Divisible money with partially directed search

Monetary search models are difficult to analyze unless the distribution of money holdings is made degenerate. Popular techniques include using an infinitely large household (Shi 1997) and adding a centralized market with quasi-linear utility (Lagos and Wright 2005). Wallace (2002) suggests as an alternative to have two-member households who can somehow direct their search, thus creating a degenerate distribution in a different way. This idea is modelled here for the first time by modifying the partially directed search model of Goldberg (forthcoming). The Friedman rule is optimal, but the costs of deviating from it are different from the above mentioned models