Land Quality and Agricultural Productivity: A Distance Function Approach
the frontier, such as producer A, are inefficient because the same level of output could be
produced with less input. If the output of producer A is held constant, a reduction of input use
from a to c would move A to the frontier. This system assumes that all producers can reach the
frontier by producing efficiently.
In fact, non-controllable factors may prevent some producers from reaching the efficient
frontier, regardless of input level. Figure 10.2 adds a second frontier, inferior to the first, that
describes efficient input/output combinations for producers that are limited by some non-
controllable factor, such as poor land quality. If producer A is limited by poor land quality, the
reduction in input use needed to reach this “achievable” frontier will be less than that implied by
the unrestricted frontier. In this case, the reduction in input use that is required to make producer
A efficient with respect to the achievable frontier is from a to b; any further reduction in input
use by producer A would result in a decrease in the level of output.
Because producer A is operating in an environment less favorable than the unrestricted
environment, its efficiency computed with respect to all countries will be lower than that
computed with respect to countries sharing its own environment. The distance between b and c
in Figure 10.2 represents the magnitude of the gap between the two frontiers. This gap between
frontiers can be interpreted as the contribution of land quality to technical inefficiency measured
with respect to the unrestricted frontier. In the simple single-input/single-output system shown
in Figures 10.1 and 10.2, land quality’s contribution to technical inefficiency can be expressed as
the ratio of the reductions in inputs implied by the two frontiers, namely the ratio cb/ca. For
systems of higher dimensionality (i.e. with multiple inputs and/or outputs), the distances must be
characterized in a more general fashion.