The study was conducted primarily during the 2020/2021 cropping season in Njoro Sub-County (Appendix 1), located within Nakuru County, Kenya, positioned approximately between latitudes −0.2917 and −0.3326, and longitudes 35.9847 and 36.0007. Njoro Sub-County is widely recognized for its agricultural activities, particularly in horticulture, including the cultivation of carrots, maize, and other crops. With an average altitude ranging from 1520 m to 3098 m above sea level and annual rainfall varying from 100 mm to 1900 mm, the climatic conditions in Njoro Sub-County are conducive to diverse agricultural production. Furthermore, as the host to Egerton University, one of Kenya’s prominent institutions of higher learning, Njoro Sub-County significantly contributes to educational and socio-economic development in the region. By concentrating on Njoro Sub-County as the primary research area, the study aimed to delve into the intricacies of carrot value chains and farmer decision-making processes within this specific agricultural landscape, providing nuanced insights into agricultural market dynamics and livelihood strategies in Nakuru County.

The study adopted a comprehensive sampling approach proposed by [24] to delve into the dynamics of Nakuru County’s carrot industry and markets, which also included conducting gross margin analysis. Through consultation with the divisional agricultural officer of Mau-Narok Division, a sampling strategy was devised, resulting in the selection of 195 smallholder carrot farmers, and traders (20 brokers, 34 aggregators, 15 wholesalers, 10 exporters, and 20 retailers). Nakuru County, particularly Njoro sub-county, was identified for its significance in carrot production and its role as a potential market center, with a focus on its vibrant agricultural landscape and diverse market participation.

Structured questionnaires (Appendix 2 and Appendix 3) were utilized to collect data, emphasizing household, land, and institutional information from smallholder carrot farming households in Njoro sub-county. Various tools, including semi-structured questionnaires, focus group discussions (FGDs), and key informant interviews (KIIs), were employed to gain a comprehensive understanding of Nakuru’s carrot enterprise and markets. The multistage sampling technique ensured representation across various industry segments, with respondents randomly selected at the village level using a proportion-to-size sampling approach. Statistical and descriptive measures were applied to identify key market players, assess the prevalence and profitability of value chain functions, and create enterprise and market maps illustrating Nakuru’s carrot industry landscape. These maps underwent validation and refinement, supported by insights from FGDs and KIIs, which were thematically coded to highlight pivotal issues within the carrot enterprise and markets. The study deployed Statistical Package for Social Sciences (SPSS) and STATA software for data analysis, revealing insights into market dynamics. Data triangulation enriched understanding of the carrot enterprise’s operations, identified constraints and opportunities for value chain actors, and facilitated the development of strategies to enhance smallholder carrot farmers’ incomes. The findings informed tailored recommendations aimed at improving their welfare.

One limitation of the study was its focus solely on smallholder farmers and market intermediaries within Nakuru County, which restricted the generalizability of the findings beyond this specific region. To counteract this limitation, the study explicitly stated the scope of its conclusions to Nakuru County, acknowledging the need for caution when applying the results to other contexts. Another limitation was the reliance on recall for collecting certain information, particularly when record-keeping practices were not prevalent among participants. This could have potentially compromised the accuracy of the data. To address this challenge, the study employed proactive measures such as proper probing techniques and cross-check questions during the survey process. These strategies aimed to validate and enhance the reliability of the collected data, despite the limitations associated with recall.

Following the recommendations of [25] , a multinomial logit model (MNL) was utilized to assess the impact of household characteristics, technical aspects, socio-economic factors, external influences, and institutional elements on the selection of marketing outlets. The probability of a carrot farmer selecting one market outlet over another, given alternative options, was determined using this model.

