In this paper, we develop a two sector DSGE model with market and political power interactions. These interactions are motivated by the politico-economic systems of several South European countries, over the last half century. In these countries the state permits the existence of industries, typically related to the extended public sector, where firms and workers employed therein have market power (insiders), unlike other firms and workers in the economy (outsiders), as insiders, that dominate the major political parties, cooperate to influence government decisions, including those that pertain to the very existence of such a politico-economic system. Consistently with stylized facts of growth and the business cycle of these countries, the model predicts: (i) large negative deviations of per capita GDP from what these countries would have been capable of, if their politico-economic system was not characterized by the above mentioned frictions; and (ii) deeper and longer recessions in response to negative shocks, as their politico-economic system reacts so as to amplify these shocks.