2.1. Study Sites and Study Design
The study was conducted in the Masaka and Kamuli districts, which are in the central and eastern regions of Uganda, respectively. The two districts were purposely selected for their high levels of pig and sweetpotato production. Furthermore, several programmes aimed at boosting pig and sweetpotato production have been implemented in these two districts by several international and national (local) agricultural research institutions.
A total of 256 pig farmers were randomly selected from 16 purposive clusters. These clusters were formed at a radius of 3 km around each of the 16 farmers piloting the use of sweetpotato silage as pig feed in Kamuli and Masaka. Interviews were conducted using a semi-structured questionnaire containing a series of open- and close-ended questions in August and September 2016.
The questionnaire used included questions about farmers’ demographic characteristics, their perceptions of using sweetpotato silage-based diet as pig feed, their willingness-to-pay, and the market potential of sweetpotato silage-based diet.
2.3. Theoretical and Analytical Framework
In this study, we used the double bounded willingness-to-pay (WTP) method. WTP is a stated preference method that involves asking consumers directly, in a hypothetical survey, the maximum amount they are willing-to-pay for a good or service that has been offered [
14]. The contingent valuation method (CVM) has been used by economists for approximately thirty years to value changes in natural resources and the environment. In several other cases, CVM has been used to evaluate farmers’ preferences for crop attributes and other technical innovations, particularly where revealed preference approaches are not feasible. For this reason, CVM is ideal when it comes to measuring the value of non-market goods [
15].
The underlying framework for WTP is based on utility maximisation. Let U (X), be an individual preference function where
is a vector of private goods available at market prices:
The individual maximises utility subject to an income constraint,
y, and the indirect utility function is given by:
The minimum expenditure function is dual to the indirect utility function and is given as:
The derivative of the expenditure function with respect to price then gives the Hicksian or utility-constant demand, where the subscript indicates a partial derivative.
The negative ratio of derivatives of the indirect utility function with respect to price and income then gives the Marshallian or ordinary demand curve.
An individual will therefore be willing to pay for a good if it maximises his utility function, subject to an income constraint.
This study applied the double-bounded CVM elicitation technique. Hanemann et al. [
16] show that this method improves the efficiency of a willingness-to-pay study by offering the respondent a second bid, lower or higher depending on the first response. It further incorporates more information about an individual’s WTP and, therefore, provides more efficient estimates and tighter confidence intervals than open- and close-ended formats. Open-ended formats often tend to be problematic, since the respondent might not have sufficient information and stimuli to thoroughly consider the values they would attach to a good if a market existed, and thus might not return realistic estimates [
17]. Close-ended questions, on the other hand, are incentive-compatible in that it becomes the respondent’s strategic interest to say yes if her/his WTP is greater or equal to the price asked and not otherwise [
18]. This approach requires a large sample size and its statistical efficiency is not very high [
16].
The operationalization of the double-bounded CVM technique began with enumerators first describing and presenting pictorial illustrations of sweetpotato silage-based diet to the respondents before obtaining data on their WTP. This step was executed to create awareness, because the product was new and not yet known by all respondents. Six bids were converted from local currency to US dollars (USD) at one Ugandan shilling (UGX) to 0.0003 USD, and then randomly distributed to different respondents. The six bids selected for use were: USD 0.06, USD 0.1, USD 0.15, USD 0.19, USD 0.24, and USD 0.3 per kilogram (kg). The bid prices were chosen based on results from pre-testing in which 30 respondents were asked how much they were willing to pay per kilogram of sweetpotato silage-based diet using the double bounded CVM approach. During the pre-test, a pre-determined initial bid price of USD 0.22 per kg of sweetpotato silage-based diet was allocated to every respondent. This initial bid price was obtained by calculating the breakeven price for a kilogram of sweetpotato silage-based diet (
Table 1). An additional amount of USD 0.05 was then included to account for the entrepreneurs’ costs of storage, transport, and profit.
Using double bounded CVM, farmers were then presented with the initial bid of USD 0.22 per kg of sweetpotato silage-based diet. If the farmer’s response to the initial bid price was “no”, USD 0.01 were subtracted, and a second bid was presented. This went on until the farmer responded with a “yes”. If a farmer agreed to the initial bid price, USD 0.01 were subtracted, and a second bid was presented. This went on until the farmer responded with a “no”. The price at which the farmer said “yes” was then taken as his/her WTP.
From the pre-test results, the lowest price/kg respondents were willing to pay for sweetpotato silage-based diet was USD 0.06/kg, and the highest WTP was USD 0.3/kg. Therefore, USD 0.06/kg and USD 0.3/kg were chosen as the lowest and highest price, respectively. The same method was used by Hall et al. [
19] to determine bid values, based upon results from pre-testing. They used open-ended questions which gave them values from USD 0 to USD 260. They chose to place a bid from USD 2 up to USD 100.
