For two or more traits, each can be characterized by Equation (7) with different parameters:

When these traits are qualitative traits, breeders typically search for them independently because there are techniques enabling the breeders to incorporate only the single trait in a cultivar (i.e. by back-crossing and other methods, unwanted traits can be discarded). Thus even if traits are highly correlated, the breeder will search independently for them.4

Thus, if we set N = N1 + N2 at some level (say the optimizing level) where:

MC(N 1) = MC(N 2) = a1V1N 1 = a1 V1N1 = a2V2N2 (12)

we have the standard invention (or innovation) possibilities frontier (IPF) depicted in Fig. 1.2. (Note the depiction is in terms of traits, but these can be translated into economic units through values.)

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