at least one of the three. In each of the four scenarios, only fertilizer is used in over half of the sample where at least one of the three inputs is used. In Ethiopia, although not generally in Niger, we observe the same disconnect between household and plot level statistics; joint probabilities are always higher at the household level than the plot level. To the extent that yields could be further enhanced by combining more than two improved inputs, like the set of three described in Figure 6, it appears that households have even more to gain from coupling inputs together appropriately.

# **_4.6. Input use incentives and provisioning_**

In this section, we look at characteristics of input provisioning within and across countries using household and community level information on relevant market transactions and stated accessibility. Using comparable variables, these descriptive statistics may help to illuminate differences in the supply systems of inputs which may help to further explain variation in the incidence and rate of input use.

# <u>Input/output price ratios</u>

The incentive to use an input is best encapsulated in the ratio of the input to output prices. These values also represent the profit break-even point for application. If the marginal physical product (i.e., crop response rate) is higher than this price ratio, in principle (and ignoring risk aversion, financing costs, travel costs, etc.) it is profitable to use the input, making these variables valuable benchmarks for production analysis. One widespread belief about modern agricultural inputs in the SSA context is that they are too expensive for smallholders to afford on commercial terms, hence the need for government subsidies.

Where available, we create median input and output prices at different levels of geographic aggregation for inorganic fertilizer only. There are insufficient observations of prices for other inputs and heterogeneity among types of agro-chemicals and seed make aggregation unreliable. In the LSMS-ISA data, we generally only observe the prices paid by households that purchased fertilizer, so we may under-estimate price ratios in places where input prices are high and, therefore, households decide not to purchase. Household level prices that were specified in unconventional units for which we did not have conversion factors (e.g., heap, bag, cart) are left out of the median calculations. Fertilizer prices are calculated as total amount for the product (in kilograms), not specific to the amount of nutrients, and thus are not directly applicable to production and profitability analysis at this stage. Fertilizer prices are observed sometimes differently across surveys. In Ethiopia, no unit prices for inputs can be calculated at the household level. In Nigeria, we only use where the household did not purchase fertilizer from the government or a politician so as to not conflate commercial market prices with subsidized prices.

Figure 5 displays the relationship between the input/output price ratios assigned to households and their level of inorganic fertilizer use, for the major crop of each country. Because these price ratios act as one component of the incentive to use fertilizer, we expect a strong negative relationship, where higher price ratios are associated with lower application rates. Indeed, in Malawi and Niger, countries with very dissimilar average fertilizer application rates and a different crop chosen as most important, we observe the expected downward trend. The 40