2.1. Game Model Description and Assumptions
Assume that there is a farmer and an agricultural social service provider. The farmer does not farm himself but chooses to entrust his land to the agricultural social service provider. The farmer pays certain trusteeship fees to the agricultural social service provider, who then finishes jobs such as sowing, irrigating, fertilizing, pesticide spraying, and harvesting on the farmer’s behalf. All land output and facilities that the agricultural social service provider constructs on the farmers’ land are owned by the farmer.
A farmer may choose to sign a T-year trusteeship contract with an agricultural social service provider or a short-term trusteeship contract, i.e., deciding each year whether or not to entrust his land and whom to entrust it to. After signing the land trusteeship contract, the agricultural social service provider may choose to save costs in a way that is good for the sustainable utilization of land. The so-called long-term behaviors include building fertilizing and irrigating facilities and preparing land for mechanized farming. In contrast, the agricultural service provider may choose not to make any long-term investment and may even reduce labor costs by adopting flood irrigation and spraying a large amount of pesticide fewer times; these are called short-term behaviors. Long-term behaviors usually require a certain amount of money to be invested, but they can continuously lower farming costs and improve land quality. Short-term behaviors do not require a fixed investment, but they help little to reduce costs and, in the long run, harm land fertility and even cause irreversible pollution.
In this article, two types of trusteeship fees were considered under a two price system: A fixed-price system and a variable-price system. Here, a fixed-price system means that the farmer and the agricultural social service provider sign a contract that specifies trusteeship terms and a trusteeship price, and with these terms, the farmer pays a fixed trusteeship fee each year to the agricultural social service provider. The variable price system means that within an agreed trusteeship term, the farmer pays the agricultural social service provider a variable trusteeship fee each year that is determined based on market supply and demand. The characteristics of the long-term contract, short-term contract, fixed price, and variable price are shown in
Table 1.
Since the farmer and the agricultural social service provider affect one another in terms of returns, there is a game relationship between both parties over land trusteeship. In this article, problems with short-term behaviors in land trusteeship were reduced to a two-stage dynamic game between one farmer and one agricultural social service provider. In the first stage of the game, the farmer had two strategies to choose from: T-years trusteeship (T) and 1-year trusteeship (1). In the second stage, the agricultural social service provider chose one of the two strategies: Long-term behaviors (L) or short-term behaviors (S).
There are four game scenarios altogether. When the farmer chooses T-year trusteeship and the agricultural social service provider chooses long-term behaviors—a scenario called T-L for short—the farmer will get a return
and the agricultural social service provider will earn
. When the farmer chooses T-year trusteeship and the agricultural social service provider chooses short-term behaviors—a scenario called T-S for short—the former will get a return
and the latter will earn
. When the farmer chooses 1-year trusteeship and the agricultural social service provider chooses long-term behaviors—a scenario called 1-L for short—the former will get a return
and the latter will earn
. When the farmer chooses a 1-year trusteeship and the agricultural social service provider chooses short-term behaviors—a scenario called 1-S for short—the former will get a return
and the latter will earn
. See
Figure 1 for details.
To quantitatively analyze relations in the game between farmers and agricultural social service providers, in November 2018, a week was spent interviewing more than 20 farmers and 3 agricultural social service providers in Shangshui County, Henan Province. The interviews mainly focused on the effects that long-term behaviors and short-term behaviors in land trusteeship have on the returns of farmers and agricultural social service providers. According to the survey’s findings, on the one hand, if the agricultural social service provider adopted long-term behaviors such as constructing irrigation facilities and improving land and soil conditions, it entailed a certain fixed cost and brought about no obvious change in land output in the short run but may have lowered machine operating costs each year and improved land output in the long run. If, on the other hand, the agricultural social service provider adopted short-term behaviors like flood irrigation and excessive use of fertilizer and chose not to build facilities and improve land conditions among other things, no fixed cost was required and a relatively high land output could be guaranteed in the short run, but such behaviors involved fairly high operating costs and, in the long run, weakened soil fertility and even caused soil to harden and decrease crop yields.
To build profit functions for the farmer and the agricultural social service provider, the following four assumptions were made based on the survey conducted in Shangshui County.
Assumption 1: If the agricultural social service provider chooses long-term behaviors, then the land output follows Equation (1):
where t refers to year t of trusteeship,
means the land output in year t if the agricultural social service provider chooses L, and
,
and
are related output parameters. Assumption 1 indicates that if the agricultural social service provider chooses long-term behaviors, land fertility increases gradually. As t increases, the growth of land output is divided into three stages. In the first stage, land output grows slowly to near
; the second stage sees land output grow fast, from
to near
; and in the third stage, land output stabilizes gradually at a
level.
Assumption 2: If the agricultural social service provider chooses short-term behaviors, then the land output follows Equation (2):
where
means the land output in year t if the agricultural social service provider chooses S. Assumption 2 indicates that if the agricultural social service provider chooses long-term behaviors, land is developed in a predatory way. As t increases, land output grows quickly to near
and then decreases rapidly and stabilizes at a level near
.
