QUARTERLY JOURNAL OF ECONOMICS (The warranted rate of growth, warranted by the appropriate real rate of return to capital, equals the natural rate. In Figure I, the ray through the origin with slope n represents the function nr. The other curve is the function 8F(r, 1).It is here drawn to pass through the origin and convex upward: no output unless both inputs are positive and diminishing marginal productivity of capital uld be the case, for example, with the Cobb-Douglas function. At the point of intersection nr= sF(, 1)and r=0. If the capital-labor ratio r* should ever be established, it will be maintained, and capital and labor will grow thenceforward in proportion. By constant returns to FIGURE I scale, real output will also grow at the same relative rate n, and out put per head of labor force will be constant. But if r r*, how will the capital-labor ratio develop over time? To the right of the intersection point, when r>r", nr >8F(r, 1)and from(6)we see that r will decrease toward r*. Conversely if initially r <r*, the graph shows that nr sF(, 1),r>0, and r will increase toward r*. Thus the equilibrium value r* is stable. Whatever the al value of the capital-labor ratio, the system will develop toward a state of balanced growth at the natural rate. The time path of apital and output will not be exactly exponential except asymptote- cally. 4 If the initial capital librium ratio 4. There is an exception to this. If K=0, r=0 and the system can't ge started with no and hence no accumulation. But this