Modeling the Profitability of Milk Production—A Simulation Approach

Abstract

Dairy farm profitability in the European Union has become increasingly volatile following market deregulation, complicating farm operations and undermining food security amid geopolitical tensions. To address the need for a streamlined analytical tool, this study develops a simulation model of milk production profitability tailored to small, open economies, using Poland as a case study. The model defines a profitability coefficient as the ratio of sector-level milk revenues to feed costs and decomposes it into three dynamic components: production efficiency (milk yield per feed unit), the price spread between milk and feed, and the net effect of policy interventions on revenues and costs. Exogenous variables (milk prices, feed prices, and policy support indices) are projected under baseline, optimistic, and pessimistic scenarios, while endogenous variables (profitability, herd size, and yield) evolve recursively based on estimated lags reflecting biological and economic responses. Simulation results for 2023–2027 indicate that profitability trajectories hinge primarily on price spreads, with policy measures playing a stabilizing but secondary role. Optimistic scenarios yield significant increases in profitability, whereas pessimistic assumptions lead to significant declines. These findings highlight the need to balance key market drivers—such as the relationship between milk prices and feed costs—with appropriately designed support instruments for milk producers. The model provides policymakers with a tool to adjust interventions so that support instruments are effective but do not lead to excessive reliance on public assistance.

1. Introduction

Financial viability constitutes an indispensable pillar of sustainability in the dairy sector. Empirical evidence indicates that smallholder farms achieve satisfactory returns only when adequate milk yields coincide with remunerative market prices [1], while the competitive environment shaped by EU membership critically alters profit margins and market conduct [2]. Cross-country decomposition analyses further reveal that differential milk yields account for the pre-eminent share of profitability dispersion, surpassing both cost advantages and price premia [3]. Even dairy farms that generate additional income through on-farm processing or specialty dairy products often face challenges in maintaining profitability if they do not carefully control their production and operating costs [4]. Compounding these structural factors, pronounced cyclical fluctuations in European milk prices—generated by biological lags and magnified by policy and macroeconomic shocks—intensify income volatility [5]. Collectively, these findings underscore that robust financial performance is a sine qua non for genuine sustainability: without stable profits, dairy producers lack the capacity to invest in low-carbon technologies, animal-welfare enhancements, and resilience measures essential to long-term environmental and social objectives.

The profitability of the milk market is intricately shaped by a confluence of support mechanisms and market dynamics that vary significantly across global contexts. Government interventions—ranging from subsidies to robust risk management programs—are critical in stabilizing prices and augmenting profitability for dairy producers [6]. Despite the significant role of government and EU support systems (including CAP instruments), challenges persist, particularly when it comes to moving toward higher-value dairy processing. Numerous enterprises struggle to maintain profitability, even with enhanced revenue streams [4]. This raises a pivotal question in the modeling of the profitability of dairy producers: to what extent do political support mechanisms outweigh the necessity for production efficiency? As we explore this question, it becomes clear that while government interventions are instrumental in providing immediate relief and stabilizing income for dairy producers, the pursuit of operational efficiency and innovation is essential for ensuring sustainable profitability in the long term. Understanding these dynamics is crucial for effective policy-making in the dairy sector.

The deregulation of the European Union’s milk market has led to a notable increase in the volatility of milk prices. In the context of strong isolation of the EU market from external factors, the price volatility of milk is primarily driven by seasonal patterns and long-term trends (see Figure 1). Currently, the influence of local factors on milk prices has significantly diminished, with cyclical fluctuations now being the main source of volatility [7]. The cycles observed in the milk market are not solely determined by the breeding cycles of cows, which depend on the time required for an increase in milk production to manifest after a farmer’s decision to expand production. Political, institutional, economic, and environmental factors are increasingly influential [8]. As a result, the profitability of dairy farms is now characterized by significant fluctuations, which considerably complicates their operations. Combined with growing demands for reducing the environmental impact of agriculture and improving animal welfare, this situation discourages some farmers from continuing milk production.

