Production Diversification as a Tool for Agricultural Risk

Management: The Case of Northern Kazakhstan

TALGAT KUSSAIYNOV, GULNARA MUSSINA, SANDUGASH TOKENOVA,

SALTANAT MAMBETOVA

Saken Seifullin Kazakh Agro-Technical Research University,

Astana,

REPUBLIC OF KAZAKHSTAN

Abstract:- This paper addresses the impacts of degree of risk aversion on optimal farm plans in Kazakh

agriculture. The results obtained during the field research in the region of Northern Kazakhstan are presented.

Calculations were carried out using data from 145 peasant farms in the region for 2017-2022 based on a risk

model. It has been found that the choice of a portfolio is influenced not only by considerations of profitability

and riskiness of crops, but also by grain production traditions deeply rooted among the farmers of the region,

and the skills and knowledge associated with them, as well as the existing infrastructure. These circumstances

constrain the wider spread of oilseed crops in the region. It seems that the size of the farm does not significantly

affect the choice of portfolio, while the degree of risk aversion by the farmer affects the optimal farming plan.

The potential benefits of the farming diversification are an empirical issue, and it should be addressed on a

case-by-case basis. The question is to choose the utility function and its parameters that most accurately reflect

the preferences of a particular farmer, the authors conclude.

Key-Words: - uncertainty; diversification; crop production; income; covariance; model; decision making; risk

aversion; utility function; optimization.

Received: May 2, 2023. Revised: October 11, 2023. Accepted: October 23, 2023. Published: November 3, 2023.

1 Introduction

There is always a trade-off between diversification

and specialization. Farm planning models to find

the most referable degree of production

diversification is usually cast in the portfolio

selection framework. And the best approach is to

formulate the model in terms of direct expected

utility maximization. This type of models puts

more weight on bad outcomes and is more

consistent with the expected utility hypothesis. In

countries such as Kazakhstan, where risk-sharing

strategies have not yet become widespread, on-

farm management strategies can more readily be

used to soften the impact of downside risk. The

idea of diversification is to reduce the dispersion of

the overall return by selecting a mixture of

activities that have net returns with low or negative

correlations. Again, however, the aim should be to

find the risk-efficient combinations of activities,

not the one that merely minimizes variance. In

general, farmers will diversify more with an

increasing degree of risk aversion. However, more

diversification can be increasingly costly if it

means forgoing the advantages that specialization

confers

through better command of superior technologies

and closer attention to the special needs of one

particular market. And diversification remains a

priority on the farm to prevent or mitigate the

consequences of undesirable events (risk

reduction). Of course, they may also include

measures reflecting risk aversion on the part of the

decision-maker.

The paper is organized as follows. The next

section describes the data and methods. Then the

results are presented. The final section provides a

discussion of the results and concluding remarks.

In recent years, a number of studies have

documented how farmers in different countries are

adopting measures that rely on the use of

agricultural biodiversity in response to climatic

changes and their associated effects, [1], [2], [3],

[4], [5]. These measures can be classified in three

categories: cultivation of a larger number of

species and farm diversification overall;

introduction or increased cultivation of better

adapted crops and varieties, and livestock animals

and breeds; and integration of trees and shrubs into

production systems. Different crops are affected

differently by climate events, and this in turn gives

some minimum assured returns for livelihood

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Talgat Kussaiynov, Gulnara Mussina,

Sandugash Tokenova, Saltanat Mambetova

E-ISSN: 2224-2899

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security. Alternating cereal crops with legumes has

been a common practice for maintaining soil

nutrients, managing diseases and adapting crop

production to climatic variations that has been

widely successful, [6].

The introduction of livestock has also been

observed as a diversification strategy in response

to climate change, [7], [8]. Over the past three

decades, in many arid regions of Kazakhstan

farmers have reduced their investment in crops, or

even stop planting and focus instead on livestock

management. Different animal species and breeds

differ greatly in the extent to which they can

tolerate climatic extremes. In arid areas of

Kazakhstan, there has been a return to the breeding

of traditional animals for commercial purposes,

such as camel, sheep and horse breeding, more

adapted to the changing climatic conditions. Such

trends take place almost everywhere. For example,

[9], notices the expansion of the distribution range

of one-humped camels further south in Africa,

replacing cattle, because of their better drought

resistance. Crop diversification and crop-livestock

integration are often combined with adjustments in

agricultural practices and adoption of low-input

methods for soil fertility improvement, water

conservation and weed management. The

substitution of traditional varieties with improved,

early maturing ones has also been observed as part

of adaptation strategies in places affected by

drastic increases or decreases of temperature and

rainfall, [10], [11]. The opposite is also observed:

farmers stick to the cultivation of traditional

varieties because of their capacity to respond and

adapt to new climate patterns, [12].

