This study simultaneously tests Wagner’s law on one hand and Keynes proposition on the other hand related both government spending and output in Ivory Coast that experiencing long run economic growth and widened deficit. That challenges the country’s fiscal sustainability. With annual data from 1980 to 2020, results show that Wagner’s law holds, the elasticity of government spending to output is greater than one. There is bidirectional causality between government size and output validating Keynesian idea that public expenditure is an exogenous factor and a policy instrument for increasing national income. Wagner law and public deficit can justify Ivorian over-indebtedness.

Since the establishment of neoclassical economics in the nineteenth century, there has been a debate in the economics profession over the role played by mathematics. Mathematics can add precision to discussion of real-world empirical problems in economics, but care needs to be taken when formalizing a problem to ensure that errors of translation are not made. Formalism allows one to be sure that a chain of reasoning is correct but applying conclusions back to an empirical science problem is fraught if an error of translation has been made. We illustrate such a difficulty in the context of Arrow’s impossibility theorem, specifically the mistranslation of the non-dictatorship condition. The notion of dictatorship entails causality, but causality does not correspond to the usage of the implication sign in mathematics or logic. We use the rules of logic to illustrate that the way that dictatorship is rendered mathematically in the impossibility theorem makes the existence of a dictator (or dictators) not only reasonable but likely.