This question is meant for you to work through the entire mathematical derivation of the monetary economy's equilibrium. Consider the textbook's model of Chapter 5, Sections 5.1 through 5.2.3 in which there is growth in the nominal money supply and the money is injected into the economy via monetary transfers to the old. Also, assume that the population of young individuals increases at a rate n^ so that the gross growth rate of the young is given by n=1+n^=Nt1Nt. 1. Write down the problem of an individual born into period t. 2. Find the conditions that must be satisfied by optimal consumption and money savings by the individual. Interpret each of these in words. There should be one optimal trade-off condition between consumption in youth versus consumption in old age and a couple of period budget constraints. 3. Provide a definition for a competitive monetary equilibrium. 4. What is a "stationary equilibrium" (or a steady state) of the monetary economy? 5. Using the equilibrium conditions show how the equilibrium rate of inflation is related to growth in the nominal money supply and the growth rate of the youth population and explain why these relationships are as derived