General Equilibrium Dynamics with Naifs and Sophisticates

What is it about?

As casually observed in the unsecured consumer loan market, some people borrow with high interest and fall into bankruptcy. Empirically, a high presented-biased individual, who becomes impatient as time passes (i.e., they have time-inconsistent preference), is likely to have debt and naifs, who are not aware of their time-inconsistency, is more likely to have debt than sophisticates, who are aware of their time-inconsistency. This paper is the first study to analyze dynamic general equilibrium with interaction between naifs and sophisticates.

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Why is it important?

I construct a model of a dynamic economy in which sophisticates exploit naifs through capital transactions. This paper shows three properties of the equilibrium. (i) global dynamic stability, (ii) a bankruptcy condition, (iii) ex-post Pareto inefficiency. I show that naifs are more likely to fall into bankruptcy (i) when the degree of present bias is high, (ii) when the sophisticates-naifs population ratio is high, (iii) when the long-run discount factor is high.