The most important role in ensuring success in

farming is played by competent risk-based

planning. In a planning model accounting for

uncertainty it is usually important to take account

of the farmers' risk attitude. In countries with

transition economy, such as Kazakhstan, many

previous studies assumed complete certainty or

overlooked farmers' aversion to risk. Others who

have incorporated farmers' risk attitudes have

found risk aversion to have an important influence

on the choice of the farming plan.

Our empirical objectives are to examine the

effect on the optimal farm plan of differences in

(1) farm size, (2) farmers' risk aversion.

2 Methods and Data

A realistic planning model should take into

account the farmer's subjective assessment of the

probability of the occurrence of uncertain

consequences from the decisions made and his

preferences regarding these consequences,

reflecting the farmer’s degree of risk aversion. It is

assumed that the subjective expected utility

hypothesis is the best framework for structuring

these two components into a workable model of

risky choice, [13].

As a utility function, we used a power function

of the form   󰇡 

󰇢, where  is size of

wealth (the value of assets),  is coefficient of

relative risk aversion. This function is useful for

solving problems and interpreting their results. In

r=0 this case, the function takes a linear form  

; the linear function corresponds to the case when

the entrepreneur's attitude to risk is neutral (risk is

not taken into account when optimizing the

solution). When r=1 the power function turns into

a logarithmic one. The higher the value r, the less

likely the entrepreneur is to make risky decisions,

so the less willing they are to invest in risky

activities. The study, [14], offers the following

interpretation of the coefficients of risk aversion:

󰇛󰇜  is individual manifests an indifference

to risk (in other words, assess risky decision only

on subjective expected impact); 󰇛󰇜  is

perhaps taking the risk into account; 󰇛󰇜  is

paying attention to a reasonable degree; 󰇛󰇜 

is very cautiously accepts the risk; 󰇛󰇜  is

high level of risk prevention; 󰇛󰇜  is

extremely high degree of risk aversion. Nobel

Prize winner in economics, [15], suggests

considering the relative coefficient of risk aversion

equal to one as "normal", which is typical for most

individuals. We note that in most cases the risk

aversion coefficient is estimated in relation to the

total wealth of the enterprise, so the total value of

its assets. In practice, to make a decision, the main

argument of the utility function, as a rule, is

income, that is, the increase in the value of assets.

In this regard, there is a need to recalculate the

relative coefficient of risk aversion for income.

The recalculation is carried out with the use of a

formula that relates the coefficients of income and

risk aversion by wealth:

  󰇛󰇜 󰇡

󰇢󰇛󰇜 (1)

whereis the average annual income; is the

average annual total asset value of the enterprise.

In our problem, risk aversion was estimated by

the ratio of marginal income. At r=0, the risk is

not considered when optimizing the solution. As

the coefficient r increases, the entrepreneur avoids

making risky decisions of the production structure.

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E-ISSN: 2224-2899

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The following model has been used to solve the

problem:

 󰇛󰇜󰇛󰇜

󰇛󰇜 (2)

under restrictions:

1) use of resources

   



 󰇛󰇜

  (4)

2) the share of the area of individual crops is

the maximum allowable in the structure of crops

    (5)

3) fulfillment of contractual obligations for the

supply of individual products or by market

capacity 󰇛󰇜   (6)

4) market conditions and margin income based

on production

 



   󰇛󰇜

5) the minimum required income for fulfillment

of financial obligations in any state of production

and market conditions, for example, to repay a loan

    (8)

6) margin income expected

  󰇛󰇜



7) utility expected

󰇛󰇜 󰇛󰇜 

  

󰇛󰇜

󰇛󰇜



where:  is the guaranteed equivalent; 󰇛󰇜 is

the expected utility;  is a coefficient of relative

risk aversion;  is an index of the resource ( =1 is

the index of arable land);  is an index of crop;  is

an index of market conditions and production; 

is number of species of economic resources;  is a

quantity of types of crops;  is a set of states of

production and market conditions;  is a set of

crops (products);  is the area under the j-crop; 

is the cost of resource i per one hectare of crop j;

 is the total size of resources i used ( is the

total area of arable land under crops);  is the

overall size of resources i available on the farm;

is the maximum share of the area under crop j;

 is the yield of crop j; is the market capacity or

the amount of contractual commitments for the

supply of product j;  is the margin income per

hectare of crop j in state s of production and

market conditions;  is the total size of the margin

income from crops in state s of production and

market conditions;  is the minimum amount of

whole-farm margin income required under any

production and market conditions;  is the total

expected whole-farm margin income;  is the

probability of state s of production and market

conditions.

