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