$\text{Prob}\left(Y_J=i\right)=P_{ij}=\frac{\exp \left(X_j{\beta }_j\right)}{{{\displaystyle \sum }}^{\text{}}\exp \left(X_j{\beta }_k\right)}$(1)

where Y_J is the the probability with which a smallholder carrot farmer j chose market outlet i, that is $\text{Pr}\left(Y_J=i\right)$ and i represents the marketing channel choices. P_ij takes values 1, 2, 3, 4 and 5 each representing choice of marketing outlet: neighbour = 0, broker = 1, cooperative = 2, exporter = 3, Local trader = 4, 5, while X_i are factors affecting the choice of a marketing outlet, β were parameters to be estimated and e is random error term.

Therefore, with j alternative choices, probability of choosing a marketing outlet j is given by,

$\text{Prob}\left(Y_i=j\right)=\frac{e_{zj}}{{\displaystyle {\sum }_{k=0}^j{e}_{zk}}}$(2)

Z_j is market channel outlet chosen [26] and is given by,

$Z_j=B_j{X}_i$(3)

Z_k is alternative choice that could be chosen [26] given by

$Z_k={\beta }_k{X}_i$(4)

The model estimates are used to determine the probability of choice of a market outlet j given factors that affect the choice, X_i.

With a number of alternative choices log odds ratio is computed as,

$\ln \left(\frac{P_{ij}}{P_{ik}}\right)=\alpha +{\displaystyle \sum X_i\left(B_j-B_k\right)}+e$(5)

P_ij and P_ik are probabilities that a smallholder carrot farmer will choose a given channel and alternative outlet, respectively.

$\ln \left(\frac{P_{ij}}{P_{ik}}\right)$ is a natural log of probability of choice j relative to probability for

choice k, α is a constant, β is a matrix of parameters that reflect the impact of changes in X on probability of choosing a given channel. e is the error term that is independent and normally distributed with a mean zero N(0, σ).

Marginal effects of the attributes on choice are determined by getting the differential of probability of a given choice:

$\text{Prob}\left(Y_i=j\right)=\frac{e_{zj}}{{\displaystyle {\sum }_{k=0}^j{e}_{zk}}}$(6)

Marginal effects

$\delta =\frac{\partial P_i}{\partial X_i}=p_i\left(B_j-{\displaystyle {\sum }_{k=0}^j{P}_k{\beta }_k}\right)=P_i\left({\beta }_j-\beta \right)$(7)

Every sub-vector of β enters every marginal effect both through probabilities and through weighted average. The econometric specification for the multinomial model is indicated below, however the variables descriptions as its parametric measurements as used in multinomial logit (MNL) model are placed in Appendix 4.

$\begin{array}{c}\text{Market outlet}={\beta }_0+{\beta }_1\text{Gender\_producer}+{\beta }_2{\text{Age}}_{\text{producer}}+{\beta }_3{\text{Education}}_{\text{producer}}\\ +{\beta }_4\text{Household size}+{\beta }_5\text{land size}+{\beta }_6{\text{Access}}_{\text{capital}}\\ +{\beta }_7{\text{Acess}}_{\text{information}}+{\beta }_8\text{Farmr group}+{\beta }_9\text{means of transport}\\ +{\beta }_{10}\text{extension-contact}+{\beta }_{11}\text{experience}+B_{12}\text{output price}\\ +B_{13}{\text{Distance}}_{\text{tarmac}}+{\epsilon }_i\end{array}$ (8)

Market margins play a crucial role in understanding the economic dynamics of agro-based products along the value chain. To estimate these margins, economists employ econometric techniques that analyze price differentials (ΔP) between various stages of production and consumption. As proposed by [27] , the market margin analysis offers the best tools to analyze the performance of a market outlet/channel, and the estimation specification involves a formulaic representation as follows:

$\text{Producers'}\text{share}=\frac{\text{Producer price}}{\text{Next actor price}}=1-\frac{\text{Marketing Margin}}{\text{Actor price}}$(9)

where the marketing margin will be taken as the difference between the producer’s price and the next market actor price.

