Optimal beef cattle management under agricultural policy reforms in Finland

The supply for domestic beef has been decreasing sharply since Finland joined the European Union (EU) because profitability of beef production has been low. The goal of this study is to search for optimal beef management practices that increase returns on beef production in Finland. Numerical dynamic programming (DP) is used to simultaneously optimise feeding and timing of slaughtering. The DP-algorithm is solved under alternative subsidy, output price, and silage price scenarios. At 1998 prices and subsidies, the optimal carcass weight is estimated above 250 kg. The European Agenda 2000 reform is predicted to decrease the optimal carcass weight to 200 kg, which is 50 kg lower than under the 1998 prices and subsidies. This reform will increase farmer returns significantly and its income effect depends crucially on the price of silage. The results indicate also that the reform will result in adjustment of feeding. Particularly, farmers having high silage production costs will substitute feed concentrates for roughage in the diet. A farmer is entitled to a premium subsidy of FIM 200 ( €33.63), provided that the carcass weight of a culled animal exceeds 270 kg. But when the Agenda 2000 reform is fully implemented, this premium subsidy is not large enough to supply carcasses heavier than 270 kg. The results suggest that carcass weights of at least 270 kg would require a premium subsidy of FIM 400 –800 (€67– €134). Rearing heavy animals will significantly increase production costs and, therefore, most of the subsidy will be taken away from the farm in terms of increased costs.


Introduction
European agricultural policy reforms have resulted, and are further expected to result, in large changes in the beef sector.Particularly, in a high cost country such as Finland, these reforms have important implications for the economics of the beef sector and for farmer incentives to rear cattle.The combined effects of decreasing producer beef prices and gradually increasing forage costs have been considerable at weakening the supply for domestic beef.During the first years in which Finland has been in the European Union (EU), beef producers have had difficulty attaining profitability and more than 7% annually Pihamaa, P. & Pietola, K. Optimal beef cattle management in Finland have quit cattle operations (TIKE 2000a).Beef production has been decreasing by 3% annually (TIKE 2000b).Therefore, the traditional experience of excess supply has quickly turned into a deficiency of domestic beef.It is expected that without new domestic programs encouraging beef production the supply for beef will be further weakened.The Agenda 2000 reform, for example, has a goal of decreasing beef production in Europe and this reform is expected to have similar effects in Finland.
Enhancing domestic beef production is an important policy goal in Finland.To promote domestic beef production, the Finnish government has designed domestic subsidy programs which complement the European common programs in supporting cattle farmers.These subsidies can be characterized as direct income subsidies but they also have links so as to increase farmer incentives in rearing heavier animals.Thus, these income subsidies have a goal of increasing farmer income and strengthening the supply for beef.
The performance of the subsidy programs combined with low beef prices and high forage production costs raises at least two important questions.The first question is how efficient these subsidies are in increasing farmer income if the subsidies are not fully decoupled from production.The subsidy rates increase with the weight of the culled animal.The second question is how much these subsidy schemes affect optimal beef production management and the supply of beef.
The goal of this paper is to simulate optimal cattle management solutions under alternative policy, price, and forage cost scenarios.Policy scenarios include the Agenda 2000 reform and the domestic subsidy schemes in which the subsidy rates are linked to certain carcass weights of the culled animals.Forage cost scenarios reflect alternative (farmer specific) planning situations and horizons.In the short run model, forage production costs include only variable costs whereas the long run model includes all forage production costs.
The dynamic optimization model is con-structed in an optimal stopping framework solving the optimal decision rules numerically using the Bellman's principle of optimality and recursive Dynamic Programming (DP) (Bellman 1957).A numerical solution technique is used because the optimal feeding and optimal timing of slaughtering cannot be solved analytically in closed form.The numerical approach also has an advantage in simulating the effects of animal weight thresholds that trigger certain lump sum subsidy payments.In addition, dynamic programming is generally considered to be the preferred technique for modeling optimal animal management problems (e.g.Glen 1983, Van Arendonk 1985, Boland et al. 1993, Huirne et al. 1993).In spite of its superiority, DP has not been applied to cattle management under Finnish production and market environment using animal breeding qualities that are common in Finland.
The outline of the paper is as follows.Subsequent sections present the economic model and the dynamic programming approach used in solving the optimal decision rules.The section, thereafter, presents data on the feeding experiment, prices, and subsidy rates.The two last sections give the results and conclude the paper.

