Alter the Diamond-Dybvig model in the following way. Suppose that there are two assets, an illiquid asset that returns 1+r units of consumption goods in period 2 for each unit invested in period 0, and a liquid asset that returns one unit of consumption goods in period 1 for each unit invested in period 0. The illiquid asset production technology cannot be interrupted in period 1. The model is otherwise the same as outlined in this chapter.
(a) Determine a consumer's lifetime budget constraint when there is no bank, show this in a diagram, and determine the consumer's optimal consumption when an early consumer and when a late consumer in the diagram.
(b) Determine a bank's lifetime budget constraint, show this in your diagram, and determine the optimal deposit contract for the bank in the diagram. Are consumers who deposit in the bank better off than in part (a)? Explain why or why not.
(c) Is there a bank run equilibrium? Explain why or why not.