Question 4 - Some unpleasant monetarist arithmetic (35 points). Consider an OLG economy with the following charachteristics: The population is constant and consists of twoperiod-lived individuals. There is an initial old generation that lives for one period only. For notational simplicity, we can normalize the population so = 1. An individual born at date have linear preferences and only values consumption at date +1 = (1,, 2,+1) = 2,+1. Each young person is endowed with units and may invest in capital wchich ill return in the next period according to the production function ((). Assume that is increasing and strictly concave and that 0 < () < 1. An old individual in period also receives transfers from the government worth . There is no money in the economy, but the individual may purchase nominal government bonds , denote the price of these bonds by and in period +1 the agent sell the bonds for +1, is an interest rate paid by the governement. Answer the following questions:

A) Write down the the budget constraints of the agent.

B) Find the FOCs for capital an bonds, combine both into one equation relating return on capital and on bonds:

C) Is the real demand for government bonds increasing in real interest rates? Is it increasing in productivity of capital and inflation?

Let's introduce government regulation into this economy. Suppose that the governmet requires that the agents keep a minimum share () of its portfolio into safe assets (government bonds). In other words: ( + )

D) The constraint above may or may not be binding. If the constraint is bindind, what will be the real demand for bonds? In this case, is the return on capital lower than return on bonds? The government expends and has tax revenues every period. The other source of revenue for the governments are the nominal bonds with price and interest rate . Denote by = government deficits at time .

E) Write down the government budget constraint and solve it for Suppose the stock of nominal bonds grow at rate : = 1. From now on we focus on stationary allocations in which real variables are constant and < .

F) What is the inflation rate in this economy?

G) Rewrite the expression for deficits with only terms at time .

H) Define a competitive equilibrium for this economy. Suppose the government chooses and lets adjust to satisfy the government BC. Also assume that the regulatory constraint is binding1 . This case is known as the Ricardian Regime. I) What happens with if the monetary authority raises its policy interest rate ?

J) For a given interest rate policy, what happens with if there is an increase in the regulatory demand for Treasury securities ? Suppose the government chooses and lets adjust to satisfy the government BC. Discuss the cases when the regulatory constraint binds and does not bind. This case is known as the non-Ricardian Regime.

K) What happens with inflation if the monetary authority raises its policy interest rate ?

L) What happens with inflation if there is a flight to quality represented by decrease in the productivity of capital ?

= (1 / )