The Shapiro-Stiglitz model with non-constant marginal utility

The Shapiro-Stiglitz model plays an important role in the employment theory. Woodford pointed out the theoretic limitation of the linear worker's utility function in that model. He questioned the model's implication of the secular decline in the unemployment rate when such rate was in fact trendless. He proposed to resolve this by allowing diminishing marginal utility of income. In this paper, the Shapiro-Stiglitz model is generalized using a nonlinear utility function implicit in the Stiglitz Efficiency-wage paper, thus linking these two well-known models. The nonlinear utility function in this generalized model not only allows for diminishing marginal utility of income but also allows for the analysis of parameters representing various factors affecting the secular unemployment rate. In particular, we can specify the condition under which the diminishing marginal utility can cause such rate to be trendless.