74 QUARTERLY JOURNAL OF ECONOMICS broken line: the ray from the origin with slope -until r reaches the and then a horizontal line at height 3. In the Harrod model 8 is the warranted rate of growth 2 FIGURE IV There are now three possibilities: (a)ni>-, the natural rate exceeds the warranted rate. It can be seen from Figure IV that mr is always greater than s min (,I) so that r always decreases. Suppose the initial value of the To d、 then= m,r, whose solution is 8e-mut +8. Thus r decreases toward which is n,b 1b
THE THEORY OF ECONOMIC GROWTH in turn less than. At an easily calculable point of time t1, r reaches From then on r a( ) b ni r, whose solutionis=ea Since -<ni, r will decrease toward zero. At time ti, when r=a the labor supply and capital stock are in balance. From then on the capital-labor ratio decreases labor becomes redundant, and the extent of the redundancy grows. The amount of unemployment can e calculated from the fact that K rloen remembering that, when K capital is the bottleneck factor, output is-and employment is b (b)n2 =-, the warranted and natural rates are equal. If initially r>so that labor is the bottleneck then r decreases to and stays there. If initially r< b, then r remains constant over time, in a sort of neutral equilibrium. Capital stock and labor supply grow at a common rate n2; whatever percentage redundancy of labor there was d (c)na <- the warranted rate exceeds the natural rate. For mally the solution is exactly as in case (a) with n3 replacing ni There is a stable equilibrium capital output ratio at r Bu here capital is redundant as can be seen from the fact that the mar- ginal productivity of capital has fallen to zero. The proportion of he capital stock actually employed in equilibrium growth is any ut since the capital stock is growing(at ptotically equ to na) the absolute amount of excess capacity is growing, too. This appearance of redundancy independent of any price-wage move- ments is a consequence of fixed proportions, and lends the harrod Domar model its characteristic of rigid balance At the very least one can imagine a production function such