$\text{GMM}=\frac{\text{Actor price}-\text{Producer price}}{\text{Actor price}}\times 100$(10)

where GMMis the gross marketing margin, hence, the gross marketing margin of producers represents the share of the price paid by market actors allocated to the producer’s income. Conversely, the Net Marketing Margin (NMM) indicates the percentage of the final price obtained by the intermediary as income after subtracting marketing costs. Through the NMM, the allocative efficiency of the market outlets can be assessed. A higher NMM signifies diminished and inequitable income distribution, thereby dampening market participation by smallholder farmers.

$\text{NMM}=\frac{\text{Gross Marketing Margin}-\text{Marketing costs}}{\text{Actor price}}$(11)

The marketing margin at a given stage “i” (GMM_i) will be computed as:

${\text{GMM}}_i=\frac{\text{Next actor price}-\text{Purchasing price}}{\text{Next actors' price}-\text{Farmer' sprice}}\times 100$(12)

The total gross profit margin (TGPM) will be computed as:

$\text{TGPM}=\text{TGMM}-\text{TOE}$(13)

where TGMM = Consumer’s price − Farmers price

TOE = Total operating expenses

The profit margin at stage “i” is given as:

$\begin{array}{l}\text{Gross profit margin}\left(\text{GPM}\right)\\ =\frac{\text{Gross Market Margin}i-\text{Operating expenses}i}{\text{Total gross profit margin}}\times 100\end{array}$(14)

The results presented in Table 1 showcased variations in key metrics among surveyed households. The average household size ranged from five to six members, with a majority (56%) benefiting from extension services. Approximately half of the carrot farmers reported membership in farmer groups, predominantly led by males (71%), averaging 45.1 years in age and holding an average of 9.39 years of education. Carrot production was typically undertaken on an average land size of 1.73 acres, indicating a predominantly smallholder farming demographic. Farmers were situated an average distance of 14.95 kilometers from carrot cleaning points and traveled approximately 9.54 kilometers to reach the

***p < 0.01, **p < 0.05, *p < 0.10.

nearest market. Access to credit services was limited, with only 12% of households utilizing such services, possibly hindering adoption of advanced production technologies like irrigation. Furthermore, respondents were queried about their carrot sales during the 2019/2020 production and marketing season, including details on market outlets and buyers involved.

Moreover, the findings revealed that a significant majority (81%) of surveyed farmers participated in selling their produce through various outlets, notably the farm gate (29.94%), cleaning point (25.48%), local market (21.02%), external market (15.92%), and export market (7.64%). Consumers, brokers, aggregators, wholesalers, and retailers emerged as primary purchasers of carrots originating from Nakuru County, with aggregators notably acquiring 33.76% of produce directly from farmers across multiple market outlets. Additionally, smallholder carrot farmers sold 27.39% of their produce to brokers, 18.47% to wholesalers, 15.92% to retailers, and 4.46% to consumers, indicating diverse transactional patterns across various market outlets.

In this study, the Multinomial Logit (MNL) model was employed to scrutinize the factors influencing the choice of marketing outlets among carrot farmers in Nakuru County. The selection of this model was based on the understanding that data related to market outlet preferences for carrot production are context-specific, with each independent variable having a unique value for each case. Furthermore, the MNL model operates under the assumption that the dependent variable (chosen market outlet) cannot be precisely predicted from the independent variables for any given case. The analysis encompassed various independent variables, including gender, age, education level, distance to the market, land size, years of experience, land allocated to carrots, household size, access to credit, membership in carrot groups, and distance to the carrot cleaning point. Upon analyzing the MNL results, as illustrated in Table 2 . Gender played a significant role in the choice of market outlets, particularly affecting the cleaning point and local market preferences. Male-headed households were less inclined to sell carrots at cleaning points by 6.75% but showed a higher likelihood (12.92%) of selling at the local market compared to female-headed households. This divergence may arise from men’s propensity for risk-taking behavior, leading them to actively seek markets rather than settling for the less competitive cleaning point. Conversely, female-headed households may prioritize convenience over market competitiveness due to time constraints, opting to sell closer to home. These findings resonate with previous studies by [28] and [29] , highlighting gender disparities in market access. Age also emerged as a significant factor influencing market outlet choice, particularly favoring the farm gate and local market. Older farmers exhibited a higher likelihood (approximately 1%) of selling at both outlets, possibly due to their risk-averse nature, preferring traditional markets for their stability. This aligns with prior research by [30] and [31] , which

