, r e v e n u e s and p r o f i t s m a y be c a l c u l a t e d f o r each o f the f o u r g r o u p s o f t u r k e y s . An e x a m p l e using the MM(+) and M M ( - ) males a p p e a r s in T a b l e II.
295 TABLE II Days fed, total variable costs, revenues and profits (US $) for Mycoplasma meleagrides-infected (MM(+)) and non-infected (MM(-)) male turkeys raised from 100--160 days Days fed
100 105 110 115 120 125 130 135 140 145 150 155 160
Variable costs
Revenues
Profits
MM(+)
MM(-)
MM(-~)
MM(-)
MM(+)
MM(-)
4.44 4.78 5.14 5.49 5.85 6.22 6.59 6.97 7.35 7.74 8.13 8.52 8.91
4.41 4.75 5.10 5.46 5.82 6.19 6.56 6.94 7.32 7.70 8.09 8.48 8.87
7.22 7.61 7.99 8.32 8.63 8.92 9.17 9.38 9.56 9.69 9.78 9.81 9.80
7.14 7.53 7.89 8.23 8.54 8.82 9.06 9.27 9.45 9.57 9.65 9.69 9.67
2.78 2.83 2.85 2.83 2.78 2.70 2.58 2.41 2.21 1.95 1.65 1.29 0.89
2.73 2.78 2.79 2.77 2.72 2.63 2.50 2.33 2.t3 1.87 1.56 1.21 0.80
T h e results p r e s e n t e d in T a b l e II m a y also be r e f e r r e d to as the variable c o s t , r e v e n u e and p r o f i t schedules. T h e variable costs are a f u n c t i o n o f t i m e as well as feed c o n s u m p t i o n . With r e s p e c t to t i m e , t h e y increase in a linear t r e n d (Fig. 2). With r e s p e c t to feed, h o w e v e r , t h e y increase at an increasing r a t e for a given p e r i o d o f t i m e . This changing variable cost m a y m o s t easily be viewed b y observing the rate of change for a single g r o u p , e.g. either the MM(+) or MM(--) males. In e i t h e r case, the change in variable cost over the initial 5-day p e r i o d is a p p r o x i m a t e l y $0.33. This rate o f c h a n g e increases and reaches a m a x i m u m o f $ 0 . 3 9 t o w a r d the later p a r t o f t h e feeding regime. T h e r e v e n u e s for these t w o g r o u p s r e a c t quite d i f f e r e n t l y t h a n the costs as the age o f the birds increases (Fig. 2). F o r e x a m p l e , f r o m d a y 100 to 105, the c h a n g e in r e v e n u e is $ 0 . 3 9 for b o t h t h e MM(+) and M M ( - ) t o m s . T h e increase in r e v e n u e increases at a faster rate t h a n t h e costs until 115 d a y s w h e r e the cost increase was $ 0 . 3 5 and r e v e n u e increase was $0.33 for the MM(+) males and $ 0 . 0 1 m o r e for the M M ( - ) males in b o t h categories. Cont i n u e d feed o f t h e m a l e s results n o t o n l y in an increased daily cost, it also results in daily r e v e n u e increasing at a decreasing rate. In fact, in the final p e r i o d , 1 5 5 - - 1 6 0 days, the t o t a l r e v e n u e decreases f r o m w h a t it was in the previous p e r i o d . This results f r o m t h e birds reaching a m a x i m u m weight and t h e n losing w e i g h t w i t h the a m o u n t o f feed t h e y c o n s u m e in this final period. T h e i m p o r t a n t f e a t u r e o f T a b l e II is the p r o f i t level for each o f the t i m e periods. F r o m T a b l e II and Fig. 3, it m a y be seen t h a t the p r o f i t s f o r b o t h the MM(+) a n d M M ( - ) birds reach t h e i r m a x i m u m at a p p r o x i m a t e l y 110
296 --
tO
TR
9 Z
uJ
8
~-
7
2k . -
6
~
4
~
3
~
2
rVC (feed + t,me)
VC (feed)
VC (hme)
I
ilo
I
I00
l
I I I I 120 150 140 AGE (days) i
160
150
Fig. 2. Variable c o s t s for t i m e (VC ( t i m e ) ) , feed (VC (feed)) and total (TVC (feed + t i m e ) ) and total r e v e n u e ( T R ) for Mycoplasma meleagridis-infected male t u r k e y s f r o m ] 0 0 to 1 6 0 days o f age. 3oo F
25
i
0
~
00i rSO
F0
I00 \ " MM (+) moles MM {-] males
rr
13.
