ECON 4721, Money & Banking

Reference: Modeling Monetary Economics (2016, Fourth Edition, Cambridge University Press) by Bruce Champ, Scott Freeman and Joseph Haslag.

Problem.1

Consider an overlapping generations model with agents who live for three periods --- young, middle aged and old. Suppose there are 1000agents in each population. They only have an endowment when young. Agents can either invest in capital which produces1.5units of the consumption good intwoperiods or store a certain fraction of their endowment, which pays a gross rate of return equal to one. Capital can be sold for1.3goods after one period, however the seller has to pay0.7goods to verify their capital investment. There are two types of agents. Type 1 only consumes when middle aged, type 2 only when old. When making their savings decision, agents do not know their type. Assume precisely half of the population is type 1 and the other half is type 2. Banks store half of the goods deposited and invest the other half in capital. Banks pay a gross interest equal to one on deposits demanded after one period and1.5if withdrawn in two periods. What is the maximal number of agents who could show up after one period and get thetotalpromised return on their demand deposit?