### Switching of Techniques and Consumption Per Head: An Economic Clarification

Michael Bruno, Edwin Burmeister, Eytan Sheshinski
1970 Quarterly Journal of Economics
Using the notation of our original paper,' we summarize different techniques by (nXn) input matrices a, b, c, . . . and the corresponding labor requirement vectors ao, bo, ... When one sets the wage w=1 as a normalization, the price vector Pa, associated with any technique a, is a function of the interest rate r: (1) pa(r)=ao[I-(1+r)a]I . [In equilibrium, prices exactly cover costs, pa= ao (direct labor costs) + (1 +r)pa (cost, including interest, of inputs, i.e., circulating capital); (1)
more » ... the solution for pa.] The nonsubstitution theorem assures that, given any r, say ro (smaller than the maximum possible rate), there is one technique, say a, which minimizes all prices, i.e., pa(ro)=aO[I-(1+ro)a] -'b0 [I-(1+ro)b] '=Pb(rO) for any other technique we choose to label b. Consider now the steady-state consumption possibility frontier of this economy. Suppose that the economy grows at a rate g, and initial labor is normalized at 1. Then, when technique a is employed, per capita consumption possibilities are given by (3) ao[I-(1+g)a] -lc= 1 where c is the consumption vector. This can also be written (4) Pa() c= 1. Ozga's point is the following. Suppose that, for the rates of interest ro and r, (r, > ro), the corresponding optimal techniques are a and b. Is it true that the consumption possibility frontier of technique b, associated with the higher interest rate r, and given by (5) Pb (9) C= 1, is necessarily lower than that associated with technique a, the optimal technique at the lower interest rate ro? The answer is no. For this to be true, every element (price) in the vector Pa(9) must be lower than the corresponding element in Pb(g). Examples to the contrary can be easily constructed. Diagrammatically, the con-1. "The Nature and Implications of the Reswitching of Techniques," this Journal, LXXX (Nov. 1966).