~
050
ioo to5 Jr Ji izo m5 p3o ~35 f4o 145 tS0
t55 i60
AGE (days) Fig. 3. S h o r t - r u n p r o f i t s f o r Mycoplasma m e l e a g r i d i s - i n f e e t e d ( M M ( - ) ) males f r o m 1 0 0 to ] 6 0 days o f age.
( M M ( + ) ) and - n o n i n f e e t e d
days, $2.83 and $2.77, respectively. Prior to this age, profits were increasing at an decreasing rate, initially at $0.05 per 5-day period and $0.02 for the 1 0 5 - - 1 1 0 day period, for the MM(+} males. After maximum profits were realized (day 110), extension beyond this date resulted in the profits decreasing at an increasing rate, i.e. - $ 0 . 0 2 for days 110--115; - $ 0 . 0 5 for days 115--120, and - $ 0 . 4 0 for the final period of 155--160 days, for the MM(+)
297 males. This p a t t e r n is similar to that shown for the MM(-) males. From Table II, it may be concluded t hat given this econom i c information, the p r o d u c e r would raise male turkeys for approxi m at el y 110 days in order to maximize his profits at $2.85 for MM(+) t om s and $2.79 for MM(-) toms. Thus the MM(+) birds would yield a relative profit of $0.06 per male. The short-run profit function directly produces the expected profits for a given age as well as the optimal profit. It is derived by considering the shortrun costs of the variable inputs and the price received for the o u t p u t . In this example, we assumed variable costs of $0.01 per day to retain the birds and $0.09 per p o u n d of feed cons um ed by the turkeys. F u r t h e r m o r e the price o f t u r k e y was set at $0.40 per pound, measured on a liveweight basis. The profit f u n c t i o n m a y be written as follows: Pr = P Y ( Y ) - ( E X i P X i )
where Pr = profit (US $ per bird); P Y = price of t urkey (US $ per p o u n d ) ; Y = liveweight of the t u r k e y , determined from the p r o d u c t i o n function presented above; X i = level of input i (time and feed) used; and P X i = price of input i (time and feed). Thus in the above equation it may be seen t h a t the profit is calculated as the difference between the total revenue ( P Y ( Y ) ) a n d the total costs ( E X i P X i ) . To find the optimal time and corresponding level of feed given to the turkeys, the derivative of the profit function with respect to time (MPr) was determined. The o p t i m u m , or m a x i m u m , profit occurs when the MPr is equal to zero. In order to insure t hat this level corresponds to a local maxim u m and n o t minimum, it is necessary to also look at the second derivative. If the second derivative is less than zero, then we have a p r o d u c t i o n level which maximizes profit. If the value of the second derivative at the given level o f the input is greater than zero, the o u t p u t will minimize the profit. Thus it is i m p o r t a n t to determine the value of the second derivative as well as the first. The first derivative of profit, with respect to time, or the marginal profit (MPr), is written as dPr
= P Y * ( 5 . 5 3 3 6 . 1 0 -2 + 4 . 6 0 6 . 1 0 -3 (T) - 3 . 1 8 0 . 1 0 -s (T) 2 ) - P T
MPr =--
dT
+ P F * ( 3 . 9 4 3 1 . 1 0 -2 + 8 . 5 2 2 . 1 0 - 3 ( T ) - 2 . 5 0 2 . 1 0 -s (T)2).
The second derivative of profit, with respect to time is written as d2Pr -
P Y * ( 4 . 6 0 6 . 1 0 -3 - 6 . 3 6 0 . 1 0 -s (T)) + P F * ( 8 . 5 2 2 . 1 0 - 3 - 5 . 0 0 4 . 1 0 -s
dT 2 -
5 . 0 0 4 " 1 0 -s (T)).
