On the Price of Commitment Assets in a General Equilibrium Model with Credit Constraints and Tempted Consumers

We analyze a three period production economy, where households exhibit problems of self-control and face credit constraints. Apart from liquid assets, a single commitment (illiquid) asset is available that allows to commit to a planned consumption path. We compare general equilibrium allocations of the two models: one, where households choices are determined using Gul and Pesendorfer (2001, “Temptation and Self-Control.” Econometrica 69:1403–35; GP, henceforth) model and the other, where households choices come from a (β–δ) quasi-hyperbolic discounting model. Contrary to the results of Kocherlakota (2001, “Looking for Evidence of Time-Inconsistent Preferences in Asset Market Data.” Quarterly Review 13–24) or Gabrieli and Ghosal (2013, “Non-Existence of Competitive Equilibria with Dynamically Inconsistent Preferences.” Economic Theory 52:299–313), we show that, when a production sector is incorporated into the economy with commitment asset and credit constraints, we can restore the equilibrium existence (without recalling measure space of consumers (see Luttmer and Mariotti 2006, “Competitive Equilibrium When Preferences Change Over Time.” Economic Theory 27:679–90)) and unlike Gul and Pesendorfer (2004b, “Self Control, Revealed Preferences and Consumption Choice.” Review of Economic Studies 7:243–64), we show that the equilibrium allocations of both models (GP and β–δ) imply positive consumption of the commitment asset and corner consumption of one of the liquid assets. We also provide an example showing, when equilibrium allocations of both models are different.