***p < 0.01; **p < 0.05, *p < 0.1. (Standard errors in parentheses).

emphasized the age-related preference for traditional markets. However, [32] observed different trends, indicating the complexity of market dynamics across agricultural contexts. Furthermore, geographical proximity significantly affected market outlet choices, with increased distance leading to varied preferences among the farm gate, local market, and external market. For every 1-kilometer increase in distance, there was a 2% rise in the likelihood of selling at the farm gate, a 2.67% decrease at the local market, and a 1% increase at the external market. These findings align with [33] observations on the impact of distance on market choices, emphasizing the importance of minimizing transportation costs.

Moreover, land size owned by households influenced market outlet preferences, particularly favoring cleaning points and external market outlets. An increase of 1 acre corresponded to a 2.46% increase in selling at cleaning points and a 1.88% increase at external market outlets. This suggests a shift towards market-oriented farming practices with larger landholdings. Similar trends were observed regarding farming experience, with experienced farmers exhibiting a higher likelihood of accessing formal market outlets such as the external market and export market. These findings corroborate [34] observations on the positive impact of farming experience on market access. The size of land allocated to carrot cultivation and household size also influenced market outlet choices. An increase in carrot land size by 1 acre resulted in a 4.34% decrease in selling at cleaning points and a 2.27% increase at export market outlets. Additionally, household size had a significant positive influence on external market outlets, with a 1-member increase corresponding to a 2.34% rise in selling at these outlets. These findings contrast with [35] observations on household size’s negative impact on market outlet choice for tomato producers. Finally, distance to the cleaning point positively influenced all market outlet choices, indicating that proximity to cleaning points influences farmers’ decisions, with greater distances leading to varied preferences among the available options.

The examination of gross margins within the carrot value chain in Nakuru County provides critical insights into the economic viability and operational dynamics of carrot farming and marketing activities. As depicted in Table 3 , the presence of positive average gross margins across all market outlets signals the potential profitability of carrot cultivation in the region [33] . Particularly striking is the observation of higher average gross margins per acre in the export market, followed by the external market, local market, cleaning point, and farm gate. This pattern underscores the potential for farmers to maximize returns by targeting higher-value market segments such as export and external markets [36] . Additionally, the variation in gross margin ratios across different market outlets sheds light on the distribution of sales revenue among farmers after accounting for production and marketing costs. The lower ratio observed in the export market suggests that despite the prospects of higher revenue, a substantial portion is absorbed by operational expenses [37] . Moreover, the predominant role of brokers and aggregators as key buyers at the farm gate and cleaning point, respectively, highlights the importance of engaging with formal traders to optimize returns, as evidenced by comparatively higher profits compared to direct sales [38] .

Table 4 provides a breakdown of gross margins for various market intermediaries, revealing significant profits per unit of carrots sold and indicating potential market influence. However, the disparities in margins between traders and farmers underscore the need to address challenges related to market concentration, price manipulation, and inefficiencies within the value chain [34] . To foster a more equitable and sustainable carrot industry in Nakuru County, interventions targeting the reduction of transaction costs, improvement of market access, and enhancement of farmers’ capacity is imperative [27] [29] . These measures are essential for creating an inclusive and resilient market environment that benefits all stakeholders involved in the carrot value chain.

