4.1.1. Optimal Level of Land Engagement

Area payments are characterized by linking the amount of granted support to the area of agricultural land used. Figure 1(a) illustrates the zero variant, i.e., a situation where this instrument is not applied. On the horizontal axis of the coordinate system, the amount of land input (in surface units, e.g., hectares) is plotted. Moving rightward along this axis reflects decreasing agricultural suitability of the land, as the most fertile and easily accessible plots are engaged in production first. Meanwhile, the vertical axis represents the level of a given economic variable, expressed in monetary units per unit of land input (homogeneous, single agricultural plot). The economic variables included in the chart in Figure 1(a) are marginal production cost, covering inputs of non-land production factors (i.e., labour and capital in the classical sense), and marginal revenue from the sale of agricultural produce. In the chart shown in Figure 1(b), the marginal revenue function graph in position MR₁ – besides revenue from the sale of agricultural products – also includes revenue from area payments.

The graph of the marginal cost (MC) function, understood as the increase in total costs (i.e. non-land production inputs) resulting from an increase in land input by one unit, is a declining line because the less fertile the land, the lower the amount of labour and capital required to maximize economic result (Sadłowski 2017). The graph of the marginal revenue function (MR₀), understood as the increase in total revenue from an increase in land utilization by one unit, is also a declining line. The negative slope of this line results from the fact that the most productive lands, generating the highest revenue from the sale of agricultural produce at given inputs, are engaged in production first. As less fertile and more peripherally located lands are engaged in the production process (moving rightward along the horizontal axis), the marginal revenue from each subsequent unit of land decreases.

The relative position of the graphs of the marginal cost and marginal revenue functions in Figure 1 is a consequence of the assumption that there are lands on which agricultural production is profitable even without area support (MR₀ runs above MC; these are lands located to the left of L₀, i.e. those with the greatest agricultural usefulness), and at the same time there are lands on which agricultural production would result in a loss (MR₀ runs below MC; these are lands located to the right of the L₀ point).

The area under the marginal cost (MC) curve represents total costs (TC), while the area under the marginal revenue (MR₀) curve represents total revenue (TR). The optimal level of land resource utilization in agricultural production is determined by the first coordinate of the intersection point of the MC function with the MR₀ function (E₀), i.e., L₀. At this level of land input, the economic result, understood as the surplus of total revenue over cost, is maximized, so the input of production factors other than land is also optimal.

Figure 1Level of land resource utilization in the variant without area payments (a) and with area payments (b) 

In contrast, Figure 1(b) illustrates a situation where agricultural activities are subsidized through the provision of financial support to farms proportional to the area of agricultural land used. In this case, production factors engaged in the production process are remunerated not only by the market (in the form of revenues from the sale of agricultural produce) but also by the state (in the form of area payments).

The rates of direct payments can be counted among the parameters of the economic calculation, which constitute the systemic conditions of management in agriculture. Farmers are forced to take payment rates into account in their economic decisions, although this is not enforced administratively, but by the threat of obtaining a worse economic result (Sadłowski 2023).

The area payment rate is uniform (not differentiated regionally or by land quality), so the introduction of this instrument can be graphically represented by a parallel upward shift of the MR₀ revenue function graph – by a segment |BC|, the length of which corresponds to the area payment rate PR – into position MR₁. As a result, the new equilibrium point for the farm will be point E₁, corresponding to a higher level of land input (L₁>L₀). Thus, lands that were previously not used for agricultural production (in the absence of area support) will be engaged in agricultural production. The length of the |L₀L₁| segment reflects the size of the additional land area (i.e., land engaged in production due to the introduction of area payments).1

Thus, area support provides an incentive for farms to increase land input, leading to an increase in the total area of agricultural land used in the country. However, if resource management is to be rational, there is no justification for increasing this area for reasons other than improved market conditions in agriculture.

4.1.2. Effects of Price Changes

The model allows for the consideration of price changes (in any direction) in both the markets for production factors and agricultural products. An increase/decrease in the prices of agricultural inputs or wages would result in an upward/downward shift of the marginal cost (MC) function graph. Meanwhile, an increase/decrease in the prices of agricultural products would be reflected in an upward/downward shift of the marginal revenue (MR) function graph.

4.1.3. Impact of Agricultural Tax

The presented model can also incorporate the impact of agricultural tax on the analysed variables. Given that the amount of agricultural tax decreases with the declining agricultural suitability of land, its effect can be represented by a non-parallel upward shift of the marginal cost function graph, proportional to the tax amount, such that the new function (MC₁) converges with the original function (MC₀) as it moves rightward along the horizontal axis. However, in the first quadrant of the coordinate system (where the analysis is conducted, as it corresponds to the values of the examined variables that make economic sense), there would be no intersection of these function graphs.

