3. Consider the OLG model with money we saw in class. Assume that the population of...

 

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3. Consider the OLG model with money we saw in class. Assume that the population of the economy is growing at the deterministic rate n, that is N₁ = (1 + n)N-1, n > 0. Assume that money is constant in this economy, that is M, M₁-1. The endowment that each young generation is born with is assumed to be fixed at y. At the start of the economy, the newly created money is given to the initial old. Given that the utility function of a typical agent is: u(C1,t, C2,4+1)= In c₁, +Bln c2+1, 0<B<1 (1) (a) Under a monetary economy, what are the first and second-period budget constraints? Combine these constraints into a lifetime budget constraint. [8 marks] (b) Find an expression for the real rate of return on fiat money in this economy [4 marks] (c) Explain why the real rate of return of money is changing in this economy [3 marks] (d) Compute the monetary equilibrium of this economy. That is find the optimal value for c₁ and ₂ [15 marks] (e) If 3 falls, what are the effects on the optimal allocation c₁ and ₂. Explain why. [5 marks] (f) What factors or policies by the government can influence the value of 8? [5 marks] 3. Consider the OLG model with money we saw in class. Assume that the population of the economy is growing at the deterministic rate n, that is N₁ = (1 + n)N-1, n > 0. Assume that money is constant in this economy, that is M, M₁-1. The endowment that each young generation is born with is assumed to be fixed at y. At the start of the economy, the newly created money is given to the initial old. Given that the utility function of a typical agent is: u(C1,t, C2,4+1)= In c₁, +Bln c2+1, 0<B<1 (1) (a) Under a monetary economy, what are the first and second-period budget constraints? Combine these constraints into a lifetime budget constraint. [8 marks] (b) Find an expression for the real rate of return on fiat money in this economy [4 marks] (c) Explain why the real rate of return of money is changing in this economy [3 marks] (d) Compute the monetary equilibrium of this economy. That is find the optimal value for c₁ and ₂ [15 marks] (e) If 3 falls, what are the effects on the optimal allocation c₁ and ₂. Explain why. [5 marks] (f) What factors or policies by the government can influence the value of 8? [5 marks]

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a In the monetary economy the firstperiod budget constraint is MPC1 t1 M y C1 t1 The secondperiod budget constraint is MPC2 t2 M y C2 t2 The lifetime ... View the full answer