The dynamic programming model
The goal of farmers is to maximize the discounted net present value (V t ) of beef bull production by choosing optimal animal feeding (u t f ) and timing of slaughtering (u t s ).The optimization problem has a recursive structure such that it obeys the Bellman equation (Bellman 1957) x t is the live weight of the animal (also referred to as animal weight), R t is the one period return, . 11 (2002): 3-11.β is the exogenous discount factor and it corresponds to the annual interest rate of 8%.The subscript t refers to time.In the transition equations, f (.) determines animal growth, provided the animal is not slaughtered.x 0 is the live weight of the new calf that is replaced for the slaughtered animal.

Vol
In a Nordic production environment, the standard is that cattle are raised indoors for most of the time and the matured animal has to be culled before the stable can have space for a new calf.Therefore, the optimal value function (V t ) and the one period return function (R t ) are standardized per unit of capacity to grow one animal.Stacking the continuation and stopping regions together, the one period return function takes the form where C(u t f ,x t ) is the feed cost, S t CAP is the Common Agricultural Policy (CAP) subsidy, and S t NAT is the domestic (national) subsidy.CAP and domestic subsidy rates are a function of animal weight.The parameter L is the percentage of carcass weight from the animal weight.P t m is the producer price for meat, S t S is the lump sum subsidy paid per animal when it is slaughtered, and P t C is the price of the calf.The calf price includes all transaction costs of animal replacement.
The one period function includes two parts: returns over the continuation region and returns upon stopping.In the continuation region we have u t s = 0 implying that the returns (or costs) are the feeding costs and the realized subsidy rates depending on the current weight of the animal.Over this region, the next period weight is controlled by optimal feeding (u t f ) through the animal growth function f.When it is optimal to cull the animal, we have u t s = 1 and the farmer receives the returns from slaughtering, subtracted by the price of a new calf.
At the end of the planning horizon (at t = T), the animal is always culled and the terminal value function is The data Animal growth and feed uptake The data are cattle feeding experiments carried out by Agricultural Research Centre of Finland (nowadays MTT Agrifood Research Finland) in 1995-1996(Rinne et al. 1998, Nissi and Pietola 1999).The experiments included 16 Ayrshire bulls with an average initial live weight of 94 kg at an initial age of 82 days.Two different feeding ratios were applied.Barley was the main concentrate and silage the main roughage of the diet in the experiment.For the first block of animals, the concentrate was given at a rate of 50 g DM kg -1 LW 0.6 (where DM is the amount of dry matter and LW is live weight) and for the second group of animals, the concentrate was given at a rate of 100 g DM kg -1 LW 0.6 .Grass silage was given ad libitum.These feeds were supplemented by a necessary amount of minerals.Bulls also received some rape seed during the first four months of the experiment.Feed ratios varied in a moderate range and no significant path dependency was observed (Nissi and Pietola 1999).Therefore, the animal growth satisfies the Markov property such that the current state (e.g.live weight) and feeding determines the animal growth.Path dependency is also referred to as compensatory growth such that if a period of poor feeding is followed by rich feeding the animal will grow faster than applying constantly the rich feeding.
Animal growth and the demand for barley and silage were estimated by the standard Ordinary Least Squares (OLS) method.As suggested by the biological theory on animal growth, an exponential Gompertz-function was fitted in the data.The live weight gain was estimated separately for both feeding groups.
The demand of silage was estimated as a nondecreasing logarithmic function of live weight.Maintenance requirements are expected to increase with animal weight such that the demand for silage never decreases when live weight increases.The demand for barley was estimated Pihamaa, P. & Pietola, K. Optimal beef cattle management in Finland as a power function of live weight.The estimated animal growth and feed demand functions and the observed data points are presented in Appendix 1.
The length of the planning horizon (T) was set at 2,282 days, which corresponds to about 6 years and 3 months.The length of the single time period (the node in the DP algorithm) is 7 days and the state space for live weight is any integer between 94 and 600 kg.The initial weight of 94 kg is based on the average weight of the calves when they entered the experiment.

