Consider an Overlapping generations economy with constant population NV = 100 of young individuals are born each period. Individuals are endowed with y units of the consumption good when young and y2 when old, the initial old also starts with y2. The utility function of one typical agent is: (c1, (2) = log(c ) + 1. Consider the case in which y1 = 5 and y2 = 2.(a) State and solve the Planner's Problem. (b) Suppose the initial old are endowed with a total of M = 100 units of fiat money. Write down equations that represent the constraints on first and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint. (c) Find the Stationary Competitive Equilibrium. 2. Consider the case in which y1 = 2 and y2 = 5. (a) State and solve the Planner's Problem. (b) Suppose the initial old are endowed with a total of M = 100 units of fiat money. Write down equations that represent the constraints on first and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint. (c) Find the Stationary Competitive Equilibrium