Economics of Money and Banking Assignment -

Part A -

Question 1 - Consider the following version of the model in chapter 6. There is no population growth. The number of young individuals born on island i in period t, Nⁱ, is random according to the following specification:

Nⁱ = 4/5 N with probability 0:5

= 1/5 N with probability 0:5

Assume that the fiat money stock grows at the fixed rate z_t = z in all periods.

a) Set up the budget constraints of the individuals when young and when old in terms of l_tⁱ. Also set up the government budget constraint and money market-clearing condition. Find the lifetime budget constraint (combine the budget constraints of the young and old by substituting for l_tⁱ).

b) On which island would you prefer to be born? Explain with reference to the rate of return to labor.

c) Show how the rate of return to labor and the individual's labor supply depend on the value of z.

For the following parts, assume that the growth rate of the fiat money stock z_t is random according to

z_t = 1 with probability θ

= 4 with probability 1 - θ

The realization of z_t is kept secret from the young until all purchases of goods have occurred (i.e., individuals do not learn Mt until period t is over). Given these changes in assumption, answer the following questions:

d) How many states of the world would agents be able to observe if information about every variable were perfectly available? Describe those possible states.

e) How many states of the world are the agents able to distinguish when there is limited information (i.e., they do not know the value of z_t)?

f) Draw a graph of labor supply and the growth rate of the fiat money stock in each possible state of the world when there is limited information. What is the correlation observed between money creation and output?

g) Suppose the government wanted to take advantage of the relation between money creation and output. If it always inflates, will the graph you derived in part f remain the same? Explain fully.

Part B -

Question 1 - Individuals are endowed with y units of the consumption goods when young and nothing when old. Assume that people face a lump-sum tax of τ goods when old and a rate of expansion of the fiat money supply of z > 1 (that is, M_t = zM_t-1). The tax and the expansion of the fiat money stock are used to finance government purchases of goods per young person in every period (g_t). Let G_t represents total government purchases, i.e. G_t = N_tg_t.

There are N_t people born in time t and gross rate of population growth is n.

a) Write down the feasible constraint. Rewrite it for stationary case.

b) Find the individual's budget constraints when young and when old. Combine them to form the individual's lifetime budget constraint.

c) Find the government's budget constraint.

d) Find the rate of returne on money.

e) Find the stationary monetary equilibrium when z = 1 and n = 1. Compare the stationary feasible set with the stationary lifetime budget constraint.

Question 2 - Let N_t = nN_t-1 and M_t = zM_t-1 for every period t, where z and n are both greater than 1. The money created each period is used to finance a lump-sum subsidy of ρ goods to each young person. The difference between this question and Question 1 is that a young receives lump-sum subsidy of ρ and there is no direct tax. Hence, he first period budget constraint is

c_1,t + v_tm_t = y + ρ (1)

The budget constraint of an old person

c_2,t+1 = v_t+1m_t

Hence the lifetime budget constraint obtain by finding m_t from the second period budget constraint and substitute that into the first period budget constraint.

c_1,t + v_t/(v_t+1)c_2,t+1 = y + ρ

Similar to Question 1 the rate of return on money is obtained from market clearing condition. The money market-clearing conditions is given by total money demand is equal to total money supply. That is v_tM_t = N_t(y-c_1,t). Hence,

v_t = N_t(y-c₁)/M_t (2)

The rate of return of fiat money (under a population growth n and no change in endowment).

v_t+1/v_t = (N_t+1(y-c₁)/M_t+1)/(N_t(y-c₁)/M_t) = (M_t/M_t+1)(N_t+1/N_t) = n/z

a) What is the government budget constraint? Use the market clearing condition for money and find ρ.

b) Rewrite the life time budget constraint by substituting the rate of returne of money and ρ. Impose the stationary equilibrium.