We study the synchronization of two coupled idealized economies. In the present work, we consider a recently developed economic system that shows a richness of dynamical behavior. By means of the Lyapunov exponents, we analyze that there is overly complex behavior in the transitions in the dynamics of an isolated economy, oscillating between chaotic attractors and limit cycles. Then, for two coupled economies, we analyze the synchronization states for the space of all control parameters as a function of the network coupling parameter. Interestingly, we have evidenced that there is a broad region of fully synchronized states and as we increase the coupling, some phenomena such as a smooth and intermittent loss in synchronization emerge. In the same way, we observe phase synchronization for one of the control parameters. Ultimately, in order to confirm this loss of synchronization, we inspect the stability of synchronized states through the master stability function method for some control parameters. Here, we corroborate what was previously observed, the unexpected vast range of control parameter values of instability corresponding to desynchronization.