We study models that display growth with financial deepening and increasing inequality along the way to perpetual steady state growth. A benchmark model is essentially a complete markets model but with transaction costs of financial intermediation. New proofs are required and thus provided for stochastic dynamic programming for the case of unbounded return functions and perpetual growth with a non-convex transaction technology. We calibrate the model and report quantitative predictions for Thailand during 1976-96. We find a discrepancy between the model and the data, suspect barriers to financial deepening as a cause, and evaluate the associated welfare loss.