Assumption 3: If the agricultural social service provider chooses L, they need to make a fixed investment of z and the variable cost of production each year is . If the agricultural social service provider chooses S, then no fixed investment is needed and the variable cost of production each year is ; .
Assumption 3 suggests that to the agricultural social service provider, long-term investment in land can reduce costs more effectively than short-term behaviors do.
Assumption 4: The trusteeship price x fluctuates as the state of market competition changes, and the expected value of the trusteeship price for T years is .
In this study, two game models were built: One based on a fixed-price system and the other on a variable-price system. Currently, in land trusteeship practices in China, the fixed-price system is largely adopted and it is probably the main economic reason for farmers to enter into short-term contracts and for agricultural social service providers to adopt short-term behaviors. This study tried, through a comparison of results from the two models, to unravel relations among the fixed-price system, short-term contracts, and short-term behaviors in land trusteeship and to explain how the variable price system works on long-term contracts and long-term behaviors in land trusteeship. Thus, it aimed to encourage farmers and agricultural social service providers to adopt the variable price system, build a good cooperative relationship, and improve the sustainable utilization of land.
2.2. Game Model Based on the Fixed-Price System
Considering a situation where the farmer and the agricultural social service provider adopted the fixed-price system, this study established profit and loss functions regarding both parties in four game scenarios: T-L, T-S, 1-L, and 1-S.
Scenario 1: The farmer chooses T-year trusteeship and the agricultural social service provider chooses long-term behaviors.
In this scenario, the profit function for the farmer,
, is shown in Equation (3) and that for the agricultural social service provider,
, is shown in Equation (4).
In Equation (3),
is good land output that the farmer gets in T years when the agricultural social service provider chooses long-term behaviors, and
is the trusteeship fees that the farmer pays in T years when the variable price system is adopted. Equation (3) shows that, given the fixed-price system, the farmer’s return in this scenario is the difference between the good land output and the fixed trusteeship fees for T years, as well as the investment in land that the agricultural social service provider makes.
In Equation (4),
is the accumulated income in T years of using the agricultural social service provider when the fixed-price system is adopted, and
is the sum of variable costs and fixed investment each year when the agricultural social service provider chooses long-term behaviors. According to Equation (4), given the fixed-price system, the agricultural social service provider’s return in this scenario is the difference between trusteeship fees and operating costs related to the long-term behavior minus the fixed investment.
Scenario 2: The farmer chooses T-year trusteeship, and the agricultural social service provider chooses short-term behaviors.
In this scenario, the profit function for the farmer,
, is shown in Equation (5) and that for the agricultural social service provider,
, is shown in Equation (6).
In Equation (5),
is the bad land output that the farmer gets in T years when the agricultural social service provider chooses short-term behaviors, and
is the trusteeship fees that the farmer pays in T years when the fixed-price system is adopted. Equation (5) shows that given the fixed-price system, the farmer’s return in this scenario is the difference between the bad land output and the trusteeship fees for T years.
In Equation (6),
is the total expected income in T years of using the agricultural social service provider when the fixed-price system is adopted and
is the sum of variable costs each year when the agricultural social service provider chooses short-term behaviors. According to Equation (6), given the fixed-price system, the agricultural social service provider’s return in this scenario is the difference between the trusteeship fees and operating costs related to short-term behaviors.
Scenario 3: The farmer chooses a 1-year trusteeship and the agricultural social service provider chooses long-term behaviors.
In this scenario, the profit function for the farmer,
, is shown in Equation (7) and that for the agricultural social service provider,
, is shown in Equation (8).
In Equation (7),
is the good land output that the farmer gets in T years when the agricultural social service provider chooses long-term behaviors and
is the trusteeship fees that the farmer expects to pay in T years when he chooses to entrust an agricultural social service provider each year. Equation (7) shows that given the fixed-price system, the farmer’s return in this scenario is the difference between the good land output and the expected trusteeship fees for T years as well as the investment in land that the agricultural social service provider makes.
In Equation (8),
is the number of years of trusteeship that the agricultural social service provider expects to get in T years
when the farmer chooses to entrust an agricultural social service provider each year,
is the total income that the agricultural social service provider expects to earn in T years, and
is the sum of variable costs and fixed investment in T years when the agricultural social service provider chooses long-term behaviors. According to Equation (8), given the fixed-price system, the agricultural social service provider’s return in this scenario is the difference between the expected trusteeship fees and operating costs related to short-term behaviors minus the fixed investment.
Scenario 4: The farmer chooses a 1-year trusteeship and the agricultural social service provider chooses short-term behaviors.
In this scenario, the profit function for the farmer,
, is shown in Equation (9) and that for the agricultural social service provider,
, is shown in Equation (10).
