QUARTERLY JOURNAL OF ECONOMICS that no balanced growth equilibrium might exist. 5 Any nondecreasing function F(, 1)can be converted into a constant returns to scale production function simply by multiplying it by L; the reader can nstruct a wide variety of such curves and examine the resulting solutions to(6). In Figure III are shown two possibilities, together F( 2(,) FIGURE III with a ray nr. Both have diminishing marginal productivity through out, and one lies wholly above mr while the other lies wholly below. The first system is so productive and saves so much that perpetual full employment will increase the capital-labor ratio (and also the output per head)beyond all limits; capital and income both increase 5. This seems to contradict a theorem in R. M. Solow and P. A Sa Balanced Growth under Constant Returns to Scale, "Econometrica, XXI (1953) 12-24, but the contradiction is only apparent. It was there assumed that every commodity had positive marginal productivity in the production of each com- modity. Here capital cannot be used to produce labor. 6. The equation of the first might be s FI(, 1)=nr +yr, that of the second P2(r,1)=