ECON 4721, Money & Banking

Reference: Modeling Monetary Economics (2016, Fourth Edition, Cambridge University Press) by Bruce Champ, Scott Freeman and Joseph Haslag.

Question 5 - Capital and Money. Imagine an OLG economy where the government has to build roads and bridges totalling an amount of G units of the con- sumption good each period. The government may finance its purchases printing money with a rate of expansion of the fiat money supply of 2 2 1. Denote governement consumption per capita by gt = Gt/Nt where N is the number of people in the generation born at time t. Population is grows constantly at rate n. Each young person receives y amounts of the good as labor income. Besides money, the agent may invest in capital k. Each unit invested in capital as young will become f(k) when old. 1. Find the individual's budget constraints when young and when old. [TIP: Government purchases g are not in the agent's BC] 2. State the following: (a) Total GDP at time t; (b) Feasibility Constraint; (c) Government's budget constraint; (d) Money Market Clearing Condition. From now on assume that the utility function of a typical agent is given by: u(C1,t, (2,t) = log(Ci,t) + log(cat) and f(k) = Akl/2 3. State and find the solution to the Planner's Problem as a function of parameters. 4. Define a Competitive Equilibrium. 5. Find the Equilibrium Allocations c20, (kt, Ci,t, C2,t), as a function of parameters. In which cases the solution to the Planner's Problem and the equilibrium allocation are the same? From now on, assume y = 10, n = 2 and A = 1. 6. Is GDP higher in the Planner's optimal allocation or in the equilibrium? What about consumption in periods 1 and 2? 7. How does consumption and capital in each period changes when a changes? Your answer needs a proof. 8. Find an expression for g in equilibrium as a function of z. 9. What is the maximum amount the government can spend per capita? [HINT: find the maximum of g(2)] 10. What is the c1, c2, k value when = + co? [HINT: You already found them in this homework.]