In Equation (9),
is the bad land output that the farmer gets in T years when the agricultural social service provider chooses short-term behaviors, and
is the trusteeship fees that the farmer expects to pay in T years when he chooses to entrust an agricultural social service provider each year. Equation (17) shows that given the fixed-price system, the farmer’s return in this scenario is the difference between the bad land output and the trusteeship fees for T years.
In Equation (10),
is the total expected income of the agricultural social service provider in T years when the farmer chooses to entrust an agricultural social service provider each year and
is the sum of variable costs each year when the agricultural social service provider chooses short-term behaviors. According to Equation (10), given the fixed-price system, the agricultural social service provider’s return in this scenario is the difference between the expected trusteeship fees and operating costs related to short-term behaviors.
2.3. Game Model Based on the Variable-price System
Considering the situation where the farmer and the agricultural social service provider adopt the variable price system, this article establishes profit and loss functions regarding both parties in four game scenarios: T-L, T-S, 1-L, and 1-S.
Scenario 1: The farmer chooses T-year trusteeship, and the agricultural social service provider chooses long-term behaviors L.
In this scenario, the profit function for the farmer,
, is shown in Equation (11), and that for the agricultural social service provider,
, is shown in Equation (12).
In Equation (11),
is the good land output that the farmer gets in T years when the agricultural social service provider chooses long-term behaviors and
is the trusteeship fees that the farmer expects to pay in T years when the variable-price system is adopted. Equation (11) shows that given the variable-price system, the farmer’s return in this scenario is the difference between the good land output and the expected trusteeship fees for T years, as well as the investment in land that the agricultural social service provider makes.
In Equation (12),
is the total income that the agricultural social service provider expects to earn in T years when the variable-price system is adopted and
is the sum of the variable cost and fixed investment each year when the agricultural social service provider chooses long-term behaviors. According to Equation (12), given the variable price system, the agricultural social service provider’s return in this scenario is the difference between his expected trusteeship fees and operating costs related to long-term behaviors minus the fixed investment.
Scenario 2: The farmer chooses T-year trusteeship and the agricultural social service provider chooses short-term behaviors.
In this scenario, the profit function for the farmer,
, is shown in Equation (13) and that for the agricultural social service provider,
, is shown in Equation (14).
In Equation (13),
is the bad land output that the farmer gets in T years when the agricultural social service provider chooses short-term behaviors and
is the trusteeship fees that the farmer expects to pay in T years when the variable price system is adopted. Equation (13) shows that given the variable-price system, the farmer’s return in this scenario is the difference between the badland output and the trusteeship fees for T years.
In Equation (14),
is the total expected income in T years of using the agricultural social service provider when the variable price system is adopted and
is the sum of variable costs each year when the agricultural social service provider chooses short-term behaviors. According to Equation (14), given the variable price system, the agricultural social service provider’s return in this scenario is the difference between the expected trusteeship fees and operating costs related to short-term behaviors.
Scenario 3: The farmer chooses a 1-year trusteeship and the agricultural social service provider chooses long-term behaviors L.
In this scenario, the profit function for the farmer,
, is shown in Equation (15) and that for the agricultural social service provider,
, is shown in Equation (16).
In Equation (15),
is the good land output that the farmer gets in T years when the agricultural social service provider chooses long-term behaviors L and
is the trusteeship fees that the farmer expects to pay in T years when the variable price system is adopted. Equation (15) shows that given the variable price system, the farmer’s return in this scenario is the difference between the good land output and the expected trusteeship fees for T years, as well as the investment in land that the agricultural social service provider makes.
In Equation (16),
is the total income that the agricultural social service provider expects to earn in T years when the variable-price system is adopted and
is the sum of the variable cost and fixed investment in T years when the agricultural social service provider chooses long-term behaviors. According to Equation (16), given the variable price system, the agricultural social service provider’s return in this scenario is the difference between the expected trusteeship fees and operating costs related to short-term behaviors minus the fixed investment.
Scenario 4: The farmer chooses a 1-year trusteeship and the agricultural social service provider chooses short-term behaviors.
In this scenario, the profit function for the farmer,
, is shown in Equation (17) and that for the agricultural social service provider,
, is shown in Equation (18).
In Equation (17),
is the bad land output that the farmer gets in T years when the agricultural social service provider chooses short-term behaviors L and
is the trusteeship fees that the farmer expects to pay in T years when the variable price system is adopted. Equation (17) shows that given the variable-price system, the farmer’s return in this scenario is the difference between the bad land output and the trusteeship fees for T years.
In Equation (18),
is the total expected income in T years of the agricultural social service provider when the variable-price system is adopted and
is the sum of the variable costs each year when the agricultural social service provider chooses short-term behaviors. According to Equation (18), given the variable price system, the agricultural social service provider’s return in this scenario is the difference between the expected trusteeship fees and operating costs related to short-term behaviors.