Economic Growth and Wicksell's Cumulative Process

Assume a homogeneous production function, a constant rate of population growth and a monetary policy which keeps the rate of interest fixed. With initial unemployment there exists an unstable process of balanced growth. Under initial full employment there exists a natural rate of interest (possibly zero or infinite) such that (1) at interest rates below the natural rate balanced growth is attained and the price level is rising; (2) at interest rate above the natural rate both employment and the price level are falling. Explicit solutions are given for Cobb-Douglas production functions. The “optimal” rate of interest which maximizes per capita consumption at any time during balanced growth is shown to equal the rate of growth.