In order to find the a m o u n t of time necessary to raise the MM(+) males to the weight which would maximize profits, the two necessary conditions which must be m et are t hat MPr = 0 and d 2 P r / d T 2 < O. The first condition is approached by setting M P r = 0 and then solving for T. Results of the
298 TABLE III Liveweights, levels of feed, time, cost and revenue associated with short-run profit maximization for Mycoplasma meleagridis-infected (MM(+)) and noninfected (MM(--)) male and female turkeys Sex
MM status (+]-)
Weight (lb)
Time (days)
Feed (lb)
Variable cost (US $)
Revenue (US $)
Profits (US $)
Male Male
+ -
19.97 19.67
110.2 109.7
44.91 44.30
5.14 5.08
7.99 7.87
2.84 2.78
Female Female
+ -
14.13 13.84
101.0 100.4
32.23 31.63
3.91 3.85
5.65 5.54
1.74 1.68
TABLE IV A sensitivity analysis for the predicted time (days) requirement, final liveweight (lb), and profits (US S/bird) from male turkeys according to MM status, assuming various input and output prices (US $) Prices of inputs and outputs
Optimal time
Optimal weight
Profits
Feed
Time
Meat
MM(+)
MM(-)
MM(+)
MM(-)
MM(+)
MM(-)
0.09 0.09 0.09 0.09
0.005 0.010 0.015 0.020
0.40 0.40 0.40 0.40
114.1 110.2 106.0 101.4
113.7 109.7 105.5 100.9
20.65 19.97 19.21 18.34
20.35 19.67 18.90 18.03
3.41 2.85 2.31 1.79
3.34 2.78 2.25 1.73
0.06 0.12 0.15
0.010 0.010 0.010
0.40 0.40 0.40
125.6 92.6 72.5
125.2 92.1 72.0
22.37 16.55 12.17
22.06 16.26 11.91
4.36 1.67 0.84
4.28 1.62 0.81
0.09 0.09 0.09 0.09 0.09 0.09 0.09
0.010 0.010 0.010 0.010 0.010 0.010 0.010
0.30 0.35 0.40 0.45 0.50 0.55 0.60
89.1 101.6 110.2 116.4 121.1 124.8 127.8
88.5 101.2 109.7 115.9 120.7 124.4 127.4
15.81 18.38 19.97 21.02 21.75 22.27 22.66
15.52 18.09 19.67 20.72 21.44 21.96 22.35
1.02 1.88 2.85 3.87 4.94 6.04 7.17
0.99 ] .84 2.78 3.80 4.85 5.94 7.04
0.12 0.12 0.12 0.12
0.015 0.015 0.015 0.010
0.40 0.45 0.50 0.50
87.2 97.6 105.1 108.5
86.7 97.1 104.7 108.1
15.41 17.57 19.05 19.68
15.11 17.27 18.75 19.38
1.22 2.05 2.96 3.50
1.18 1.99 2.89 3.43
FORTRAN program provided not only the optimal time and hence feed cons u m p t i o n a n d w e i g h t f o r t h e i n i t i a l p r i c e s ( T a b l e I I I ) , b u t also v a l u e s f o r a v a r i e t y o f p r i c e c o m b i n a t i o n s in a s e n s i t i v i t y a n a l y s i s ( T a b l e I V ) . T h e o p t i m a l w e i g h t f o r t h e M M ( + ) b i r d s w a s a p p r o x i m a t e l y 0 .3 lb h e a v i e r
299 than their MM(-) cohorts. Also, the additional feed (0.61 and 0.59 lb) necessary to produce these weights and the time (0.5 and 0.6 days) requirement were greater for the MM(+) toms and hens respectively (Table III). It may be seen from Table III t h a t both the MM(+) toms and hens were predicted to yield a profit greater by $0.06 per bird than their MM(-) cohorts, assuming PT = $0.01, P F = $0.09 and P Y = $0.40. However, upon evaluation of the results from the profit function (Table III) rather than the schedule presented in Table II, a less accurate measure, the optimal period required to raise the MM(+) birds is greater than that of the MM(-) cohorts, 0.5 days for the males and 0.6 days for the females. In reality, it is more probable t h a t the birds will be raised an identical period of time with the final weights being different. This would not change the profit advantage demonstrated by the MM(+) birds. In order to evaluate the impact of MM infection when faced with prices other than the initial prices, several simulation runs were performed and the optimum weight-time-feed for each calculated. Results obtained from a sample of runs for the males are presented in Table IV. In the sensitivity analysis the price of feed was allowed to vary from a low of $0.06/lb up to a high of $0.15/lb. The variable price of time ranged from $0.005 up to $0.02/day. The impact of a price change on turkey meat was evaluated over a range of $0.30 to $0.60/lb liveweight. Results showed that for all prices considered, the profits from MM(+) birds were superior to those from MM(-) birds at each price combination. The impact of the sensitivity analysis demonstrated that while this advantage remains at varying price levels, there is a change in the relative advantage. That is the profit advantage varied from $0.03 to $0.13/bird depending on the prices assumed. The importance of this will be addressed in the discussion section. DISCUSSION In this paper, the liveweight prices of both males and females were set at $0.40 per pound. While there will most likely be a different price for hens and toms, a single price was assumed for ease of analysis. Any problems which might have been created by the simplification should have been obviated in the sensitivity analysis and by not comparing the results of the toms and the hens. This analysis was conducted for a short-run problem. If it were being considered over a long-run period, e.g. more than 6 months, all of the costs involved in raising the turkeys, i.e. the fixed as well as the variable costs would have been considered as being variable. In such a situation, the conclusions reached in this paper m a y have been different. However, it is felt that the effect would not be significant and the results would be similar to those presented in this short-run evaluation. In the short run, the size of the fixed costs will not affect the optimal production level and may therefore be ignored in the short-run profit evaluation.