Maintaining the production potential of the dairy sector is a crucial component of the European Union’s food security, particularly in the context of the current geopolitical tensions. Consequently, the high volatility of milk purchase prices presents a significant challenge for economic policy measures aimed at stabilizing the incomes of milk producers. At present, dairy farmers’ incomes are indirectly stabilized through the so-called “safety net” [9]. This mechanism includes the possibility of intervention purchases on the market for skimmed milk powder and butter, but also other instruments such as payments for private storage, which are used in countries such as Spain, France, and Italy. At the same time, the European Commission has access to non-standard support instruments for agricultural producers in crisis situations [10]. Another example was in 2023, when the Commission provided support for grain and oilseed producers due to increased supply from Ukraine [11]. Given the growing importance of unconventional support tools used to stabilize farmers’ incomes, the question arises as to how to measure their impact on the profitability of milk production. This is crucial for the calibration of implemented support programs and the efficient use of public funds. Insufficient support may prove ineffective in improving farmers’ incomes, while excessive support could lead to further market destabilization.

There are numerous simulation models that can be utilized to conduct analyses of the dairy market. One of the most significant models is AGMEMOD (Agricultural Member States MODelling), which was specifically designed to assess the effects of agricultural policy in European Union countries. It has been employed, for instance, to evaluate the consequences of dairy market deregulation [12,13], the effects of the United Kingdom’s exit from the EU [14], policies aimed at reducing agriculture’s negative impact on the climate [15], and long-term projections concerning the state of EU agriculture [16].

Another example of a model used for simulation purposes is CAPRI (Common Agricultural Policy Regional Impact). Applications of the CAPRI model include simulations of the impact of EU dairy market deregulation on the competitiveness of Polish dairy products [17] and modeling greenhouse gas emissions from the livestock sector [18]. A widely used alternative is the FAPRI (Food and Agricultural Policy Research Institute) model, which is also a dynamic system of partial equilibrium models. It has been applied to simulations assessing the impact of Brexit on UK agriculture [19], the effects of trade liberalization associated with the WTO Doha Round on Ireland’s dairy sector [20]. Another frequently utilized tool is the AGLINK-COSIMO model, which is also a dynamic system of partial equilibrium models. This model is employed by the FAO and OECD to produce medium-term projections for key agricultural markets [21]. The AGLINK-COSIMO model has also been applied in studies such as [22] on the impact of economic growth volatility on food security and [23] on the effects of a low-carbon economy on agriculture.

The models discussed above are highly complex simulation tools that rely on numerous interdependencies between markets. When conducting simulations in small, open economies, such as Poland, where agricultural commodity prices should generally be treated as exogenous variables, these models may appear to exceed the actual analytical needs. Therefore, the objective of this study is to fill this gap in the literature by proposing a simplified simulation tool tailored to the analysis of agricultural policy effects in small, open economies.

The aim of this article is to introduce a simulation tool that allows for the modeling of milk production profitability and its implications for the entire dairy sector, with a particular focus on the balance between political support mechanisms and production efficiency. This tool can aid in making economic policy decisions, not only from the perspective of interventions aimed at stabilizing farmers’ incomes but also in assessing the impact of regulations affecting agricultural operating costs. Although the model was calibrated with Polish data, its framework is applicable to other agricultural markets and EU countries.

The article is structured as follows. The Section 1 outlines the background of the study, reviews the key literature, and presents the main research questions, including the motivation for developing a new simulation tool. The Section 2 describes the theoretical framework, key assumptions, and the approach used for forecasting and scenario analysis. The Section 3 introduces the estimated model and simulates milk production profitability for the years 2023 to 2027 for the baseline, optimistic, and pessimistic scenarios. The Section 4 summarizes the presented model and the results obtained and outlines the conclusions drawn from the analysis.

2. Materials and Methods

2.1. Assumptions of the Simulation Model

The starting point for developing a simulation model was the proper definition of the profitability coefficient for dairy production. At the sectoral level of dairy production, it can be defined by the following formula:

$$O{P}_t={\displaystyle \frac{Y_{mt}·P_{mt}}{X_t·P_{xt}}}$$

(1)

where:

$O{P}_t$ represents the profitability coefficient of dairy production in year t;

$Y·P_{mt}$ represents total revenue, calculated as the product of the total volume of milk collected at sector level $Y_{mt}$ ($Y_{mt}={\sum }_i^n{y}_{mti}$, where $y_{mti}$ is the quantity of milk collected from an individual producer), and the average milk purchase price at sector level $P_{mt}$ (defined as: $P_{mt}={\displaystyle \frac{{\sum }_i^n{p}_{mti}}{Y_t}}$ where $p_{mti}$ represents the price received by an individual milk producer);

$X_t·P_{xt}$ represents the cost of feed used for dairy cattle at the sector level, determined as the product of total feed consumption and the price paid for its purchase, where $X_t={\sum }_i^n{x}_{ti}$ and the average feed price at the sector level is $P_{xt}={\displaystyle \frac{{\sum }_i^n{P}_{xti}}{X_t}}$, where $x_{ti}$ and $p_{ti}$ represent the quantity of feed used and the price paid by individual dairy producers, respectively.