In-depth field studies and interviews with carrot producers in Nakuru County, Kenya, have unveiled a myriad of challenges and opportunities inherent in carrot

cultivation, profoundly impacting decision-making processes. These insights align with the conceptual framework’s five categories of influence: endogenous influences of socio-economic characteristics, informational influences, experiential influences, and influences of relative change [39] [40] [41] . This section of the manuscript delves into carrot farming-specific issues within these categories, directly or indirectly shaping the decision-making of small-scale farmers regarding subsistence versus commercial farming and alternative crop choices. Key factors include farming and market experience, return on investment, relative production costs and pricing, farm size, information sources, and relative changes in economic conditions. Experiential and observational learning play pivotal roles in shaping farmers’ decisions, with efforts to enhance smallholding farm profitability potentially leading to a transition to commercial carrot farming. Currently perceived as a subsistence crop, carrots hold untapped potential as a cash crop, given their demand in both rural and urban markets. This paradigm shift could prompt a significant portion of the farming population to adopt carrot cultivation, driven by the prospect of increased profit margins due to competitive advantage, as suggested by [42] . However, the realization of this potential hinges on the success of pioneering farmers, rendering this behavioral shift speculative.

In light of current research, addressing the complexities of improving carrot farmers’ decision-making processes remains a formidable challenge. Primarily, the predominant mode of carrot sales occurs through farmer trade, necessitating the implementation of various strategies to enhance backward linkages. Farmer organizations, notably cooperatives, emerge as pivotal actors in bridging smallholder farmers with markets [43] [44] . Contracting arrangements between farmers and buyers offer promising avenues to facilitate market access for smallholders in Kenya, fostering stronger ties between farmers and agribusiness entities. Furthermore, it enhanced produce quality and quantity, alongside reduced transaction costs through streamlined search and information dissemination, as well as minimized price negotiation efforts, which was similar to the suggestion of [45] . Notably, these contracts not only elevate and stabilize smallholder incomes but also enhance production techniques, crop quality, and access to essential resources such as credit and farm inputs. Additionally, to circumvent the inefficiencies and fragmentation prevalent in smallholder carrot markets, vertical integration strategies, such as group formation or collaboration to directly supply supermarkets, present viable alternatives. Crucially, the effectiveness of these strategies hinges on the presence of incentives guiding the decision-making process, with the optimal approach contingent on the socio-economic, political, and cultural context. Policy interventions aimed at enhancing smallholder market participation demand stakeholder engagement and a comprehensive understanding of the prevailing market structure. This proactive approach ensures the mitigation of unintended negative consequences and will be expounded upon in subsequent policy analysis sessions.

1. Respondent’s name __________________________________________

2. Fill the respondents’ relevant information where applicable in the table below.

3. What is the highest level of education of the respondent? Fill in the number of years in each.

4. Are you the head of the household?1 = Yes 0 = No

5. If no please provide the information below regarding the household head

6. When did you start carrot production? Please state the year you began. _______________

7. Please, fill the following table with the information regarding the household members.

8. Please list the top three sources of income for the household.

Income sources:TickRank

1 = Production/sale of crops

2 = Production/sale of livestock & livestock products

3 = Agricultural output trading,

4 = Agricultural input trading

5 = Salaried employment

6 = Casual laborer

7 = Pension

8 = Remittances (income from relatives/friends etc)

9. Others (specify)………………………………………..

9. How much total land do you have? Please state in acres. ____________

10. Indicate the land tenure system on the land in use?________

1 = Communal 2 = Rented/lease 3 = Privately owned

11. If you do not own land, are you satisfied with the arrangement on the land that you are using? Explain

__________________________________________________________________________________________________________________________________________________________________________________________

12. How much of this land was under carrot last season? ___________________

13. Did you use any inputs (fertilizers, manure, pesticides) in carrot production last season?__

1 = Yes 0 = No

14. If yes which ones did you use and how much? KES______________

15. Do you participate in Carrot marketing?1 = Yes 0 = No

16. What is the main reason for selling carrots?

1 = I need cash for home consumption2 = I need money for input purchases

3 = I need money to pay school fees4 = I want to repay loan

5 = Other (Specify) _____________________

17. Do you perform price surveys, before selling? _____1 = Yes 0 = No

18. How do you rate the availability of labour used in carrot production? _____________

0 = unavailable 1 = easily available 2 = Available

19. How did you sell your carrots _________1 = individually 2 = through a group

20. Where was your point of sale (outlet)?

1 = Sold at home (Farm gate) 2 = Cleaning point3 = Local market (nearest market/town within the County)4 = External market (main markets/towns outside Nakuru County)5 = Export market (Markets outside Kenya)6 = Other (Specify) _____________

21. How is a price set during the sales? _________

1 = we negotiate 2 = It is market driven 3 = It is set by buyers4 = Other (Specify) ________________

22. State the buyer you use to sell your carrots, level of satisfaction and the most rewarding carrot channel in your area in the table below.

