Structured questionnaires were randomly administered in Chepyuk and Mitira wards at household level with the main aim off establishing the main economic activities. The study employed a random sampling method for data collection. A sample size was calculated with a confidence level of 90 percent, a margin error of 0.1 and a Z-score of 1.645. A confident level of more than 95 percent could not be achieved especially in Chepyuk where movement becomes difficult due to heavy rains as the data was collected during the onset of wet season. The questionnaires were geocoded by uploading them on Kobo collect app that rans on android phones. This program made it possible to gather data offline, which was then uploaded to a server for analysis. Data was submitted daily to guarantee correctness, verify facts, and fix any problems that might have impeded the procedure. This method enabled for real-time monitoring of the data collection process and reduced data entry error. Research assistants were trained and later dispatched to the field to collect the data.

Another set of data was collected from key informants specifically traders at the Chwele and Kagio markets located in Chepyuk and Mitira wards respectively. Key informant interview were also contacted targeting land experts within the two sites. Most farmers in rural areas do not keep production cost, therefore to test whether breakeven was being made production cost for carrot farming from various agronomy sites was used which gave a production cost of kshs 95,500 [56] per acre. The production per acre was estimated to be 15 tons, with the estimates cost being inclusive of labour and all farm inputs.

Some challenges that were observed during data collection included language barriers, network issues, and accessibility to households especially during the rainy season because most of the rural roads are untarmacked and many households are situated in remote areas. Challenges of connectivity were however addressed by the fact that KoboCollect can be used offline. Other complexities were met by using local data collectors who helped in resolving issues such as language barriers, and designing the schedule for data collection to consider access barriers where applicable.

Approaches to assess the impact of rural roads improvement have been based on changes of consumption at household level [57] [58] . Apart from consumption patterns [24] included other indicators such as choice of mode of transport and crop production to assess the effect of road network improvement. In their study done in Morocco [59] used schooling decision and employment to gauge the impact of rural roads improvement where it was established that there is a positive impact to young males with a marked improvement in enrolment and transition level. [60] in their study carried out in Ethiopia, Zambia and Vietnam found a positive correlation between road improvement and expansion of social service provision. Rural roads are a key sector supporting the attainment of Sustainable Development Goals (SDGs) which are linked to good governance, good health, gender, education climate change and environment [14] .

In both of the relieved studies correlating road network and rural development both qualitative and quantitative data [61] has been applied. It is the same approach applied in this study with agricultural productivity and road network being the center of focus.

Bid rent income theory will be applied. The assumption is the rent that is the income from investment on is determined by yield less production and transport costs as indicated in Equation (3). A reduction on transport cost implies an improvement in net incomes. In this study carrot crop is selected to assess the break even by the farmers.

Equation (1): Rent Income Calculation per unit area: Adopted from [62]

$LR=y\left(m-c\right)-\left(t\ast d\right)$

LR = location rent per unit area of land;

y = is yield per unit land;

m = the market price per unit commodity;

c = production cost per unit of community;

t = transport rate per unit of distance;

d = distance to market.

To get the estimates on transport cost, travel time on the main transport corridor within the study area was measured. The average measured travel speed in Chepyuk ward of Bungoma County was 15 km/hour. This speed was measured by driving along Kopsiro-Chepyuk-Kipsikkrok-Cheptonon Mulembe road which connects to the interior of Chepyuk ward via the main administration center. For the Mitira ward the travel time was estimated on the main road that is Othaya-Mukurweini-Kagumo and an average speed of 65 km/hour was recorded.

The transport charges can be estimated from the cost of hiring transport means [1] . The cost for hiring a truck was based on one of the vehicle hiring company [63] at a rate of Khs.12,250. To factor in friction due road condition, a constant value was estimated using the maximum allowable speed on rural roads which is 80 km/hour for vehicles offering public service.

Equation (2): Friction constant Calculation

$k=\frac{m}{a}$

k = friction constant;

m = Maximum allowance speed per given segment;

a = actual maximum speed per given segment.

