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We study the relationship between corruption in public procurement and economic growth within the Solow framework in discrete time, while assuming that the public good is an input in the productive process and that the State fixes a monitoring level on corruption depending on the tax revenues. The resulting model is a two-dimensional, continuous and piecewise smooth dynamic system which describes the evolution of the capital per capita and that of the corruption level. We prove that the model admits multiple equilibria: their stability and the structure of their basins is studied. We also present numerical simulations for economic meaningful parameter values, useful to explain the role of parameters in the long–run path of the model. Our study aims at demonstrating that stable equilibria with positive corruption may exist (according to empirical evidence), even though the State may reduce corruption by increasing the wage of the bureaucrat or by increasing the amount of tax revenues used to monitor corruption.