Prices and subsidy rates
The prices for meat, calves, barley, rape seed, and minerals are average market prices in 1998 and their expected prices in the year 2002.The price expectations in year 2002 are based on future intervention prices.The price of silage is based on its production costs, as they are estimated in the enterprise budgets of agricultural extension services (named as HILA-accounts).Three alternative silage prices are simulated.These prices are denoted later as "high," "medium," and "low" prices of silage.The high price is the average production cost of silage in the HILA-accounts.This cost reflects the long run planning horizon when all costs have to be taken into an account, or, alternatively, producers who buy the harvest service from a contractor who is assumed to charge average production costs of harvesting the silage.Total production cost is 60% higher than the medium price which equals average variable cost and reflects the short run planning horizon.The low price is 20% lower than the average short run cost in HILA-accounts.This price reflects the short run planning situation on farms which show better than average economic performance.The low price is also justified in situations when farmers have excess silage inventories.The nominal production costs of silage are assumed to increase annually by 2% during the years 1998-2002.The prices of silage and other inputs are given in Table 1.
The optimal decision rules are solved under alternative beef prices and under three policy scenarios.The first policy scenario is based on prices and subsidies observed in 1998.The second scenario mimics the Agenda 2000 reform and it is based on expected prices and subsidies in 2002.The third scenario uses the expected prices in 2002 but it adds a premium subsidy for heavier animals (paid at slaughtering).The premium subsidy is determined such that it is large enough for enhancing domestic beef production by supplying heavier animals in the market.The goal of the third simulation is to get information on how animal subsidies could be used in strengthening the supply for domestic beef and how efficient they are in increasing farmer income.
The Agenda reform is expected to decrease the intervention price of beef by 20% between 1998 and 2002 (Table 2).These market price Subsidy rates are set in the model as they are paid to a beef producer, located in Central Finland (subsidy area C2).In 1999, for example, more than 40% of domestic beef was produced in this area (TIKE 2000c).The results also generalize other most important beef production areas in Finland.
Beef producers receive national subsidies and subsidies included in the Common Agricultural Policy (CAP) of the EU.National Northern aid is paid annually for every bull that is older than six months.The national transitional aid was paid for slaughtered bulls in 1998 but the subsidy was cancelled in 1999 and will not be paid in 2002 (MMM 1998).This subsidy was the highest for bulls over 220 kg carcass weight.
The Agenda reform is expected to increase the CAP subsidy such that it will be more than 40% higher in 2002 than in 1998.Also the payment schedule will be delayed.In 1998 the subsidy was paid according to the live animals on the farm but in 2002 farmers receive the payment after the animal is slaughtered.The minimum carcass weight required for the subsidy is 185 kg.Also, a new CAP subsidy for slaugh-tered bulls was introduced with Agenda 2000 reform (EU 2000b).The complete set of subsidy rates in 1998 and their expected values in 2002 are given in Table 3.
The third policy simulation is to solve the DP algorithm under the expected prices for 2002 including increased premium subsidies for heavier animals.The subsidy rate is determined for having an optimal carcass weight of at least 270 kg.

Decision rules and value functions at 1998 prices and subsidies
At 1998 prices and subsidies, the optimal timing of slaughtering was estimated at 14.4 months when the carcass weight exceeds 250 kg.The 250 kilogram weight hits the quality adjustment threshold such that the meat price was higher for carcasses exceeding 250 kg than for carcasses below the 250 kg (Fig. 1, Table 4).The price of silage does not significantly affect the optimal timing of slaughtering but it affects farmer returns and animal feeding.When the price of silage is decreased by 20%, from medium to low, the feeding remains practically unchanged but farmer returns increase by 10%.

Pihamaa, P. & Pietola, K. Optimal beef cattle management in Finland
If the silage price is increased from medium to high, concentrates substitute for a substantial amount of silage in animal feeding and farmer returns are decreased by 30% (Table 4).

Decision rules and value functions at 2002 prices and subsidies
At 2002 prices and subsidies, the optimal timing of slaughter was estimated at 10.9 months of age and at a carcass weight of 194 kg.Now, the optimal timing of slaughter is at the point were the bull reaches the first quality adjustment (price increase) after reaching the minimum weight required for the CAP subsidy (Fig. 1, Table 5).Thus, the Agenda 2000 reform is predicted to decrease farmer incentives to raise heavier animals, which will result in a weakened supply of beef given a fixed number of calves available for production.The reform will, nevertheless, increase farmer returns by FIM 2,330-3,650 (€392-€615) per capacity unit over the planning horizon.In annual terms, the corresponding increase is FIM 372-584 (€62.7-€98.3)per capacity unit.The returns are predicted to increase the most for farmers paying high prices for silage.Substantial adjustment in animal feeding will also be realized.Particularly, farmers producing silage at the medium price will substitute more concentrates for silage than before the reform (Tables 4 and 5).

Decision rules and value functions at 2002 prices and premium subsidies
In this scenario, the size of the premium subsidy Table 4. Optimal decisions rules and value functions at 1998 prices and subsidy rates.