4.2.1. Land Rent as a Residual Amount

The remuneration for land, as a resource engaged in the production process, is a residual amount representing the surplus of revenues from the sale of agricultural produce (in the variant with area payments – increased by the revenues from these payments) over the production costs, which include inputs of non-land production factors. This is equivalent to economic profit. This conclusion recalls the Physiocratic thesis that land is the only surplus-generating production factor (Landreth & Colander 2001).

In the variant without area payments, as shown in Figure 1(a), the total remuneration for land at the farm’s equilibrium point (E₀) is represented by the area of triangle AE₀B. Meanwhile, the amount of land rent per unit of land area (homogeneous in terms of agricultural suitability) is symbolized by the vertical distance between the marginal cost (MC) function graph and the marginal revenue (MR₀) function graph. The amount of land rent decreases as we move rightward along the horizontal axis of the coordinate system, corresponding to the engagement of increasingly less agriculturally suitable land in the production process. The marginal cost (MC) function graph lies below the marginal revenue (MR₀) function graph for land that, at given production costs and agricultural product prices, is sufficiently suitable for profitable engagement in production.

4.2.2. Measures of the Impact of Area Payments

This section proposes the concept of three indicators, consistent with the presented model, for measuring the scale of area payments’ impact on the distribution sphere:

The subsidy coefficient for agricultural activities is defined as the ratio of the amount of granted area support to the farm’s total revenue, which includes revenue from the sale of agricultural products (sourced from the market) and revenue from area payments (sourced from the state). Thus, it indicates the portion of total revenue represented by area support. In other words, it shows what percentage of production factor remuneration is financed by the state.

The subsidy coefficient for agricultural activities (C_ASS) is expressed by the formula:

Where PR is the area payment rate, expressed in monetary units per area unit (m.u./ha); L is the land area covered by area support, expressed in area units (ha); and TR₁ is the total revenue from land covered by area support, including revenue from the sale of agricultural products and revenue from area payments, expressed in monetary units (m.u.).

The subsidy coefficient for agricultural activities is thus dimensionless and can take any value in the closed interval from 0 to 100%. The coefficient equals zero when the remuneration of production factors is entirely derived from the production of goods, which only occurs when the sole source of funding for inputs is the market. This situation corresponds to the zero variant shown in Figure 1(a). In contrast, in the variant shown in Figure 1(b), the value of this coefficient is greater than zero and increases as the agricultural suitability of the land decreases (i.e., the lower the land’s productivity, the greater the portion of production factor remuneration that comes from area support). However, it does not reach 100%, as long as agricultural activities on the marginal land L₁ generate any revenue from the sale of agricultural products (in Figure 1(b), the amount of this revenue is represented by segment |L₁D| ). The development of the subsidy coefficient for agricultural activities about the land’s agricultural suitability is illustrated by the dotted line graph in Figure 2. The second coordinate of the points on the graphs presented in Figure 2 should be interpreted as the value of a given coefficient in relation to a unit, homogenic agricultural plot (with area close to zero), included in a farm, which is in the equilibrium point under the conditions of application of area support of a given payment rate (E₁), and thus involves L₁ agricultural land inputs in the production process. The graph is illustrative; it shows the development of the analysed variables at a given relation of the payment rate to the production costs and revenue from the sale of the cultivated agricultural product.

In Figure 1(b), the value of the subsidy coefficient for agricultural activities for a specific homogeneous, one hectare land plot is the ratio of the vertical distance between the MR₀ line and the MR₁ line (i.e., the area payment rate PR) to the vertical distance between the horizontal axis and the MR₁ line. Meanwhile, the value of this coefficient for a farm at equilibrium point E₁ (i.e., using land input of size L₁ for production) is the ratio of the area of parallelogram CBDE₁ to the area of trapezoid COL₁E₁.

Within the proposed model, a theoretical decomposition of production factor remuneration is made into income from non-land production factors and land rent. For the variant with area payments, these two fractions of remuneration are further divided into part financed by the market and part financed by the state. This allows for the introduction of two additional indicators: the state co-financing coefficient of land rent and the land rent-creation coefficient by area payments.

Based on Figure 1(b), it can be concluded that area support entirely contributes to land remuneration in the case of land that was used for agricultural production even in the absence of area payments (0<L≤L₀). However, for land that was brought into production only after the introduction of area payments at rate PR (L₀<L≤L₁), area support partly constitutes land remuneration and partly constitutes remuneration for other production factors. It is worth noting that, as we move rightward along the horizontal axis of the coordinate system from L₀, an increasing portion of area support contributes to the remuneration of labour and capital, while the portion allocated to land remuneration decreases. This means that, as land productivity decreases, the market’s role in remunerating labour and capital diminishes, while the state’s role increases. In the extreme case of the marginal land plot L₁, area support entirely contributes to labour and capital remuneration, while land rent equals zero.