Calculations were carried out using data from

145 farms of North-Kazakhstan region for 2017-

2022. Farms were divided into 6 groups according

to the size of the arable land. Then the average

farm size for each group was determined. Further

calculations based on the model were carried out

on average farms. The main constraints in the

model are (1) land constraint, (2) rotational limits

(to avoid the build-up of pests and diseases it is

assumed that no more than a quarter of the area can

be oilseeds).

Farms under consideration grow crops such as

wheat, barley, oats, buckwheat, peas, rapeseed for

seeds and flax. The size of acreage in farms ranges

from 16 to 3082 hectares. The first group consisted

of 19 farms (with crop area 16 to 49 hectares), the

second group includes 37 farms (with crop area 50

to 125 hectares), the third group comprises 43

farms (with crop area 126 to 344 hectares, the

fourth group includes 25 farms with a sown area of

345 to 799 hectares, the fifth group consisted of 14

farms (with crop area 800 to 1734 ha), 7 farms

make up the sixth group with crop area of 1735

and more hectares. Table 1 (Appendix) shows

marginal income by crops on the farms for the

period from 2017 to 2022.

3 Results and Discussion

In all groups of farms, oilseeds are the dominant

crops in terms of economic efficiency. Flax is

represented in each group, while rapeseed only in

the 5th group of farms. It should be borne in mind

that the most stable is the income from oilseeds.

Peas on the farms of the 1st and 4th groups have

the lowest efficiency in terms of income, barley in

the 2nd group of farms, oats in groups 3 and 6. At

the same time, peas turn out to be the most

economically risky crop, while other crops occupy

an intermediate position in terms of variability.

These circumstances, of course, have a decisive

influence on the processes of structural

optimization of production.

Table 2 (Appendix) shows the results of

optimizing the production structure based on

model (2)-(11). The economic conditions of each

year are assumed to be equally probable, namely,

the probability of each of them is 0.17.

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The results of calculations show that in the

farms of the 1st group, with an indifferent attitude

to risk (the risk aversion coefficient is zero), wheat

(75.0%) and flax (25.0%) are included in the

production structure. The expected margin income

per 1 hectare is 75.5 thousand tenge, the variability

is 47.0%. As the coefficient of relative risk

aversion increases (the entrepreneur is more

careful when making a decision), the share of

wheat decreases, and barley is included in the

structure. With a "normal" degree of risk aversion

characteristic of most entrepreneurs (in the

conditions of the problem, this corresponds to a

coefficient of relative risk aversion for marginal

income of 0.3), the shares of wheat, barley, and

flax are 66.9%, 8.1%, and 25.0%, respectively. The

expected marginal income per 1 ha is 75.4

thousand tenge with a variability of 46.6%. In case

of risk aversion with a coefficient of 0.6 or higher,

barley (75.0%) and flax (25.0%) remain in the

optimal production plan, and wheat is excluded.

On the farms of the 2nd group, the optimal

sowing plan includes wheat, peas and flax with any

attitude to risk. The change in the value of the risk

aversion coefficient affects the ratio of the share of

these crops in the plan. In the case when the value

of the risk coefficient is zero, wheat, peas and flax

occupy 23.5%, 51.5% and 25.0%, respectively.

The expected margin income from 1 ha is 85.4

thousand tenge with a volatility of 56.6%. With an

increase in the degree of risk aversion, the

dominance of wheat in the structure of crops

increases. With the coefficient of relative risk

aversion for marginal income equal to 1.2, the

optimal structure of crops is as follows: wheat

occupies 65.8%, peas 9.2%, and flax 25.0%. The

expected margin income per 1 ha is reduced to

77.5 thousand tenge, but the variability is also

reduced to 46.8%.

