The binary quality price function: theory, empirical testing, and application to Israeli tomato export

When the quality traits of a quality-differentiated product are
defined in a binary form, the resulting binary quality price
function (BQPF) is shown to be convex. This imp1ies that when many
units of the good are sold in a single transaction, marketing it in
packages of homogeneous product is more profitable, than in
heterogeneous ones. Therefore, if sorting is possible, and
relatively inexpensive, it should be undertaken. Another
implication of the convexity of the BQPF concerns the case when
quality uncertainty of each unit of the product exists at the time
of sale. Providing quality guarantee in this case is equivalent to
sorting in the former case.
The convexity of the BQPF is tested empirically using data of
Israeli export glass-house tomatoes. An estimate of this BQPF has
been used to determine actual quality-differentiated transfer prices
paid by the single exporting agency to the various growers of this
produce. A method of estimating an autoregressive model of the
first order with missing observations was developed and utilized in
this study and is reported in the Appendix.