Differential Interest Rates on Unbalanced Growth Paths

The paper studies an unbalanced multisectoral growth path in which cost-minimizing producers are subjected to a system of differential interest rates. We ask whether such differentials in capital charges are compatible with the existence of competitive equilibrium. In Part I, we study the price-quantity equilibrium for given final demand and a given level of interest rates. We find that existence is ensured if interest-rate differentials are "in tune" with physical productivity differentials. Our proof is constructive; we show that an equilibrium solution can be computed by applying Lemke's complementary pivoting algorithm to the data of the problem. In Part II, we study how the level of interest rates and the level and structure of final demand adjust to changes in activity levels, prices and income. We find that the interest-rate differentials from Part I do not prevent the required equilibrium adjustments. This confirms our principal insight from Part I, namely that interest rate differentials are consistent with equilibrium as long as they are in tune with productivity differentials.