For the 3rd group of farms, agricultural crops

include wheat, peas and flax, while the share of

each of these crops varies depending on the degree

of risk aversion by the farmer. With the

entrepreneur's indifferent attitude to risk, the share

of wheat is 6.6%, peas 68.4%, flax 25%. The

expected margin income per 1 hectare is 117.3

thousand tenge with a variation of 55.9%. With an

extreme degree of risk aversion (it corresponds to

the coefficient of relative risk aversion for margin

income of 1.2), the share of wheat increases to

65.7%, the share of peas decreases to 9.3%, and

the share of flax remains unchanged. The amount

of expected income from 1 ha of crops is reduced

to 105.1 thousand tenge, the variability also

decreases to 44.0%.

The structure of crops of the 4th group of farms

with an indifferent attitude of the entrepreneur to

the risk includes wheat (75.0%) and flax (25.0%).

At the same time, the expected marginal income

from 1 hectare is 89.2 thousand tenge, the

variability is 46.3%. If the coefficient of relative

risk aversion for margin income is 0.9, peas are

included in the crop structure, and the share of its

crops increases as risk aversion increases. With

extreme reluctance to take risks, wheat (70.2%),

peas (4.8%) and flax (25.0%) are included in the

optimal structure of crops. The amount of expected

income from 1 ha of crops is reduced to 86.3

thousand. tenge, the coefficient of variation is

reduced to 41.4%.

Wheat (75.0%) and rapeseed (25.0%) are

included in the production structure of the 5th

group of farms with an indifferent attitude to risk.

At the same time, the expected margin income per

1 hectare is 96.9 thousand tenge, the variability of

income is 36.2%. The composition of crops and the

structure of crops with a coefficient of relative risk

aversion of 0.3 looks like this: wheat (66.7%),

buckwheat (8.3%), rapeseed (25.0%). The

expected margin income per 1 hectare with such a

degree of risk aversion is 96.7 thousand tenge, the

variability is 33.1%.

On the farms of the 6th group, wheat (75.0%)

and flax (25.0%) predominate in the production

structure. With an extreme degree of risk aversion,

barley appears in the optimal plan: wheat (42.4%),

barley (32.6%), and flax (25.0%). The amount of

expected marginal income per 1 hectare of crops is

decreased from 122.6 thousand tenge to 121.3

thousand tenge, the variability of income is

reduced from 45.7% to 44.5%.

Note that when solving the problem, it was

assumed that there were no restrictions on the

volume of sales of products. The presence of such

conditions, of course, will make changes to

production plans.

In general, there is a certain pattern in changes

in the structure of production, depending on the

degree of farmer’s risk aversion. This pattern is

manifested in the fact that the stronger the risk

aversion, the more diversified the structure of

crops becomes. This feature is consistent with the

findings previously made by many international

and national researchers who studied issues related

to agriculture risk, [16]. It is worth noting that the

long-term predominance of cereals, in particular

wheat, in northern Kazakhstan, inherited from the

former Soviet agriculture, certainly affects the pace

and features of crop diversification in the region.

About 60% of the acreage is still occupied by grain

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crops. About 70% of the sown area is still occupied

by grain crops, and wheat is the only sown crop on

some farms. In the last decade, the government, by

providing subsidies, began to encourage farmers to

introduce other crops. As a result, oilseed crops

have significantly increased and currently account

for over 20%.

4 Concluding Comments

Farmers in Northern Kazakhstan have limited

flexibility in the choice of activities, which is

caused by relatively unfavorable geographical and

climatic conditions, as well as policy and market

conditions. In these circumstances, it seems that

the size of the farm does not matter much to

influence the choice of a farm plan. The results

indicate that the degree of risk aversion of the

farmer affects the optimal farming plan. Having

only two or three activities, which is normal, can

often capture the majority of risk-reducing benefits

from diversification. The choice of a portfolio is

influenced not only by considerations of

profitability and riskiness of crops, but also by

grain production traditions deeply rooted among

the farmers of the region, and the skills and

knowledge associated with them, as well as the

existing infrastructure. These circumstances

constrain the wider spread of oilseed crops in the

region. And it seems that the size of the farm does

not significantly affect the choice of portfolio. The

potential benefits of farming diversification are an

empirical issue, and it should be addressed on a

case-by-case basis. The question is to choose the

utility function and its parameters that most

accurately reflect the preferences of a particular

farmer.

