EC3115 Monetary Economics

Section A

Answer all EIGHT questions from this section.

Indicate whether the following statements are true or false, or uncertain and give a short explanation. Points are only given for a well reasoned answer.

1. In most countries fiat money is quantitatively larger than credit money.

2. Keynes identified three types of demand for money.

3. For financial institutions, liquidity and profitability are conflicting objectives.

4. The baseline Real Business Cycle model predicts a negative association between inflation and real output in the case of technology shocks.

5. Most modern central banks focus on money aggregates in their policy announcements.

6. High interest rates often cause high inflation.

7. In a Keynesian model with sticky prices, the systematic component of monetary policy has real effects.

8. Upwards sloping yield curves indicate that interest rates are expected to rise in the future.

Section B

Answer THREE out of FIVE questions from this section.

9. Suppose a Keynesian economy with 400 people is set up so that everybody supplies 10 units of labour per period no matter how small or large the real wage. In this economy there are also 1000 competitive firms, each maximising their profit function: Π = Y P − W N, where Y is output, P is the price of output, W is the nominal wage and N is the number of units of labour. Suppose each firm is identical in every respect and each has a production function: Y = √N.

(a) (5 points) Derive the demand for labour of one firm, its output and the aggregate demand for labour in the economy.

(b) (5 points) Draw on a graph the aggregate demand and supply of labour. Compute algebraically the equilibrium wage (W/P) ∗ and equilibrium level of labour supply N*.

(c) (5 points) Suppose the aggregate demand for goods in the economy is given by Y = 1/2 (M/P) and the money supply is equal to 100. What is the aggregate supply function for goods in the economy? Calculate Y* and P*.

(d) (5 points) Suppose that the government increases once and for all the money supply. Does this improve the position of the workers in the economy?

10. Assume that the banking sector is described as follows:

D = d0 − d1(i − iD)

L = d0 + l1(i − iL),

where L stands for bank loans, D stands for bank deposits, iL the loan rate, iD deposit rate and i is the market interest rate. For convenience assume that the constant is d0 in both equations. Also assume that banks do not have operating costs and are not required to hold reserves.

(a) (5 points) Calculate the competitive equilibrium. Illustrate the equilibrium in a diagram.

(b) (5 points) How do your results from (a) change when the government sets deposit rates equal to iD = a, with a < iL. Provide intuition.

(c) (5 points) Now instead suppose that government introduces a mandatory reserve ratio, r*, such that R = r*D. How do your results change compared to (a)? What are the implications of such a reserve ratio policy on interest rates, deposits and loans? Provide intuition.

(d) (5 points) Sometimes, it is suggested that the reserve ratio policy can be an alter-native to targeting interest rates or monetary aggregates. Can this be an effective policy to stabilize output and inflation fluctuations?

11. Consider the three equation IS-PC-MR model described in Carlin and Soskice (2006). Let the IS curve be given by

y1 = A − ar0,

where y1 is actual output in period 1, A is an autonomous expenditure variable, r0 is the real interest, set in period 0, and a is a constant. The simplified Phillips curve is given by

π1 = π0 + α(y1 − ye),

where π1 is inflation in period 1 and π0 is the inflation in period 0; and ye is the ‘trend’ output associated with a constant level of inflation. Lastly, the loss function of the central bank is given by

L = β(π1 − πT )2 + (y1 − ye)2,

with π T defined as the target rate of inflation and where the parameter β measures the relative importance of inflation against the output gap in the loss function. Also let rs be the ‘natural real rate of interest’ that would prevail at trend output.

(a) (5 points) Derive algebraically the monetary rule (MR-AD equation) that outlines the equilibrium relation between output and inflation in period 1.

(b) (5 points) Derive algebraically the interest rate (IR) rule that outlines the relation between the equilibrium interest rate and deviations from target inflation.

(c) (5 points) Discuss a situation in which an interest rate rule is unlikely to be effective in stabilizing the economy.

(d) (5 points) Show graphically the effect of a demand shock in the IS-PC-MR model. Make sure to explain what the time path of the variables is.

12. Consider the original Baumol-Tobin model. A cash manager is paid in bonds and spends money (or makes transactions) at a constant, known rate. Let T equal the value of the cash manager’s expenditures, equal in this case to her income: i is the interest rate earned on bonds, b is the fixed cost of making a transfer between bonds and cash and Z is the value of money transferred each time, equal to the amount of bonds sold each time. If the money is spent at a constant, known rate then the average money balances will be equal to M = Z/2.

(a) (5 points) Set up the cash manager’s cost minimisation problem.

(b) (5 points) Solve for the average money demand, interest and income elasticities of money demand.

(c) (5 points) Show graphically how money holding and financial wealth evolve over time.

(d) (5 points) Discuss how well the Baumol-Tobin succeeds to model the stylized facts about actual cash balances held by firms.

13. Consider Poole’s model of optimal monetary instrument choice. Assume that the param-eters and structure of the model are known with certainty. Define IS and LM schedules as:

Y = a − bR + ∈

M = c − dR + eY + η.

where Y is the real output, R is the nominal interest rate, M is the real money balances, a, b, c, d, e are positive parameters and finally ∈ and η are additive mean zero IS and LM shocks whose variances are σ∈ 2 and ση 2 respectively. For simplicity ignore the price level in the LM curve. The Central Bank can either control the money supply, M, or the interest rate, R, as policy instruments but not both. Assume that its goal is to minimise the variance of output.

(a) (7 points) Suppose that the economy is subject to IS shocks only. Derive real output volatility for each policy instrument separately. Which monetary instrument is appropriate for the Central Bank? Provide a discussion.

(b) (7 points) Suppose that the economy is subject to LM shocks only. Derive real output volatility for each policy instrument separately. Which monetary instrument is appropriate for the Central Bank? Provide a discussion.

(c) (6 points) Show your analysis above (for IS and LM shocks) diagrammatically.