Efficient Nash equilibria in a federal economy with migration costs

We consider a federation of two regions populated by identical individuals, in which interregional migration is costly. We define a federation as an economy in which migration may not be restricted by governments. We compare and contrast first-best efficiency (with migration controls) and federal efficiency (without migration controls). We show that first-best efficiency requires maximising total product net of migration cost, while federal efficiency does not. We also show that migration costs may lead to a discontinuous federal utility—possibility frontier and to discontinuous regional reaction functions. We establish that decentralised equilibrium allocations may not be first-best efficient but are federally efficient. We conclude by tying together well-understood results from the limiting cases of free mobility and immobility with our results for the intermediate case.