# Leakage Adjusted Money Multiplier

Suppose the ratio of deposits that banks hold in the form of reserves is 7 percent. Suppose further that people want to hold 8 percent of their deposits in the form of cash. Then, if the fed wants the money supply to be $6,228 billion, what is the necessary level of high powered money?

Assume an economy in which the reserve ratio is 15 percent, people hold 10% of their deposits in the form of cash, and there are no other leakages. (a) Compute the value of the money multiplier. (b) If the current level of high-powered money is $1,500 billion, what is the money supply in this economy? (c) How much does the money supply change if the fed buys $30 billion of U.S. government treasury bills from a government bond dealer? How about if banks borrowings of reserves from the fed decline by $6 billion? (d) if the fed set a target money supply of $6,424 billion what would it have to do to achieve that target?

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#### Solution Preview

The first thing you need for this is to define the leakage adjusted money multiplier.

Assume the required reserve ratio is r, the banks' propensity to hold excess reserve, as a fraction of total reserves is e and borrowers' tendency to hold cash, as a fraction of cash is c. Then,

the leakage-adjusted money multiplier = 1/(r+e+c)

In this case banks do not have a tendency to hold excess cash, and hence e = 0. The required reserve ratio in the first case is 7%, and the borrowers' tendency to hold ...

#### Solution Summary

The leakage adjusted money multiplier is explained with calculations in 372 words.

Macroecomics Questions

1. (4 marks) Explain the impact of an increase in the government expenditure

on the economy (1) under conditions of classical aggregate supply and (2)

under conditions of Keynesian aggregate supply.

2. (3 marks) In a closed economy, the consumption function is :

C = 1.15 + .75 ( Y - T).

The tax function is:

T = 0.1Y + .1

Planned investment is $1 billion, and planned government expenditures are

$ 1.5 billion.

Calculate:

a. Real GDP at the equilibrium expenditure

b. Consumer expenditure

c. Saving

d. The investment multiplier

e. The government budget deficit

f. The leakages from and injections in to the circular flow of income and

expenditure. Do leakages equal injections?

3. (4 marks) In an open economy, the consumption, tax, and import functions

are as follows:

C = 1.7 + .8 (Y - T)

T = .1Y +.2

IM = .06 + .1Y

Planned investment is $2 billion, planned government expenditures are $ 1

billion, and planned exports are $ 1 billion.

Calculate:

a. Real GDP at equilibrium expenditure

b. The investment multiplier

c. The autonomous tax multiplier

d. The marginal tax rate multiplier

e. The government budget deficit

f. Net export

g. The change in GDP resulting from a $ 1 billion rise in government

expenditures

i. In problem (g) the changes in saving, consumer expenditures and

government budget deficit.

4. (3 marks) In problem 3, the government is planning to change taxes to

balance its budget.

a. If the government adjusts only autonomous taxes, by how much do they

change?

b. If the government adjusts only marginal tax rate, by how much does it

change?

c. Compare the effects of the tax changes in (a) and (b) on real GDP.

Which plan would you recommend the government adopt? Why?

5. (4 marks) Consider the following numerical version of the IS-LM model:

C = 180 + .08 Yd

I = 100 - 18 R + .1Y

Yd = Y - T

T = 400

G = 400

Md = 6Y - 120 R

Ms = 5400

R is the interest rate, Md is Money demand, Ms is Money supply.

a. Write down the equation of IS curve.

b. Write down the equation of LM curve.

c. Solve for equilibrium real output.

d. At equilibrium, what is the level of consumption and investment.

6. (4 marks) One of the attractive features of the IS-LM model is that it can be

used to illustrate some of basic principles of monetary and fiscal

stabilization policies.

a. Use the IS-LM model to show that in an economy which is subject to

shock in the goods market (for instance, autonomous changes in planned

investment) monetary policies could not be used to stabilize real output

without exacerbating the fluctuations of the interest rate.

b. Use the IS-LM model to show that in an economy which is subject to

shock in the money market (for instance, autonomous changes in

demand for money) fiscal policies could not be used to stabilize real

output without exacerbating the fluctuations of the interest rate.

Macroeconomic Theory and Its Applications 1 ECON 2470 5

7. (3 marks) Let's assume that investment is a function of both interest rate (R)

and income (Y). Investment spending depends positively on income and

negatively on interest rates. We can formalize this as follows:

I = aY - bR

a. What is the expression for the IS curve in this case?

b. What will be the implication for the slope of IS curve? Will it be steeper,

flatter, or the same, relative to the case where investment depends only

on interest rate?

c. What will be the implication for the slope of AD curve? Will it be

steeper, flatter, or same, relative to the case where investment depends

only on interest rate?

See attached file for full problem description.

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