Question 1 Consider a representative consumer who lives infinitely, and whose utility can be summarized by the lifetime utility function 1-0 Each period, individuals recieve income Y and choose their consumption ".money holdings Me,and their asset positions in risk free government bonds, B, and stocks at. (a) Write down the nominal budget constraint for the consumer in each period explaining any new notation that you need to. Set up the sequential Lagrangian problem. (b) Derive the first order conditions for all choices made by the consumer. (c) Derive the demand for real money balances for the consumer as a function of consumption and the real interest rates. (Note: The superscript d denotes demand). Now suppose that the government increases the supply of money after the consumer has made his decision, such that M> > M*. (d) Assuming that prices are completely flexible, what would the effects of this policy be? (e) What would the effects of the policy be in a regime of rigid prices