Low
Medium High Carcass weight at slaughter kg 255.9 255.9 253.9 Age at slaughter months 14.9 14.9 14.4 Value function FIM 13,145.911,803.98,177.9Concentrate/roughage ratio % DM* 24/76.924/76.935/65.9* The %-share of concentrate over the %-share of silage in total amount of dry matter in the diet.Vol. 11 (2002): 3-11. is determined so that it provides incentives to raise animals to the carcass weight of at least 270 kg.The results suggest that the premium subsidy should be FIM 400 (€67) at the low silage price, FIM 500 (€84) at the medium silage price and FIM 800 (€135) at the high silage price (Table 5).Thus, the premium subsidy granted for heavier animals should be FIM 200-600 (€34-€86) higher than it was in 2001.Similar effect could also be generated by a price premium of FIM 0.75-2.22(€0.17-€0.32)per kilogram of meat granted only for carcasses heavier than 270 kilograms.These threshold levels of the premium subsidies and prices would, nevertheless, be inefficient in subsidizing farmer income because most of the premiums would be lost in extra feeding costs to increase carcass weights (Tables 5 and 6).
The premium subsidy will also have implications for optimal feeding ratios.It would increase the share of concentrates on farms having the low silage price but keep the feeding ratios practically unchanged on farms having the high silage price (Table 6).

Results of sensitivity analysis
The simulated 15% changes in the meat and calf prices do not change the optimal timing of slaughtering but they have large impacts on farmer returns.If the meat price decreases by 15% the value of the optimal value function decreases by 17%.The decrease of 15% in calf price, on the other hand, increases the value of optimal value function by 9%.These simulation results are reported in more detail in Appendix 2.

Concluding remarks
Estimated optimal cattle feeding and slaughtering indicate that the Agenda 2000 reform has significant effects on the beef sector and on farmer incentives to raise animals in a country like Finland with its high production costs.If the European common reform is not supplemented by any domestic programs it will weaken the Table 5. Optimal decision rules and value functions at 2002 prices and subsidy rates.

Low
Medium High Carcass weight at slaughter kg 191.9 191.9 194.9 Age at slaughter months 10.9 10.9 10.9 Value function FIM 15,475.914,289.911,828.9Concentrate/roughage ratio % DM* 32/68.933/67.942/58.9 * The %-share of concentrate over the %-share of silage in total amount of dry matter in the diet.The predicted supply effect of the Agenda 2000 reform is large, because the subsidy payments dominate farmer decisions to choose most profitable timing of slaughtering.The reform will make these payments even more dominant than they were in 1998.It will also reschedule the subsidy payments earlier such that farmer incentives to rear heavy animals is significantly decreased.
The Agenda reform has also important implications for optimal feeding ratios.The general tendency is that concentrates are substituted for silage more than before the reform, because silage price is based on high domestic production costs but the price of concentrates follow decreased market prices.When silage is priced at average variable costs (medium price in the text), the amount of silage in the optimal feeding ratio is predicted to decrease by 12%.The share of silage will be decreased in feeding by 9%-points (from 76% to 67%).The Agenda reform gives reason to be concerned about animal welfare, since it will alter the optimal diet apart from the ruminants' natural diet.Rich feeding ratios are expected to decrease ruminants welfare (Huhtanen 1998).
The Agenda reform is predicted to increase farmer returns because subsidies are increased and farmers will adjust feeding and the timing of slaughtering to the decreased prices.Nevertheless, if Agenda reform is supplemented by a domestic subsidy enhancing the supply of beef, this subsidy has negligible effects on farmer income.Raising heavier animals increases the production costs of beef.Thus the subsidy can be interpreted as a subsidy for consumers rather than an income subsidy for beef producers.
In summary, the results of this study support the foundations of Seppälä et al. (1999) indicating that Agenda reform increases farmer income and the share of concentrates in the optimal feeding ratios, but the optimal carcass weight decreases and hence the supply for domestic beef.Vol. 11 (2002)

Fig. 1 .
Fig. 1.Meat price thresholds and the optimal carcass weights in 1998 and 2002.

Table 1 .
Input prices in 1998 and 2002.

Table 3 .
Subsidy rates for beef production in 1998 and 2002.

Table 6 .
Decisions rules and value functions under a premium subsidy for heavy animals.The %-share of concentrate over the %-share of silage in total amount of dry matter in the diet. * : 3-11.