Economics of Money and Banking Assignment -

Part A -

Question 1 - Consider an economy with a shrinking stock of fiat money. Let N_t = N, a constant, and M_t = zM_t-1 (z < 1) for every period t. The government taxes each old person τ goods in each period, payable in fiat money. It destroys the money it collects. Hint: Follow the steps of the equilibrium with a subsidy, noting that a tax is like a negative subsidy.

a) Find and explain the rate of return in a monetary equilibrium.

b) Prove that the monetary equilibrium does not maximize the utility of the future generations.

c) Do the initial old prefer this policy to the policy that maintains a constant stock of fiat money? Explain.

Question 2 - Consider the following economy: individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money stock is constant. The population grows at rate n. In each period, the government taxes each young person  goods. The total proceeds of the tax are then distributed equally among the old who are alive in that period.

a) Write down the first- and second-period budget constraints facing a typical individual at time t. Combine the constraints into a lifetime budget constraint. (Hint: Be careful; remember that more young people than old people are alive at time t)

b) Find the rate of return on fiat money in a stationary monetary equilibrium?

c) Does the monetary equilibrium maximize the utility of future generations?

d) Does this government policy have any effect on an individual's welfare?

e) Does your answer in part d change if the tax is larger than the real balances people would choose to hold in the absence of the tax?

Part B -

Question 1 - Consider an economy with a constant population of young and old. Let N denote the number of young which is equal to the number of old. Young individuals are endowed with y units of the consumption good when young and nothing when old. We want to look at a monetary equilibrium with money. The problem facing a young person born at t is to maximize her/his lifetime utility subject to the budget constraint. The lifetime utility is a function of consumption in both periods of life: ln (c_1,t) +  ln (c_2,t+1)

where 0 < β  < 1 is the discount parameter and is it constant and c_1,t and c_2,t+1 represent the consumption of young and old in period t and t + 1, respectively.

a) Write down equations that represent the constraints on first- and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint.

b) Let q_t = v_tm_t denotes a young person's real demand for fiat money. Solve for a young person's real demand for fiat money by maximizing the lifetime utility subject to the lifetime budget constraints.

c) Suppose in total there is M units of fiat money. Write the market clearing condition for the money market in an arbitrary period t? What is the value of money in period t, v_t? Use this condition to find the real rate of return of fiat money v_t+1/v_t.

d) What are the optimal consumption in the first and second period of life?

Question 2 - Consider a fiat money/barter system as in the lecture. Suppose the number of goods J is 100. Each search for a trading partner costs an individual 2 units of utility.

a) What is the probability that a given random encounter between individuals of separate islands will result in a successful barter?

b) What are the average lifetime search costs for an individual who relies strictly on barter?

c) What are the average lifetime search costs for an individual who uses money to make exchanges?

Now let us consider exchange costs. Suppose it costs 4 units of utility to verify the quality of goods accepted in exchange and 1 unit of utility to verify that money accepted in exchange is not counterfeit.

d) What are the total exchange costs of someone utilizing barter?

e) What are the total exchange costs of someone utilizing money?

Question 3 - Consider a commodity money model economy like the one described in this chapter but with the following features: there are 100 identical people in every generation. Each individual is endowed with 10 units of the consumption good when young and nothing when old. To keep things simple, let us assume that each young person wished to acquire money balances worth half of his endowment, regardless of the rate of return. The initial old own a total of 100 units of gold. Assume that individuals are indifferent between consuming 1 unit of gold and consuming 2 units of the consumption good.

a) Suppose the initial old choose to sell their gold for consumption goods rather than consume the gold. Write an equation that represents the equality of supply and demand for gold. Use it to find the number of units of gold purchased by each individual, m^g_t, and the price of gold, v^g_t.

b) At this price of gold, will the initial old actually choose to consume any of their gold?

c) Would the initial old choose to consume any of their gold if the total initial stock of gold were 800? In this case, what would be the price of gold and the stock of gold after the initial old consumed some of their gold? Compare your answer in this part with your answer in part a. Does the quantity theory of money hold.

d) Suppose it is learned that a gold discovery will increase the stock of gold from 100 units to 200 units in period t^*. Assume the government uses the newly discovered gold to buy bread that will not be given back to its citizens. Find the price of gold at t^* - 1 and at t^*. Also find the rate of return of gold acquired at t^*- 1.