## Consider an OLG economy with an infinite horizon. Individuals live for three periods. You can call these stages young, middle-age, and old. Individuals do not want to consume when young, but want to consume in both middle-age and when old.

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##### Description

Consider an OLG economy with an infinite horizon. Individuals live for three periods. You can call these stages young, middle-age, and old. Individuals do not want to consume when young, but want to consume in both middle-age and when old. That is, an individual born in period t receives utility that depends on their consumption in middle and old age given by il(c2.+i,c3,s÷2).

Each young individual is endowed with y goods when young and nothing in middle age and when old. Here we consider a stationary equilibrium so that C1.t = = O, c2,1 = c2, and c3,2 = c3 for all t.

The number of young born in each period is growing at rate n > 1 so that N = nN_1 and the money stock is constant at ?iJ so that z = 1. One unit of the consumption good can be converted into one unit of capital in any period. Capital takes two periods to mature and each unit of capital produces X > n2 units of the consumption good when it tnatures. Unmatured capital cannot be bought or sold. Money can be acquired and traded in any period.

(a) (10 marks) Consider an individual born in period t. Suppose there are no banks so individuals must choose how to allocate their endowment between capital and flat money when they are young.

Carefully explain the liquidity mismatch problem faced by the individual. In your answer please include a figure, make specific reference to the one and two-period returns on fiat money and capital, and include the young, middle-age and old budget constraints.