A More Precise Classroom Treatment of the Solow Model

Abstract This paper exposes a pervasive flaw in how both graduate and undergraduate classes teach the law of motion for the capital stock in the Solow model. Essentially, the derivative of the capital stock with respect to time, derived correctly for a continuous-time Solow model, is presented as the discrete-time change in capital stock. This causes graphical representations of equilibrium and convergence to equilibrium to be confusing, because such graphs can only depict discrete changes in the capital stock. This also causes the rate of convergence to the steady state to be overstated, predicts changes in the capital stock that do not match results in spreadsheet exercises, and can also cause the steady-state capital stock to be wrong. This flaw appears in the published literature at least once. The paper clarifies how the law of motion for the capital stock and the steady-state per capita capital and income should be stated.