23. In terms of the outlet, you use regularly, what are the main benefits? _________

1 = high prices 2 = understand the contract 3 = nearer4 = provide inputs

5 = come for produce in the farm6 = Other Specify………………………………..

24. What was the payment duration from your preferred buyer?

1 = cash on the spot 2 = 2 - 7 days3 = 8 - 14 days4 = 14 - 30 days5 = After 30 days

25. Do you have any contractual agreements or a guaranteed/ready market (formal or informal) with any agribusiness outlet e.g Hotels, Supermarkets etc? ________1 = Yes 0 = No

26. Do you have regular customers, who always buy from you? ________1 = Yes 0 = No

27. If Yes, how long have you been trading with these customers? ___________ years

28. Before selling your produce what value adding activities do you perform?

29. How much did you sell in the past season?__________(Kgs)

30. How much per kilogram did you get in KES_________

31. Have you ever declined a selling price and ended up not selling? ________1 = Yes 0 = No

32. What type of transport do you use?1 = Manpower 2 = Wheelbarrow 3 = Vehicle

4 = Donkey 5 = Other Specify_______________________

33. How much did you pay for transport in KES___________

34. What general problem do you experience when moving your carrots?

1 = Small size transport2 = Lack of transport means

3 = High transport cost4 = Other specify______________________

35. When selling, do you combine your carrots with that of other farmers? ______1 = Yes 0 = No

36. If no, state the main reason ______________

1 = you don’t sell at the same time2 = you don’t sell at the same market

3 = you have a conflict with them4 = Other (Specify) ____________________

37. Do you receive market information prior to sales? ___________1 = Yes 0 = No

38. If yes, what is/are your source(s) of information? ______________

1 = Radio 2 = TV 3 = Extension officers 4 = Extension publications

5 = Co-farmers 6 = Middlemen/women 7 = Development partners

8 = Other (Specify) ________________________

39. In what form would you like the price information to be delivered?

1 = Price per bag _____ 2 = Price per kilogram ____3 = Other (Specify)_______________

40. Do you receive extension services?1 = Yes ____ 0 = No_____

If Yes, How many times did they visit in a production and marketing season?

1 = Once 2 = Twice 3 = Three 4 = More than three ___________

41. What services does he/she provide?_________

1 = Advise on crop husbandry2 = Advise on carrot marketing3 = Advice on record keeping

4 = Advice on good variety5 = Other (Specify) ________________

42. Did you access any credit financial services in the last production season? _____1 = Yes 0 = No

If yes, name the source

1 = Commercial banks_______2 = AFC ______3 = Agricultural cooperatives___

4 = Credit unions (merry-go-round) 5 = Family and friends

6 = Other (Specify) ___________________________________

43. Has anyone in the household attend a farmers training last year?1 = Yes ____ 0 = No_____

If yes, how many times for the whole year? _______________

44. What was the training about? _____________

1 = Soil erosion2 = Fertilizer/input use3 = Carrot production and marketing

4 = Safety and quality standards5 = record keeping6 = Other (Specify) _____________

45. Does any member of the household belong to a local or external organization?1 = Yes 0 = No

46. If yes, what type of group? ________________

1 = Self-help group 2 = Welfare group 3 = Cooperative society4 = Other (Specify) __________

47. What are the main activities of the group? _________

1 = Farming2 = Business 3 = Advocacy4 = Other (Specify) ____________

48. List what you consider to be the major problems you face in marketing your carrots

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

49. Suggest ways in which such problems can be addressed

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________