Question

Consider an economy in which people live two-period lives in overlapping generations but are endowed only in the first period of life. Capital has a minimum size, k ∗ , which is greater than the endowment of any single individual but less than the total endowment of a single generation. Capital pays a one-period gross real rate of return equal to x. The population grows 10% in each period. There exists a constant nominal stock of fiat money owned by the initial old.

(a) In what sense is capital illiquid in this economy? Is fiat money subject to this same liquidity problem?

(b) Describe an intermediary that might overcome the illiquidity of capital so that intermediate capital may be used to acquire consumption in the second period of life.

(c) Suppose there is only one person in each generation who is able to run an intermediary. What is the minimum rate of return that a person must offer to attract depositors? For what values of x can this person make a profit?

(d) What rate of return will be offered on deposits if there are many people in each generation able to run an intermediary?

Answer 1

Solution:

Fiat money:

Money which has no intrinsiic value but has exchange value because it is generally accepted. Originally money was accepted by users because it consisted which were themselves valuable such as gold or silver. In present day money consists of paper notes with negligible intrinsic value of book o computer entries. So, modern is fiat money.

a)

The capital size K* is larger than everyone's endownment but smaller than single generation's total endownment implies that each individual, without any lending from others is unable to switch her endownment for the capital. This means capital is illiquid. Fiat money, on the other hand,is liquid because fiat money i exchanged often other than capital. In other words, fiat money is held for longer term.

b)

A bank can accept deposits from the young and invest all of the deposits into capital. Since the sum of the deposits will be greater than K*, the capital will earn X next period. Hence the bank can pay back to the old with these capital earnings, and the old can consume.

c)

It is assumed here that the bank offers an interest rate which is least equal to the fiat money that the people own. Hence, depositors will be willing to open savings accout. The bank may be able to make profit then the capital's rate of return must greater than interest rate presented by the bank for the savings account. That is X.r must be true.

d)

If it is perfectly competitve market that the bank is operating, then profits made will zero. This happens when then the capital's rate of return is equal to the rate of return on interest rate for the savings account. That is , r=x.

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