By incorporating sector-wide data, this method provides a comprehensive approach to analyzing the economic viability of dairy farming in small, open economies. The profitability coefficient OP_t > 1 means that milk production is profitable, with the model focusing solely on milk revenues and feed costs, excluding other related activities. This choice reflects the fact that feed constitutes the largest and most volatile component of production costs in dairy farming and thus has the most direct impact on profitability. This simplification allows the profitability coefficient to be clearly separated into revenue and cost components, making the model a practical tool for policy and market analyses in small, open economies. To evaluate the efficiency of dairy producers, it is important to distinguish between production efficiency (milk yield per cow) and the milk-to-feed price ratio as the main determinants of profitability.

The profitability coefficient $O{P}_t$ can thus be reformulated as an index of production efficiency and price relations (price spread):

$$O{P}_t={\displaystyle \frac{Y_{mt}}{X_t}}\ast {\displaystyle \frac{P_{mt}}{P_{xt}}}\ast 100\%=e{f}_t\ast p_{mxt}\ast 100\%$$

(2)

where:

$e{f}_t=\left({\displaystyle \frac{Y_{mt}}{X_t}}\right)$ = (${\displaystyle \frac{Y_t={\sum }_i^n{y}_{mti}}{X_t={\sum }_i^n{x}_{ti}}}$) represents production efficiency, which, in this context, is defined as the volume of milk production relative to the quantity of feed used for dairy cattle, measured at the sectoral level;

$P_{mxt}={\displaystyle \frac{P_{mt}}{P_{xt}}}$ $\Leftarrow$ {$p_{mt}={\displaystyle \frac{{\sum }_i^n{p}_{mti}}{y_t}}$}/$\{p_{xt}={\displaystyle \frac{{\sum }_i^n{p}_{xti}}{x_{t\}}}}\}$ represents the price ratio of milk to feed costs (i.e., the price spread), calculated for the entire sector.

Equation (2) distinguishes two main drivers of profitability: production efficiency and the price spread between milk and feed. Analyzing changes in these components over time helps to better reveal how profitability evolves in response to market or policy shifts.

A key element in constructing the model is incorporating the effects of economic policy into Equation (1), including sectoral interventions and other forms of direct or indirect support that increase revenues and/or reduce costs. The extended Equation (1) can be expressed as:

$$O{P}_t={\displaystyle \frac{Y_{mt}\ast P_{mt}\ast W_{Yt}}{X_t\ast P_{xt}\ast W_{Xt}}}$$

(3)

where:

$W_{Yt}={\sum }_{i=1}^n{\displaystyle \frac{w_{Yti}}{P_{mt}}}$ is the price enhancement index, which reflects the impact of various support instruments on the purchase price of milk, measured as the sum of financial support that increases producers’ revenues relative to the market price of milk. In other words, it represents the total amount of subsidies or financial aid that effectively raises milk producers’ incomes;

$W_X={\sum }_{i=1}^n{\displaystyle \frac{w_{Xti}}{P_{xt}}}$ is the cost reduction index, which represents the effect of various intervention measures on reducing input costs. It is calculated as the sum of financial support that lowers production costs, relative to the market price of feed inputs.

In the next step, for dynamic analysis, the model is expressed in logarithmic and differentiated form (Equations (4)–(6)).

