Consider the overlapping generations model (as discussed in the lecture) in which the utility function (U) of the individual is given by

U = (C1,t)1/2 + (C2,t+1)1/2

where C1,t is the consumption by the individual in the first period of life in period t and C2,t+1 is the consumption by the individual in the second period of life in period t+1. Suppose the individual is endowed with 90 units of consumption good in the first period of life, and mt is the amount of money acquired by the individual by giving up some of the consumption good in period t. Assume that vt is the value of one unit of money in terms of the amount of consumption good in period t, and vt+1 is the value of one unit of money in terms of the amount of consumption good in period t+1.

(a) Using the model, explain how fiat money can have value by providing the means for individuals to acquire the goods that they do not possess.

[7 marks]

(b) Determine the real demand for money which maximizes the utility of the individual subject to the budget constraints in the first period and second period of life for the individual. [5 marks]