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5. [8 marks) Consider the standard OLG model of money. Individuals are endowed with 3,! units of the endowment good when young and nothing when old. There are JV individuals in each generation. Each generation has identical preferences 1 3 1 2 u [61,153 mid-1) = 01:; + 021;...1: where an individual values consumption in each period of the life. There exists one asset in the economy - money. The money supply M' is constant. The initial old are endowed 1with M" units of money. In the following, we focus on stationary allocations. (a) Find an individual's budget constraints 1when young and when old. Combine them to form the individual's lifetime budget constraint. (1 mark) (b) Solve for the optimal consumption allocation [($05] chosen by the individual in a stationary monetary equilibrium. {2 marks) {c} 'Write down the resource constraint faced by the planner and solve for the golden rule allocation. (1 mark) (d) Is the monetary equilibrium allocation the same as the golden rule allocation? Ex- plain. {1 mark)