To achieve this, Equation (3) was transformed using natural logarithms:

$$\mathit{ln}{OP}_t={\mathit{ln}Y}_{mt}+\mathit{ln}{P}_{mt}+ln{W}_{Yt}-ln{X}_t-\mathit{ln}{P}_{xt}-ln{W}_{Xt}$$

(4)

Subsequently, to capture the sources of changes in the profitability coefficient in a dynamic framework, Equation (4) was differentiated with respect to time:

$$r_t^{OP}={\displaystyle \frac{\dot{Y_{mt}}}{Y_{mt}}}+{\displaystyle \frac{\dot{P_{mt}}}{P_{mt}}}+{\displaystyle \frac{\dot{W_{Yt}}}{W_{Yt}}}-{\displaystyle \frac{\dot{X_t}}{X_t}}-{\displaystyle \frac{\dot{P_{xt}}}{P_{xt}}}-{\displaystyle \frac{\dot{W_{Xt}}}{W_{Xt}}}$$

(5)

where $r_t^{OP}$ represents the rate of change in the profitability of dairy production in year t.

As Equation (5) demonstrates, the rate of change in dairy production profitability is primarily determined by the ratio of the growth rate of revenues to the growth rate of the inputs required to generate those revenues, with additional adjustments stemming from the impact of agricultural policy support measures. Intuitively, the relationship between revenue dynamics and input cost dynamics should be the dominant factor shaping profitability changes, while the policy-induced support effects should play a corrective role.

If, instead, policy support effects were the primary driver of profitability changes, this would imply that government interventions, rather than market fundamentals, are sustaining dairy production. While this may be a common scenario at the level of individual farms, if applied to the entire sector, it would suggest that its operation lacks economic justification and is sustained purely through economic policy interventions. Such a situation would raise concerns about the long-term viability and market efficiency of the sector, highlighting its dependence on external support rather than competitive economic performance.

A key aspect of analyzing changes in dairy production profitability is the relationship between the variables that determine the dynamics of revenues, costs, and agricultural policy support effects. This approach allows for sensitivity analysis of dairy production profitability under different assumptions within simulation frameworks. Accordingly, Equation (5), which expresses the dynamics of profitability, can be rewritten as the sum of the growth rates of its individual components:

$$r_t^{OP}=\left(r_t^{Y_m}+r_t^{{\mathrm{P}}_{\mathrm{m}}}+r_t^{W_Y}\right)-(r_t^X+r_t^{{\mathrm{P}}_{\mathrm{x}}}+r_t^{W_X})$$

(6)

where:

$r_t^{OP}$ represents the rate of change in the profitability of dairy production in year t;

$r_t^{Y_m}$ denotes the growth rate of milk production in year t;

$r_t^{{\mathrm{P}}_{\mathrm{m}}}$ represents the growth rate of milk purchase prices in year t;

$r_t^{W_Y}$ refers to the growth rate of policy interventions aimed at supporting milk producers’ revenues in year t;

$r_t^X$ represents the growth rate of feed consumption by dairy cows in year t;

$r_t^{{\mathrm{P}}_{\mathrm{x}}}$ denotes the growth rate of feed prices for dairy cattle in year t;

$r_t^{W_X}$ represents the growth rate of policy interventions aimed at reducing dairy production costs in year t.

This formulation allows for a decomposition of profitability changes into the fundamental drivers thereof: production dynamics, price fluctuations, and policy interventions. By reorganizing the components of Equation (6), three primary determinants of the dynamics of dairy production profitability in year t can be distinguished:

$$r_t^{OP}=(r_t^{Y_m}-r_t^X)+(r_t^{{\mathrm{P}}_{\mathrm{m}}}-r_t^{{\mathrm{P}}_{\mathrm{x}}})+{(r}_t^{W_Y}-r_t^{W_X})$$

(7)

where:

$(r_t^{Y_m}-r_t^X)$ represents the dynamics of production efficiency in year t;

$(r_t^{{\mathrm{P}}_{\mathrm{m}}}-r_t^{{\mathrm{P}}_{\mathrm{x}}})$ captures the dynamics of the price spread in year t;

${(r}_t^{W_Y}-r_t^{W_X}$) denotes the dynamics of the profitability support index in year t.