By inserting the constant k in Equation (1) we get below equation

Equation (3): Net Rent Income Calculation with constant k

$LR=y\left(m-c\right)-k\left(t\ast d\right)$

The total length of road network is 72 and 99 kilometers for Chepyuk and Mitira wards respectively. The entire Chepyuk ward do not have any tarmac road compared to Mitira which has tarmac roads of 11 kilometers of running length. The 52 kilometers of gravel in Chepyuk ward is rarely maintained marking it unusable during rainy days. Being located in a mountain region movement in Chepyuk is curtained as it rains throughout the year based on climatic conditions indicated in Table 1 . This limits the flow of goods and services in Chepyuk Ward. On the other hand, Mitira ward has slightly better roads condition. The summary of road surface within the two study area is summarized in Table 2 . The use of donkeys as a means of transport for Chepyuk stands at 28 percent can be explained by the condition of roads. This implies some zones cannot be accessed by motorized transport. In Mitira 26 percent of household access the market using motorbikes which is an indication of good roads. It is therefore evident traders and farmers can access markets in Mitira ward faster compared to Chepyuk which reduces time wastage and possible losses especially for vegetables which are perishable goods if not consumed within a short period of time after harvest unless preserved in a refrigerator.

Table 2. Road surface in Chepyuk and Mitira Wards.

The data from the household survey indicates 95.6 percent of r Chepyuk esidents depend on agriculture as a source of livelihood either fully or partially. In Mitira ward the percent of those that depend on agriculture stands at 68.2 percent. The agricultural enterprises in both the study area are in harmony with the recommendations of the farm management handbook [18] . The enterprises which are in the form of crops includes maize, potatoes, beans, onions, kales, potatoes, beans, cabbage, carrots, coffee, banana, avocados, napier grass, passion fruits among others. The primary market in Chepyuk for selling crops is Chwele accounting for 65% of the respondent’s center of sales. Other markets include; Kapkateny, Kipsigon, Chepyuk, Cheptais, Kastaay, and Bondeni. In Mitira Ward, the primary markets for selling crops are Kagumo and Mugaya accounting for 59% and 14% respectively. Other markets include Gathuthuma, Kagio, Kiamaina, Kathiti tea buying center, Kariko, Kerugoya, Kamuiru, Gatwe/Kagumo, Gathera, Gathuthumu, Gatwe, Kianduku, Kamugoiyo, Kianjagi, Kiambungu, Kanjii, Kagio market, Mununga tea factory, and Kagumo coffee farmers.

The average distance traveled from the farm in transporting crops to the market varies between the two wards. In Mitira Ward, 2.58 km, taking approximately 20 minutes while in Chepyuk Ward, 14.13 km, taking approximately 117 minutes. Mitira farmers benefit from much shorter distances to markets, which likely contributes to reduced transportation costs. In contrast, Chepyuk farmers face longer travels, which may increase transportation costs and risks of crop spoilage, particularly for perishable goods. In both wards transport-related constraints account for the largest percentage in Chepyuk ward at 73% while in Mitira ward at 44%.

Apart from crop production the two study areas also support livestock farming which relate to recommendation of [17] . Chepyuk Ward has a strong focus on cattle, with 55.17% of livestock being cattle, 12.07% sheep, and 10.34% goats. Mitira Ward shows more diversity; 42.62% cattle, 25.14% chicken, and 15.30% dairy cattle. Milk is one of the key product of the livestock industry, selling price of one liter of milk is kshs.36.65 in Chepyuk while at Mitira Kshs.55.08. The high price per liter of milk in Mitira ward is linked to diverse market potential including home consumption and value addition factories including Fresha Milk, Mount Kenya Dairy, KCC, Brookside among others which is facilitated by good roads. On contrary side, Chepyuk farmers have to sell their milk at lower market price due to limited market. Brookside dairy and KCC factory are located in Eldoret, the only constraining factor is the condition of roads which reduces accessibility and selling price.

To estimate the rent per unit value of land, carrot production agricultural enterprise was selected. The survey data indicates both Chepyuk and Mitira wards have an average household landholding size 2.27 and 2.42 acres. With both areas having almost similar land acreage and same agro-ecological zones as shown in Table 1 and on assumption same crop probation measures will be applied the production per acre is estimated at 15 tons per acre [64] and [56] . The production and transport costs are indication in Table 3 .