To measure what portion of land remuneration is financed by the state, we can introduce the state co-financing coefficient of land rent (cLRf) expressed by the formula:

Where TC is the total cost, i.e. non-land production inputs, in relation to the land area covered by area support, expressed in monetary units (m.u.).

Like the subsidy coefficient for agricultural activities, the state co-financing coefficient of land rent is dimensionless and can take any value in the closed interval from 0 to 100%. Taking into account Figure 1(b), we can see that for the unit plot L₀ and for plots located to the left of it, the state’s contribution to financing land rent is expressed by the ratio of the area payment rate (PR) to the vertical distance between the MC line and the MR1 line. This ratio increases as one moves rightward along the horizontal axis. For plots located to the right of L₀ (up to and including L₁), the state’s contribution to financing land rent is 100% (since, in this case, both the numerator and the denominator of the fraction expressing this contribution represent the same number corresponding to the vertical distance between the MC and MR₁ lines). However, this does not change the fact that, in absolute terms, land rent decreases as one moves rightward along the horizontal axis of the coordinate system. The dashed line graph in Figure 2 illustrates how the value of the state co-financing coefficient of land rent changes depending on the agricultural suitability of the land. In relation to the entire farm located at the equilibrium point E₁, the state’s contribution to financing land rent is expressed as the ratio of the area of trapezoid CBE0E1 to the area of triangle CAE₁ (Figure 1(b)).

The land rent-creation coefficient by area payments (C_LRc) indicates what portion of area support increases land rent. This indicator can be expressed using the following formula:

Where ΔLR is the increase in land rent due to the introduction of area payments, expressed in monetary units (m.u.).

Figure 2Values of the indicators measuring the impact of area payments on the distribution sphere depending on the agricultural suitability of the land 

Just like the indicators expressed by formulas (1) and (2), the land rent-creation coefficient by area payments is dimensionless, and the possible values for this indicator range from 0% to 100%. Based on Figure 1(b), it can be concluded that for land that was used for agricultural production even in the absence of area support (0 <L ≤ L₀), the value of this coefficient is 100%. However, for land that was brought into production only after the introduction of area payments at rate PR (L₀ <L ≤ L₁), this coefficient is less than 100% and decreases as one moves rightward along the horizontal axis of the coordinate system (reaching zero for the unit plot L₁). For example, for a homogeneous, one hectare unit plot L_H, the land rent-creation coefficient equals the percentage ratio of the length of segment |GH| to the length of segment |FH| (segment |FH| reflects the area payment rate PR). Observing the continuous line graph in Figure 2, one can see how the value of this coefficient changes depending on the agricultural suitability of the land. Meanwhile, the value of the land rent-creation coefficient by area payments for all land included in the farm located at the equilibrium point E1 can be calculated as the percentage ratio of the area of trapezoid CBE₀E₁ to the area of parallelogram CBDE₁ (Figure 1(b)).

4.2.3. Implications for Lease Rent and Agricultural Land Prices

In cases where the user of the land is not its owner, land rent takes the form of lease rent. As a result of area payments being at least partially transformed into land rent, there is a phenomenon of “capturing” support by landowners through corresponding increases in lease rent or land sale prices. In situations where land ownership is separate from land use, the land rent-creation coefficient measures the extent to which area payments are “captured” by landowners.

The “capture” of area support by agricultural landowners manifests itself in higher lease rent rates and higher agricultural land prices, i.e., the capitalization of payments. This occurs when the landowner is not identical to the land user, and when the land is subject to market transactions. “Capturing” the payments involves factoring part or all of the area support into the lease rent (in the case of leasing) or the land price (in the case of selling), as a consequence of increased discounted income from agricultural land due to the area payments.

The increase in the stream of discounted income from area payments (∆DIS_AP) can be calculated using the following formula:

Where C_LRc is the land rent-creation coefficient by area payments (dimensionless); r is the annual interest rate; and (n+1) is the number of years of area payment application.

The increase in lease rent for a given year following the introduction of area payments corresponds to the increase in the annual income stream due to these payments, while the entire increase in the stream of future discounted incomes will be capitalized in the land price. Therefore, the first component of the sum in formula (4) represents the theoretical increase in lease rent in the first year of area payment application, while the entire sum represents the theoretical increase in land price in the event of a sale at the time the payments are introduced.

Calculating the future stream of income from area payments requires predicting payment rates in subsequent years. In addition to issues related to predicting future income streams from area support, various institutional conditions influence the process of “capturing” area payments by agricultural landowners. In particular, the long-term nature of lease agreements and their inflexibility result in inertia in lease rent rates (Góral & Kulawik 2015), while legal restrictions on the agricultural land market may slow the process of payment capitalization into land prices (Sadłowski 2017).