By dividing Equation (7) by the growth rate of dairy production profitability in year t, the relative contributions of each component to profitability dynamics can be derived:

$$1={\displaystyle \frac{r_t^{Y_m}-r_t^X}{r_t^{op}}}+{\displaystyle \frac{r_t^{{\mathrm{P}}_{\mathrm{m}}}-r_t^{{\mathrm{P}}_{\mathrm{x}}}}{r_t^{op}}}+{\displaystyle \frac{r_t^{W_Y}-r_t^{W_X}}{r_t^{op}}}$$

(8)

Simplifying Equation (7), it becomes evident that the dynamics of dairy profitability can be decomposed into three core elements:

Simplifying Equation (7), one can observe that the dynamics of milk production profitability are determined by the dynamics of milk yield efficiency (ef), the dynamics of the price scissors (p_mx), and the dynamics of the ratio of support indices (wywx).

$$r_t^{op}=r_t^{ef}+r_t^{pmx}+r_t^{wywx}$$

(9)

This perspective is crucial for policymakers shaping agricultural policy, as it allows for the identification of the extent to which each component contributed to changes in the profitability of milk production. It also enables the quantification of the effects of implemented agricultural policies and provides a precise assessment of how specific policy measures have influenced changes in milk production profitability. Moreover, the proposed approach facilitates the simulation of various scenarios to determine the scale of intervention required to achieve a desired change in profitability. This is critical not only for mitigating the impacts of shocks in the milk market but also for ensuring the efficient allocation of public resources.

2.2. Simulation Model for the Milk Market

In the theoretical framework of the simulation model outlined in the previous section, two categories of variables can be distinguished: endogenous and exogenous variables. The set of exogenous variables includes: $P_{mt}$, $P_{xt}$, $P_{mxt}$, $W_{Yt}$, $W_{Xt}$, $intak{e}_t$ (representing the amount of feed consumed per cow in year t, necessary for calculating milk yield), $r_t^{{\mathrm{P}}_{\mathrm{m}}}$, $r_t^{W_Y}$, $r_t^{{\mathrm{P}}_{\mathrm{x}}}$, $r_t^{W_X}$, $r_t^{ef}$, $r_t^{pmx}$, $r_t^{wywx}$.

Conversely, the set of endogenous variables comprises: $O{P}_t$, $Y_{mt}$, $X_t$, $e{f}_t$, $her{d}_t$ (representing the size of the dairy herd in year t, necessary for calculating milk yield), $r_t^{op}$, $r_t^{Y_m}$, $r_t^X$.

The relationships among variables, including those enabling the forecasting of their future values, are determined in the model using two primary methods:

• identity equations, i.e., fixed (time-invariant) mathematical relationships and formulas that allow for the derivation of the values of certain variables based on the values of others. These equations are grounded in definitional identities and structural interdependencies and were implemented in Microsoft Excel for step-by-step simulation of variable values.
• econometric equations, i.e., mathematical expressions designed to forecast the variables of interest based on estimated historical statistical relationships. These forecasts were generated using ARIMA econometric models and causal models, estimated in RStudio 4.1.2, and calibrated with expert adjustments and scenario assumptions. All data used in the model were sourced from Polish datasets (FADN, Statistics Poland, and national market reports). The Wyt and Wxt indices were estimated using the average level of financial support received by Polish dairy farms, such as direct payments and market interventions. In the baseline scenario, these indices were held constant, reflecting an assumption of unchanged policy during the forecast period.

A key feature that determines the model’s usefulness for simulation purposes is its recursive structure. in the proposed simulation model is based on causal relationships and is embedded in two core equations:

• The equation describing the size of the dairy herd is ${Herd}_t=F\left(r_{t-2}^{OP}\right)$. Here, the change in the dairy herd is modeled as a function of the change in milk production profitability observed two years prior. According to the estimated equation, an improvement in profitability leads, with a two-year lag, to an increase in the size of the dairy herd. This lag structure is consistent with the biological cycle of the dairy sector, in which a farmer’s decision to expand production and purchase heifers in response to improved profitability materializes in herd growth after approximately two years.
• The equation describing milk yield (productivity) is ${ef}_t=F\left(r_{t-2}^{OP}\right)$. The estimated relationship indicates that an increase in milk production profitability discourages farmers from pursuing higher productivity, whereas a decline in profitability incentivizes them to seek ways to increase revenues, including through improvements in milk yield.

A detailed specification of the variables and equations is presented in

Table 1. Detailed Specification of Variables and Equations Used in the Simulation Model for the Milk Market Assumptions on Exogenous Variables in the Optimistic Scenario.

