Abstract:
In the real economic world, we often suffer from the default risk—the
present financial crisis could serve as an evidence. The long established idea for
inhibiting the default behavior is to resort to collateral, and this idea has profound
effect on the market equilibrium. To study this effect, we make an investigation of the
economy wherein default risk is present, assets are collateralized and households are
risk-averse. We shall prove that the economy is in possession of an equilibrium. This
proof is distinct from the existing one, in two respects: First it shows that equilibrium
exists for the Leontief utility function, and second it is constructive. By constructive
we mean that, on the basis of this proof,we can (and we shall) develop an algorithm for
computing that equilibrium. The algorithm developed is of a path-following type. It
starts from an economy which consists of several sub-economies, each with a complete
market and a Cobb–Douglas utility function; and it terminates at the equilibrium of the
economy under consideration. The algorithm is shown by simulation to be effective.
