154 Agricultural Research and Produciivily 



2 T-T r^ +^^ l V^ it-T) d^-) -r 



aA7( 



the Lagrange multiplier jj. is 

 dViS)) 



(8.26) 



M = 



aA7( 



r) L ^2 J LaATCr) ^i;-^j ^7(0"^ 



Along the optimal path the net marginal contribution of an in- 

 crease in A7(r).r = 0, 1, 2, . . ., T-l, is the same for every r and 

 is equal to the future contribution, once search starts, of the in- 

 creased variance minus the marginal cost of increasing 7 (includ- 

 ing the future effect of an increased 7 on the cost function), all 

 discounted to / = 0. 



It is not clear how Ay{T) changes with r . On the one hand, as 

 r approaches T, the realization of increased income nears and the 

 first term on the right of equation 8.26 increases; while on the 

 other hand, with time T increases and, by equation 8.19, increas- 

 ing-variance research is more costly. In practice, research work 

 often speeds up toward the completion of a project, for instance, 

 in Dupont's R&D investment in nylon (Nelson et al. 1967, p. 91), 

 not only in reaction to the approach of the termination point of 

 investment in research and the start of income realization period, 

 but also as a result of the growing confidence in the success of the 

 venture, discovery of new avenues of study, obstacles to over- 

 come, and fear of competition. 



The model developed in this chapter is far from complete. Our 

 purpose in presenting it is to suggest a new perspective on the 

 process of technological discovery. We have shown that the pro- 

 cess has important economic allocative problems and that the 

 principle of optimization can be applied to it. 



This simple model enables something to be said about 

 diminishing returns to discovery effort and shows the effect of ad- 

 vances in scientific knowledge that shift the "structural 

 parameters" of research. The sugarcane varietal history discussed 



