Consider our twoperiod DLG model of a monetary economy. Amume that young individuals are born and receive an endowment of e1 units of the consumption good while old individuals receive e2 units of endowments, e1 2? eg. A stock of money of size H is divided equally across the initial N old individuals at time t = 1']. Each period, a cohort of young individuals of size N is born and the previous period's old leaves the economy. The size of the youth population is constant over time as is the stock of nominal money balances, M, = H. Individuals live for two periods. Their objective of an individual born in period t is to maximise lifetime utility Melly] + \"(GitHl by choice of consumption during youth, cm, and consumption in old age, 1-2ng. The utility function a{c] has the properties that the marginal utility of consumption is strictly positive, a'{c] 3.:- {i and there is diminishing marginal utility of consumption n"{c] :: Ell. Suppose that money is electronic money and that individuals trade through a perfectly competitive electronic market in which balances in their electronic money accounts are exchanged for goods; once a trade is veried, money is tranferred between electronic accounts and goods are arranged for delivery. Each period, there is a probability 1 ,o E (D, 1] that the electronic market stop functioning. In such a case, trade forever ceases to occur and individuals live in autarky. Otherwise, with probability p, there is no market failure and money balances can be exchanged for goods. As long as the electronic market has collapsed in the past, individuals have no problem to solve; they simply eat their endowments when young and when old. If the market has not yet failed then individuals might choose to hold on to money balances in order to transfer resources between youth and old age. The problem of an young individual in such a circumstance is max {nets + miss.) + {1 small} is f c1-*-""'2.I:+1"5'2.|:+1 subject to the constraints M1.t Cit = 01 - Pt M1.t C2.t + 1 = et p+1 C2,t+1 = e2. In words, the individual chooses how much consumption goods to exchange for money when young in an effort to maximize expected lifetime utility (welfare). Here the con- sumption when old is a weighted average of the utility that is obtained from consumption when the electronic market does not fail, u(c) and the utility from consumption in the event that the market collapses, u(c+1) where the respective weights are equal to the probability that the market continues to operate, p, and the market fails, 1 - p. As usual, P is the measure of money required to obtain a single unit of the consumption good in period t. 1. Assume that the optimal consumption trade-off between consumption when young and old for an individual who is young when the market has not yet failed to be, Po pu'(c2+1)- Using this together with the individual's budget constraints, provide an equation that implicitly define the young individual's demand for real money balances, m1,t- (5 Marks) 2. As the population and the stock of nominal money supply is constant, suppose that the demand for real money balances by young individuals is constant over time as long as the electronic money market continues to operate (i.e. mit = mit-1 = my as long as the money market operates). Use money market clearing to derive the value of the inflation rate, * = py, that prevails when the electronic money market continues to operate. (10 Marks) 3. Suppose that the utility function is u(c) = In(c) so that u'(c) = 2. Derive a simple expression for the young's demand for real money balances, my, as a function of p, el and ez. (10 Marks) 4. Show that the demand for real money balances changes with an increase in the probability p that the electronic money market continues to operate. Provide the economic intuition behind this result and show that the value of money, A, changes when p increases