Equation	Number	Description
see Equation (1)	(1)	The equation describes a simplified measure of milk production profitability in year t (it does not account for certain aspects of activity, such as the production and sale of livestock). The numerator reflects the aggregated revenues of milk producers in year t, while the denominator captures the aggregated costs related to feed consumption in the same year.
see Equation (2)	(2)	The transformation of Equation (1) enables the decomposition of milk production profitability into two components: one attributable to milk yield (productivity), and the other resulting from the price scissors effect.
see Equation (3)	(3)	Equation (3) represents an extension of Equation (1) by incorporating the effects of economic policy interventions in year t. These intervention effects are accounted for separately on the revenue and cost sides.
see Equation (4)	(4)	Equation (4) is the logarithmic transformation of Equation (3), allowing for the transition from levels to growth rates (dynamics).
see Equation (5)	(5)	Equation (5) is the time-differentiated version of Equation (4), which enables the representation of changes in milk production profitability in a dynamic framework.
see Equation (6)	(6)	Equation (6) is a modification of Equation (5), in which the ratios of variable increments over time to their initial levels are, for simplicity, expressed in terms of growth rates (dynamics).
see Equation (7)	(7)	Equation (7) is a rearranged form of Equation (6), aimed at isolating the following components of the dynamics of milk production profitability in year t: the dynamics of production efficiency in year t, the dynamics of the price scissors in year t, and the dynamics of the support index for production profitability in year t.
see Equation (8)	(8)	Equation (8) is derived by dividing both sides of Equation (7) by the growth rate of milk production profitability in year t. In this way, it reflects the relative contributions of the individual components to the overall dynamics of profitability: the dynamics of production efficiency in year t, the dynamics of the price scissors in year t, and the dynamics of the support index for milk production profitability in year t.
see Equation (9)	(9)	Equation (9) is a simplified version of Equation (7), which shows that the dynamics of milk production profitability consist of the dynamics of milk yield efficiency (ef), the dynamics of the price scissors (p_mx), and the dynamics of the ratio of support indices (wywx).
${Herd}_t=F\left(r_{t-2}^{OP}\right)$	(10)	The econometric equation reflects the relationship between milk production profitability in year t–2 and the size of the dairy herd in year t. The lag structure stems from the rigidity of milk supply—approximately two years are required for changes in profitability to be reflected in herd size. This equation introduces a recursive structure into the model, capturing the delayed supply-side adjustment characteristic of the dairy sector.
${ef}_t=F\left(r_{t-2}^{OP}\right)$	(11)	The econometric equation reflects the relationship between milk production profitability in year t–2 and milk yield in year t. It can be expected that high profitability reduces the incentive for milk producers to improve productivity given the existing production apparatus. Together, Equations (10) and (11) enable the forecasting of milk supply volumes within the model framework.

Source: Own elaboration.

.

This multi-equation approach allows the model to reflect interdependencies within the milk market, so changes in one variable affect the entire system. This structure is essential for simulating the broader impacts of agricultural policy interventions.

3. Results

3.1. Simulation Using the Model

To assess the applicability of the simulation tool, a sample estimation was conducted and forecasts were prepared for the period 2023–2027. The period 2023–2027 was selected to ensure that the simulation covers both the most recent data available and a relevant policy horizon for the Polish and EU dairy sectors. The simulation was based on the following assumptions regarding exogenous variables:

• In the baseline scenario, it was assumed that the global dairy market would enter an upward phase of the cycle in 2024, lasting until 2026, after which farm-gate milk prices were expected to decline again. The projected milk price trajectory is presented in Figure 2.
• In the baseline scenario, it was also assumed that feed prices would decline in 2023 and 2024, reflecting adjustments in global grain and oilseed supply following the outbreak of the war in Ukraine in 2022. The anticipated decline in the profitability of grain and oilseed production was expected to reduce supply, exerting upward pressure on prices from 2025 onward. This trend was expected to affect domestic cattle feed markets as well. The projected feed price trajectory is shown in Figure 3.

All simulations were conducted under a no policy change assumption, implying the absence of any new economic policy interventions. The data used in the simulations were sourced from Statistics Poland (GUS), Eurostat, and the Institute of Agricultural and Food Economics—National Research Institute (IERiGŻ).

Figure 4 presents the annual growth rates of milk productivity, the price scissors, and support indices, as well as the resulting growth rate of milk production profitability. The results indicated that the dynamics of profitability were shaped primarily by changes in the price relationship between milk and feed, as well as by fluctuations in policy support, while growth in productivity remained relatively stable over the forecast period. The simulation suggested that after a sharp decline in 2023, profitability was expected to gradually improve in subsequent years, mainly due to a recovery in the price scissors component.

