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hw04 - Homework 4 Econ 4721-002 Money and Banking Fall 2011...

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Homework 4 Econ 4721-002: Money and Banking, Fall 2011 Due Thursday, December 8, beginning of class Problem 1: Model of Currency and Deposits Consider an overlapping generations economy with 2-period lives. Population and stock of fiat money are constant. Stock of fiat money is M t = 30 , 000. The banking sector is competitive. Private banks are capable of borrowing money from agents and investing in capital which provides the real one-period rate of return x = 1 . 4 for each unit of goods saved in capital. The required reserve ratio γ = 20% . If consumers deposit with a bank, there is a fixed transaction cost of φ = 5 units of goods (costs at the time of deposit withdrawal regardless of deposit amount). That is, the total return from saving s i units of goods is rs i - φ units of goods where r is the rate of return on deposits offerred by banks. Consumers in this economy want to save different amounts, and will choose the option (deposits or currency) that offers them the best total rate of return, after considering the transaction cost of banking. Suppose that there are 5 types of consumers, and 10 of each type in each generation.
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