This paper presents the partial analytical solution to a model of periodic consumption that incorporates imperfect capital markets and uncertainty. Our model assumes that consumption decisions occur more frequently than income receipt. We show that the week specific consumption functions can be ordered. At low levels of wealth these functions exhibit a “ushaped” pattern between income receipts. We show analytically that changes in the level of the borrowing constraint affect only the level of consumption function and not the MPC, whilst mean preserving changes in uncertainty affect both.