The Badly Behaved Production Function: Comment

In their recent article Joan Robinson and K. A. Naqvi provide an example which they think ". . . conclusively disproves the notion that the number of switches cannot be more than the number of capital goods in the system." 1 This assertion relates to a theorem recently proved by US.2 A glance at their own example shows, however, that their conclusion is completely unwarranted. Consider their technology or "book of blue prints" which is composed of techniques A and Aa. The technology consists of three capital goods, wheat, iron, and aluminum, which we will designate by the indices 1, 2, and 3, respectively. As usual, a0 is the input coefficient of commodity i for the production of good j, and the index o denotes a labor input. Thus the technology for the RobinsonNaqvi "counterexample" must be written as follows: