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, Pesendorfer (2001) model and the other, where households choices come from a beta-delta quasi-hyperbolic discounting model. Contrary to the results of
Kocherlakota (2001) or Gabrieli, Ghosal (2013), 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, Mariotti (2006)) and unlike
Gul, Pesendorfer (2004), we show that the equilibrium allocations of both models (GP and beta-delta) 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.