Chwele and Kagio markets were selected to test the bid rent model since they were the furthest and major markets for Chwele and Chepyuk. The distance to the major markets for two production rural areas that is Chepyuk and Mitira wards are 23 kms and 21 kms respectively implying they will all pay Khs. 12,250 per trip based on transport outsourcing company [63] . By substituting maximum speed for Chepyuk of 15 kms/hour and Mitira of 65 kms/hour in Equation 2 transport charges are estimated to be as indicated in Table 3 . There will be additional friction charges of Kshs. 5588 for Mitira and Kshs. 15,750 for Chepyuk wards respectively. Due to the poor road network in Chepyuk farming households will have to spend additional Kshs. 10,162 per trip while accessing the market which reduces the incomes. Additionally, selling price per 100 kgs bag is Kshs. 1500 cheaper in Chepyuk compared to Mitira ward. This is because farmers have to dispose their fresh produce as fast as possible because the poor road conditions hinder wider market access. The situation becomes more complex in Chephyuk during the rainy season. To get the rent per acre the values in Table 3 are substituted in Equation (3). The land rent which is the income from carrot farming per season is Khs. 401,500 in Chepyuk and Khs. 639,423 for Mitira which has an extra income of Kshs. 237,923. There is a clear indication that good road network adds value to the rent gained per acre. For Mitira the good road network has opened it to other markets regional markets. Chepyuk residents have to sell their products a lower price because it lacks competitive advance accruing from road connectivity which are not passable throughout the year.

Table 3. Estimated Rent per unit of land.

Factors of production from classical economics are three and includes land, labour and capital [65] . Their availability dictates the direction of growth of any region. In this study, the factors were father split to nine as indicated in Table 4 in order gauge the general perception of what hinders the general rural development in the two study area. Household survey data indicates 81.4 percent of Chepyuk respondents perceives that the condition of road affects development followed closely by inability to access credit at 80.5%. Expensive farm inputs come third with 74.6 percent. In Mitira ward expensive farm inputs are ranked as number one factor affecting development with 65.4 percent of household stating it as the main hindrance. Other infrastructure installation including electricity, water scores above average in Chepyuk as compared to Mitira which recorded values below the first quartile. The state of road network determines the amount of presence of other services. Areas with good road network attract location of training facilities hence skills transfer. Roads improves security of an areas, with poor roads incidences of theft are recorded since the police response time will be derailed.

Table 4. factors of production in Chepyuk and Mitira Wards.

Mitira ward has benefited from government of Kenya when it comes to investment in the road sector. There has been a government project Mau Mau Road circuit [66] targeting to cover 200 Kilometer of tarmac road in the mountain region with Mitira being one of the beneficiary ward. The Mau Mau Circuit Corridor project is the main reason why Mitira has a good road network. The inequality was started by the colonial government policy [30] which targeted investment in native Kikuyu settlement with Mitira being one of geographically focus area in terms of settlement investment and securing land tenure. This is unfair treatment since both Chepyuk and Mitira wards are high agricultural production regions and should receive the same treatment when it comes to infrastructure investment. The Equalization Fund as provided for under Article 204 of the constitution of Kenya is meant to address the difference in provision of basic services between the undeveloped and the developed regions. This fund seeks to enhance infrastructure like roads, water, and electricity as well as health departments [37] . This seems to be unrealistic with more projects being implemented in more politically right regions for example being the Mau Mau circuit corridor which is located in areas where majority have voted to the ruling regime for the last twenty years.

Reports of the [67] and County Integrated Development Plans (CIDPs) detail the allocation and expenditure of the Equalization Fund. In Bungoma and Kirinyaga counties, the fund has been assigned to various developmental projects as a part of improving the physical infrastructure in rural areas [68] [69] . Both affirm the value of investing in agriculture as well as the enhancement of assets; development of existing infrastructures, particularly roads; and agribusiness. The budget is accumulated at the sub-county level with details of specific major projects. Both consider Rural development as one of their flagship projects. Challenges in fund disbursement and project implementation have significantly impacted the effective use of the Equalization Fund. Delays happen frequently especially due to bureaucratic hold up at the exchequer level and with partners resulting in delayed approval and disbursement of funds. Also, delayed procurement processes and absorption of funds stated in the County Integrated Development Plans (CIDPs) also hinders project implementation. For instance, Bungoma County revealed a significant delay in the absorption rate, where only 75% of funds were allocated for rural development within the agricultural sector [68] .

With no good road network system some regions will not attract development. For Chepyuk the impact of political formation and orientation may derail development of road infrastructure since the ethnic composition of its voters is much more different to its county voting blocs. With no proper road network Chepyuk will continue to lag behind in terms of rural regions development. The area will not attract investment including banks, training institutions and even access to wider regional markets. Chepyuk region has also recorded land tenure conflicts, the blame has been on government settlement officers who have taken long to settle land disputes.