Equilibrium efficiency with secured and unsecured assets

Economies with lack of commitment have been extensively studied using instruments like collateral and market exclusion. In collateral models agents cannot transfer wealth from the future and an efficient allocation may not be implementable even if markets are complete. We study an economy with secured and unsecured assets, the last ones are important in allowing transfers from the future. Bankruptcy punishment is the seizure of a fraction of agent’s income, this results in a non-convex budget set. We provide some conditions to implement the Arrow Debreu allocation (AD) with a large enough seizure rate, indirectly proving equilibrium existence. Further, we perform a numerical exercise with US data to prove that if agents in the lower income quartile have a positive probability of coming up to a larger one (more social mobility) then we can implement AD and the minimum seizure rate depends inversely on this probability.