The study suggests several ideas for further

research. Firstly, no financial management option

was included in the model. Fischer's separation

theorem implies that it is better to diversify

through capital markets than through activity

combinations. In Kazakhstan, the financial markets

of agricultural products are not well developed

either in terms of price or volume. However, a

possible extension of the model would be to

include some types of financial activities, such as

insurance agreements.

Acknowledgments:

The authors express their gratitude to the team of

the research project "Methodology of analysis and

optimization of the socio-economic model (based

on the materials of Northern Kazakhstan)" for the

assistance in collecting data on the socio-economic

development of rural areas. The research has been

funded by a Grant from the Science Committee of

the Ministry of Education and Science of the

Republic of Kazakhstan (Grant No. AP09259525).

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APPENDIX

Table 1. Marginal income by crops in North-Kazakhstan region, thousand tenge per hectare

Source: Authors ' calculationsнаbased on agricultural statistics Bureau of National Statistics Republic of Kazakhstan

Year

Crops

Wheat

Barley

Oats

Buckwheat

Peas

Rapeseed

Flax

Farms with an area of arable land up to 49 ha

2017

34.1

38.7

63.3

49.4

2018

19.6

36.1

-22.7

63.7

2019

45.9

32.0

38.2

82.2

2020

80.8

65.3

38.8

114.1

2021

83.1

87.1

49.3

147.6

2022

108.2

108.0

99.9

143.7

Average

62.0

61.2

33.4

91.4

Variability, %

54.8

51.0

85.8

38.6

Farms with an area of arable land of 50 to 125 ha

2017

35.9

32.2

126.4

57.3

2018

20.7

30.0

-45.2

73.6

2019

48.4

26.6

75.9

94.9

2020

85.2

54.3

77.4

132.1

2021

87.6

72.4

97.7

169.9

2022

106.5

80.5

164.3

137.1

Average

64.1

49.3

82.8

110.8

Variability, %

52.8

47.2

85.8

38.6

Farms with an area of arable land of 126 to 344 ha

2017

41.2

33.8

32.3

141.0

102.3

2018

23.7

31.5

-14.0

-50.4

131.4

2019

55.5

28.0

21.9

84.7

169.5

2020

97.6

57.1

33.9

86.3

235.8

2021

95.6

78.7

20.9

108.9

303.5

2022

116.3

87.5

16.8

183.2

244.9

Average

71.6

52.8

18.6

92.3

197.9

Variability, %

51.2

48.9

93.1

85.8

38.6

Farms with an area of arable land of 345 to 799 ha

2017

42.3

30.8

55.2

59.6

67.3

2018

24.4

28.7

-24.0

-21.3

86.5

2019

57.0

25.5

37.4

35.8

111.5

2020

100.4

52.0

58.0

36.5

155.2

2021

103.2

69.3

65.5

46.0

199.8

2022

125.5

77.0

52.8

77.4

161.2

Average

75.5

47.2

40.8

39.0

130.3

Variability, %

52.8

47.2

81.0

85.8

38.6

Farms with an area of arable land of 800 to 1734 ha

2017

42.2

35.4

47.9

162.0

97.7

159.8

50.2

2018

24.3

33.1

-20.8

92.0

-34.9

146.6

64.5

2019

56.9

29.4

32.5

-19.5

58.7

167.8

83.2

2020

100.1

59.9

50.4

66.3

59.8

153.2

115.7

2021

102.9

79.8

56.9

37.4

75.5

102.8

148.9

2022

125.2

88.7

45.9

96.8

126.9

241.2

120.2

Average

75.3

54.4

35.5

72.5

63.9

161.9

97.1

Variability, %

52.8

47.2

81.0

84.4

85.8

27.8

38.6

Farms with an area of arable land of more than 1735 hectares

2017

54.2

57.6

42.9

67.5

103.7

2018

31.2

53.8

-18.6

-24.1

133.2

2019

73.0

47.7

29.1

40.5

171.7

2020

128.5

106.2

45.1

41.3

239.0

2021

132.1

129.8

50.9

52.2

307.5

2022

160.7

160.6

41.0

87.7

248.2

Average

96.6

92.6

31.7

44.2

200.6

Variability, %

52.8

50.5

81.0

85.8

38.6

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2023.20.210

Talgat Kussaiynov, Gulnara Mussina,

Sandugash Tokenova, Saltanat Mambetova

E-ISSN: 2224-2899

2463

Volume 20, 2023

Table 2. Optimal crop structure depending on the degree of risk aversion

Relative

risk

aversion

ratio

r(z) / r(W)