According to the simulation results, the coming years are expected to bring a continued gradual increase in milk yield. This growth will be a function of past milk production profitability as well as the ongoing professionalization of dairy farms. Professionalization should be understood as the increasing share of market-oriented farms in the total number of dairy farms.

The projected decline in the dairy cattle population reflects trends observed in recent years, associated with the gradual exit of smaller farms from milk production. It is important to note, however, that the forecasted decrease in the number of dairy cows (Figure 5) will be more than offset by improvements in milk yield (Figure 6). As a result, total milk production is expected to rise over the forecast horizon.

3.2. Scenario Analysis

To conduct the sensitivity analysis presented in the previous section, two alternative scenarios were estimated: an optimistic scenario and a pessimistic scenario.

The optimistic scenario assumed that the trajectory of farm-gate milk prices Pmt would evolve above the baseline scenario while the trajectory of feed prices Pxt would remain below that assumed in the baseline. Conversely, the pessimistic scenario assumed that the milk price path Pmt would evolve below the baseline and the feed price path Pxt would turn out to be higher than projected under the baseline assumptions.

To derive the trajectories of exogenous variables required for estimating these alternative scenarios, confidence intervals calculated during the baseline forecast exercise were employed. For milk prices, the alternative paths corresponded to the 80% upper bound of the confidence interval in the optimistic scenario and the 80% lower bound in the pessimistic scenario. For feed prices, the optimistic scenario used the 80% lower bound, while the pessimistic scenario adopted the 80% upper bound of the respective confidence interval.

This approach served two main purposes. First, it reduced the arbitrariness of the assumptions regarding the future paths of exogenous variables in alternative scenarios. Second, it enabled the simulation to be interpreted as a stress test, allowing for the analysis of the resilience of domestic milk producers to price shocks in the milk and feed markets.

The projected trajectories of the exogenous variables used in the simulation are presented in the figures below (Figure 7 and Figure 8). For variables related to income support for milk producers and cost-reduction measures, the assumption of no change in economic policy relative to the baseline scenario was maintained. This was based on the reasoning that, through appropriate policy calibration, it would be possible to offset the effects of deviations in milk and feed prices relative to the baseline. However, such compensation would significantly reduce the analytical value of the alternative scenarios, which, in their current form, serve as extreme condition tests for the domestic dairy market.

At the same time, the results obtained from this approach provide a foundation for estimating the scope and nature of a potential policy response that could stabilize the market. This has important implications for policymakers responsible for shaping agricultural and economic strategies.

3.3. Optimistic Scenario

The assumptions regarding the trajectories of the exogenous variables are presented in the

Table 2. Assumptions on Exogenous Variables in the Optimistic Scenario.

	Average Farm Gate Milk Price Received by Farmers (PLN/liter)	Cattle Feed Price (PLN/kg)	Aggregate Effect of Income Support Interventions	Aggregate Effect of Cost-Reduction Interventions
	p_m	p_x	w_y	w_x
2023	2.08	1.87	1	1
2024	2.13	1.47	1	1
2025	2.79	1.44	1	1
2026	3.48	1.57	1	1
2027	3.19	1.38	1	1

Source: Own elaboration.

.

The endogenous variables estimated based on the assumed trajectories of exogenous variables are presented in Figure 9 below.

The simulation results indicate that the primary effect of the revised assumptions was a marked improvement in the price scissors (Figure 10). A more favorable ratio of farm-gate milk prices to feed prices reduced producers’ incentive to increase milk yield, although yield growth remained on a pronounced upward trajectory. Simultaneously, this improved price relationship was reflected in a slower decline in the dairy herd, notwithstanding the fact that the herd size continued to follow a substantial downward trend. Consequently, the slower growth in milk yield relative to the baseline scenario, coupled with a more modest reduction in herd size, resulted in a smaller increase in total milk production compared to the baseline projection.

According to the simulation results, the entire forecast horizon was characterized by a significant improvement in milk production profitability compared to the baseline scenario. This improvement was primarily driven by a favorable shift in the relationship between farm-gate milk prices and feed prices.

3.4. Pessimistic Scenario

The assumptions regarding the trajectories of exogenous variables are presented in the

Table 3. Assumptions on Exogenous Variables in the Pessimistic Scenario.

