Government Spending Under Non-Separability: a Theoretical Analysis

In this paper we derive analytic implicit form conditions for the qualitative analysis of government spending multipliers and the optimal level of government spending in presence of non-separability between private and public components of aggregate demand. Using the simplest neo-classical flexible price model with no capital accumulation, we show that Edgeworth dependence is not a suitable condition to automatically assess the signs of the consumption and income multipliers, for which a more complex analysis must be carried out. We propose a detailed investigation of the form and the characteristics of the involved utility functions, which are crucial to such evaluation. We also show that if Edgeworth complementarity is strong enough, a public spending stimulus can raise at the same time private consumption and real activity. In order to reconcile our general framework with existing literature, we discuss recent examples of non-separable functional forms from the standpoint of our results, and argue that their consistency relies on specific assumptions about steady- state points.