Sown area by crops, %

Margin income,

thousand

tenge/hectare

Standard deviation,

thousand tenge

Risk ratio, %

Wheat

Barley

Oats

Buckwheat

Peas

Rapeseed

Flax

Farms with an area of arable land up to 49 ha

0/0

0.750

0.000

0.250

75.5

35.5

47.0

0.5/0.15

0.750

0.000

0.250

75.5

35.5

47.0

1/0.3

0.669

0.081

0.000

0.250

75.4

35.1

46.6

2/0.6

0.126

0.624

0.000

0.250

75.0

33.4

44.5

3/0.9

0.000

0.750

0.000

0.250

74.9

33.2

44.3

4/1.2

0.000

0.750

0.000

0.250

74.9

33.2

44.3

Farms with an area of arable land of 50 to 125 ha

0/0

0.235

0.000

0.515

0.250

85.4

48.4

56.6

0.5/0.15

0.237

0.000

0.513

0.250

85.3

48.3

56.6

1/0.3

0.288

0.000

0.462

0.250

84.4

46.4

55.0

2/0.6

0.471

0.000

0.279

0.250

81.0

40.5

50.0

3/0.9

0.591

0.000

0.159

0.250

78.7

37.5

47.7

4/1.2

0.658

0.000

0.092

0.250

77.5

36.3

46.8

Farms with an area of arable land of 126 to 344 ha

0/0

0.066

0.000

0.684

0.250

117.3

65.6

55.9

0.5/0.15

0.102

0.000

0.648

0.250

116.6

64.0

54.9

1/0.3

0.277

0.000

0.473

0.250

113.0

56.9

50.3

2/0.6

0.507

0.000

0.243

0.250

108.2

49.4

45.7

3/0.9

0.606

0.000

0.144

0.250

106.2

47.2

44.4

4/1.2

0.657

0.000

0.093

0.250

105.1

46.3

44.0

Farms with an area of arable land of 345 to 799 ha

0/0

0.750

0.000

0.250

89.2

41.3

46.3

0.5/0.15

0.750

0.000

0.250

89.2

41.3

46.3

1/0.3

0.750

0.000

0.250

89.2

41.3

46.3

2/0.6

0.750

0.000

0.250

89.2

41.3

46.3

3/0.9

0.721

0.000

0.029

0.250

87.2

40.3

42.4

4/1.2

0.702

0.000

0.048

0.250

86.3

38.9

41.4

Farms with an area of arable land of 800 to 1734 ha

0/0

0.750

0,000

0.000

0.25

96.9

35.1

36.2

0,5/0,15

0.750

0,000

0.000

0.25

96.9

35.1

36.2

1/0,3

0.667

0,000

0.000

0.083

0.25

96.7

32.0

33.1

2/0,6

0.597

0,000

0.000

0.153

0.25

96.5

30.2

31.3

3/0,9

0.576

0,000

0.000

0.174

0.25

96.4

29.9

31.0

4/1,2

0.566

0,000

0.000

0.184

0.25

96.4

29.8

30.9

Farms with an area of arable land of more than 1735 hectares

0/0

0.750

0.000

0.250

122.6

56.0

45.7

0.5/0.15

0.750

0.000

0.250

122.6

56.0

45.7

1/0.3

0.750

0.000

0.250

122.6

56.0

45.7

2/0.6

0.750

0.000

0.250

122.6

56.0

45.7

3/0.9

0.750

0.000

0.250

122.6

56.0

45.7

4/1.2

0.424

0.326

0.000

0.250

121.3

54.0

44.5

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2023.20.210

Talgat Kussaiynov, Gulnara Mussina,

Sandugash Tokenova, Saltanat Mambetova

E-ISSN: 2224-2899

2464

Volume 20, 2023

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- Talgat Kussaiynov, Gulnara Mussina carried out

the simulation and the optimization.

- Sandugash Tokenova has organized and

executed the experiments.

- Saltanat Mambetova was responsible for the

Statistics.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

The research has been funded by a Grant from the

Science Committee of the Ministry of Education

and Science of the Republic of Kazakhstan (Grant

No. AP09259525).

Conflict of Interest

The authors have no conflict of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.e

n_US

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2023.20.210

Talgat Kussaiynov, Gulnara Mussina,

Sandugash Tokenova, Saltanat Mambetova

E-ISSN: 2224-2899

2465

Volume 20, 2023