	Average Farm Gate Milk Price Received by Farmers (PLN/liter)	Cattle Feed Price (PLN/kg)	Aggregate Effect of Income Support Interventions	Aggregate Effect of Cost-Reduction Interventions
	p_m	p_x	w_y	w_x
2023	1.72	2.13	1	1
2024	1.27	2.13	1	1
2025	1.21	2.76	1	1
2026	1.32	3.43	1	1
2027	1.21	3.02	1	1

Source: Own elaboration.

.

The endogenous variables estimated based on the assumed trajectories of exogenous variables are presented in the Figure 11.

The simulation results indicate that the primary impact of the new assumptions was reflected in a significant deterioration of the price scissors. The unfavorable relationship between farm-gate milk prices and feed prices would compel dairy producers to increase milk yield in order to maintain profitability. At the same time, this adverse price relationship accelerated the decline in dairy herd size.

As a result, the faster increase in milk yield—compared to the baseline—combined with a sharper decline in herd size ultimately led to a greater increase in total milk production than that projected under the baseline scenario.

According to the simulation results (Figure 12), the entire forecast horizon was marked by a significant deterioration in milk production profitability compared to the baseline scenario. This decline was primarily driven by unfavorable changes in the relationship between farm-gate milk prices and feed prices, especially between 2023 and 2025. However, it should be noted that in 2026 and particularly in 2027, the price spread began to improve again, partially offsetting the previous negative trend (see Figure 12).

4. Discussion and Conclusions

The simulation—spanning the 2023–2027 period and calibrated to Polish data—showed unequivocally that dairy profitability is governed far more by the milk-to-feed price spread than by either technical efficiency or existing policy support. In the optimistic scenario, a strong terms-of-trade gain (about thirty percentage points relative to 2022) lifted the sector’s profitability index by nearly the same magnitude, even though milk yield rose only modestly and the dairy herd kept shrinking. In the pessimistic scenario, an equally large deterioration in the spread drove profitability down by more than a quarter, despite an aggressive productivity response and accelerated culling. The baseline path, with only a mild four-point improvement in the spread, yielded a correspondingly small, two-percent increase in profits.

These outcomes highlight several regularities. First, the price spread was twice as powerful as yield growth in moving profits, confirming classic price–cost theory. Second, supply reacted asymmetrically: higher profits merely slowed herd contraction, while lower profits hastened exit; productivity adjusted in the opposite direction, rising most rapidly when margins tightened. Third, the current ‘safety-net’ policy architecture played a stabilizing but marginal role; removing it would change the baseline projection by less than one percentage point. Finally, volume growth was shown to be able to coexist with falling profits: under the pessimistic shock, total milk output still edged upward because yield gains outweighed herd decline, yet producers were financially worse off.

The simulation results obtained for Poland are broadly consistent with the findings of similar studies conducted in other European countries and internationally. For example, previous studies [2,3] indicated that fluctuations in the relationship between output prices and feed costs are the primary driver of dairy profitability, with changes in productivity and policy support playing a secondary role. Another study [4] further demonstrated that even farms specializing in value-added products are vulnerable to deteriorating input-output price spreads, emphasizing the universal importance of market fundamentals for economic viability. These results confirm the robustness of the simulation approach used in this study and underline the relevance of the price spread between milk and feed costs as a key factor for profitability, not only in Poland but also in other small, open economies and dairy markets across the EU. By referencing these comparative studies, the model’s applicability and generalizability to other contexts is further supported.

Although the simulation tool was developed and calibrated for the Polish milk market, its structure—based on exogenous price shocks and sector-level efficiency—makes it applicable to other small, open economies in the EU with similar market characteristics, provided the model is recalibrated to country-specific data. The possibility of transferring the model to other economies results from its reliance on universal economic relationships—such as the impact of global price trends, production efficiency, and support instruments—rather than country-specific institutional arrangements.

The policy implications are clear. Support instruments that are activated when the gap between milk prices and feed costs becomes unfavorable can help stabilize milk producers’ incomes more efficiently and at a lower cost than general subsidies. While support instruments aimed at improving farm productivity are important, they cannot fully offset the impact of major increases in production costs. It is therefore advisable to carry out stress tests and scenario analyses before introducing new support instruments, to ensure that public funds are allocated effectively.