300 The conclusions regarding the economic advantage associated with MM(+) birds in this study should not be construed to imply t h a t MM infection is economically beneficial. As stated earlier in this paper, the results presented were obtained from a trial in which birds were raised under environmentally controlled conditions. In considering the overall economic impact of MM infection, there is much debate concerning its true clinical impact. For example, if there is truly a 5% increase in the number of salable poults produced by MM(-) turkeys (Carpenter et al., 1981), this must be taken into consideration when evaluating the apparent $0.06 per bird profit advantage associated with MM(+) turkeys. That is, the advantage (increased salable poults) of MM(-) stock must be compared with the disadvantages, i.e. cost of producing and maintaining MM(-) birds in addition to a potential weight gain advantage of MM(+) birds. One m e t h o d in which this might be accomplished is by a break-even point analysis (Carpenter et al., 1979) where the added revenue received by raising MM(+) birds may be equated to the potential benefit from improved poult production. When this point is found, the prices yielding a break-even point should be considered as to their likelihood of occurring before a decision may be made on the economics of the infection and its control. In animal health economics, the most frequently used tool for evaluating the "economic impact" of a disease, or its associated control/eradication program has been benefit--cost analysis. In its correct form, benefit--cost analysis takes into consideration the effect on consumer surplus, producer surplus and the distribution impact of the project being analyzed. However, to date due to the dearth of sound data concerning the impact of a disease on the productivity of an individual animal and the profit-maximizing approach which the livestock producer might take, the underlying assumptions upon which such analyses are based are questionable. Hence, subsequent evaluations based on such assumptions are subject to error from the start. By using microeconomics, the true impact of how diseases actually affect the producer may be more accurately estimated. With this improved estimate, the veterinarian, producer or other decision maker, may then make a more informed recommendation to the producer and thus effect more cost-effective disease control programs.
REFERENCES
Carpenter, T.E., Miller, K.F., Gentry, R.F., Schwartz, L.D. and Mallinson, E.T., 1979. Control of Mycoplasma gallisepticum in commercial laying chickens using artificial exposure to Connecticut F strain Mycoplasma gallisepticum. Proc. 83rd U.S.A.H.A. Meet., San Diego, CA, pp. 364--370. Carpenter, T.E., Edson, R.K. and Yamamoto, R., 1981. Decreased hatchability of turkey eggs caused by experimental infection with Mycoplasma meleagridis. Avian Dis., 25: 151--156.
301 Carpenter, T.E., Riemann, H.P. and Franti, C.E., 1982a. The effect of Mycoplasma meleagridis infection and egg dipping on the weight-gain performance of turkey poults. Avian Dis., 26: 272--278. Carpenter, T.E., Riemann, H.P. and McCapes, R.H., 1982b. The effect of experimental turkey embryo infection with Mycoplasma meleagridis on weight, weight gain, feed consumption, and conversion. Avian Dis., 26: 689--695. California Cooperative Extension, 1981. The Budget Generator: Turkey production in Central California. Cooperative Extension, University of California, Davis, CA, No. 406, 6 pp. Edson, R.K., Yamamoto, R., Ortmayer, H.B. and Massay, D.E., 1979. The effect of Mycoplasma meleagridis on hatchability of turkey eggs. Proc. 28th West. Poult. Dis. Conf. and 13th Poult. Health Symp., Davis, CA., pp. 24--29. Ghazikhanian, G. and Yamamoto, R., 1974. Characterization of pathogenic and nonpathogenic strains of Mycoplasma meleagridis: In vivo and in vitro studies. Am. J. Vet. Res., 35: 425--430. Kleinbaum, D.G. and Kupper, L.L., 1978. Applied Regression Analysis and Other Multivariable Methods. Duxbury Press, North Scituate, MA, 556 pp. Nelson, R.C., 1971. Evaluation of egg dipping (1967--1970). In: Proc. Symp. on Leg Weakness in Turkeys. Iowa State Univ., Ames, IA, pp. 13--21. Rhoades, K.R., 1971. Mycoplasma meleagridis infection: development of lesions and distribution of infection in turkey embryos. Avian Dis., 1 5 : 7 6 2 - - 7 7 4 . Thompson Jr., A.A., 1981. Economics of the Firm. Prentice-Hall, Englewood, Cliffs, NJ, 635 pp. Yamamoto, R., 1978. Mycoplasma meleagridis infection. In: M.S. Hofstad, B.W. Calnek, W.M. Hemboldt, W.M. Reid and H.W. Yoder, Jr. (Editors), Diseases of Poultry. Iowa State Univ. Press, Ames, IA, 7th ed., pp. 250--270.