Depending on the response to the initial bid that was randomly offered, if the survey participant responded with a “yes”, a follow-up bid double the initial value was offered. Likewise, if the survey participant responded with a “no” to the initial bid price randomly offered, a second follow up bid half the initial value was offered (
Table 2).
Thus, there were four possible outcomes to the questions: (a) both answers are “yes”; (b) both answers are “no”; (c) a “yes” followed by a “no”; and (d) a “no” followed by a “yes.” [
13]. These four probabilities are then denoted as follows:
where
Pryy: probability of answering “yes” “yes”;
Pryn: probability of answering “yes” “no”;
Prny: probability of answering “no” “yes”; and
Prnn: probability of answering “no” “no”; B: price in the first question; B
u: higher price in the second question; B
d: lower price in the second question; WTP: willingness-to-pay; and F: cumulative distribution function (CDF).
Combining the probabilities of the four outcomes, the log-likelihood function (
lnL) for a sample then takes the form:
where
yy,
yn,
ny, and
nn are dummy variables. If one respondent says yes–yes (
yy) to two questions, then
yy = 1, otherwise it will be zero. Kimenju and De Groote [
20] point out that the parameter could be estimated by maximising the likelihood function. The mean WTP was then evaluated using the following equation, adopted from Shultz and Soliz [
21]:
where
is the estimated constant;
are the estimated co-efficient parameters;
are the mean values of the explanatory variables; and
is the estimated co-efficient of the bid.
2.4. Factors that Influence the Willingness to Pay for Sweetpotato Silage-Based Diet as Pig Feed
A binary logit regression model was fitted to assess the factors that influence the farmers’ willingness to pay for sweetpotato silage-based diets. Following Chen and Chern [
22] and Kimenju and Hugo [
13], a logit model was specified to examine the relationship between WTP and socio-economic variables, price, and perceptions about the product. Formally, the binary logistic model explaining consumers’ WTP is specified as:
where WTP is the willingness-to-pay {1 if the consumer is willing to pay for sweet potato silage-based diet and 0 otherwise};
is the bid price;
is a vector of explanatory variables;
are vectors of unknown coefficients; and
is the identically, independently distributed variable with zero mean.
The variables used in the binary logit model are presented in
Table 3. Most of these explanatory variables were selected based on theory and previous studies. For example, the bid price was expected to have a significant negative effect on farmers’ willingness to pay for sweetpotato silage-based diet following the theory of demand and supply, which indicates that price is inversely related to demand. Credit was treated as a liquidity constraint, while age was linked to the lifecycle hypothesis in technology adoption. The education level of the farmers was linked to the human capital theory, which states that skills are learnt or acquired, and that skills enhance the conceptualization of ideas. The number of pigs sold, the land under sweetpotato production, and the access to credit were assumed to be wealth indicators that have impact on the farmers’ decision-making process. Lastly, the extension was linked to exposure and collective learning.
2.5. Estimation of Market Potential for Sweetpotato Silage-Based Diet
The number of potential buyers (households) for sweetpotato silage-based diet was obtained based on the population estimates for the Masaka and Kamuli districts in 2014. The National Population and Housing Census conducted by Uganda Bureau of Statistics (UBOS) [
7], in 2014 estimated 75,306 and 93,789 households in Masaka and Kamuli, respectively, for a total of 169,195 households in the two districts combined. According to the national livestock census report [
7], 42.3% and 15.5% of the households in Masaka and Kamuli, respectively, are involved in pig rearing. These figures indicate a total of 31,854 and 14,537 pig-rearing households in the two districts, respectively. Further analysis of the primary data collected indicated that 43% of the pig rearing households in Masaka and 47% in Kamuli expressed a willingness-to-pay above the mean price of USD 0.20 per kg of silage-based diet. This finding indicated a potential buying population of 13,697 and 6833 pig-rearing households for Masaka and Kamuli, respectively.
Considering the fact that the average annual demand for sweetpotato silage-based diet was 0.955 and 0.673 tons per household in Masaka and Kamuli, respectively, the overall annual demand for each district was then derived by multiplying the average annual demand for sweetpotato silage-based pig diet per household by the number of households willing to pay the mean price and above. The market potentials for both Masaka and Kamuli were then computed using the formula below, as derived by Wolfe [
23].
where MP: market potential;
N: number of possible buyers at price
P;
P: mean willingness-to-pay or average selling price; and A: average annual consumption. Since the price of a commodity is a key driver of demand and supply in the market, further analysis explored the effect of increasing or decreasing the mean price of sweetpotato silage-based pig diet on its demand and supply.