session 9 money market equilibrium - … · college of education school of continuing and distance...

College of Education

School of Continuing and Distance Education2014/2015 – 2016/2017

Session 9 –MONEY MARKET EQUILIBRIUM

Lecturer: Dr. Priscilla Twumasi Baffour, Department of Economics Contact Information: [email protected]

Session Overview

• After our lengthy discussion on money demand and money supply in

sessions 7 and 8, this session brings together both the exogenous

money supply and the money demand functions to discuss how

equilibrium is determined in the money market which at the same

time is a discussion on interest rate determination. The discussion

continues through an analysis of the link between the money market

and the goods market and ends with an illustration of how changes in

the interest rate affects aggregate expenditure through investment

Priscilla T. Baffour

Session Outline

The key topics to be covered in the session are as follows:

• Determinants of interest rate

• Derivation of equilibrium interest rate

• How equilibrium is restored in the money market

• Interest rate and money supply changes

• Connection between the money and goods markets

• Effects of changes in the interest rate on aggregate demend.


Learning Outcome

• After completing this session, you should be able to; Discuss equilibrium in the financial market and how interest rate

is determined

Explain why equilibrium in the money market indicatessimultaneous equilibrium in the bonds market

Be able to determine how equilibrium is restored in the moneymarket when there is a disequilibrium

Trace how the money market influences the goods market (thelevel of the GNP)

Carry out an analysis of the relationship between money, outputand prices.

Illustrate the effect of a change in the interest rate on aggregatedemand.


Reading List

• Read Chapters 17 & 18 of John Sloman; Economics, 8th Edition, 2011, Pearson

• Session Slides

• Any other Economics text books available to students


Determinants of the interest rate

• The interest rate which in simple terms is the price ofmoney is the result of the interaction between moneydemand and money supply. AS a result, determinants of theinterest rate include;– 1. Changes in Money Supply

– 2. Changes in demand for money

– 3. Both 1 & 2

From our discussion on money demand and supply, it has beenestablished that money supply is autonomous (determined by thecentral bank) and money demand is downward sloping depicting anegative relationship between interest rate and the real moneybalance.

The interest rate is therefore determined in figure 1 below;


Quantity of Money

The Equilibrium Interest Rate (Figure1)

MD

E0

MS

M0

i0


The equilibrium interest rate arises where demand formoney equals supply of money.

A given amount of money, M0, is shown by the verticalsupply curve Ms.

The demand for money is Md; its negative slope indicatesthat a fall in the rate of interest causes the quantity ofmoney demanded to increase.

Equilibrium is at E0, with a rate of interest i0..

The Equilibrium Interest Rate


MD

i1

E0

M1

i0

M0

MS

Quantity of Money

The Equilibrium Interest Rate (Figure 2)


From figure 2 above;

• If the interest rate is i1, there will be an excess demand formoney of M1-M0. Bonds will be offered for sale in an attempt toincrease money holdings.

• This will force the rate of interest up to i0 (the price of bondsfalls), at which point the quantity of money demanded is equalto the fixed supply, M0.

• If the interest rate is i2 on the other hand in figure 3 below,there will be an excess money balance. This will lead to anincrease in the demand for bonds (price of bonds increase) andthe rate of interest decreases to i0, at which point the quantityof money demanded has risen to equal the fixed money supply,M0.

The Equilibrium Interest Rate


i2

M2

MD

i1

E0

M1

i0

M0

MS

Quantity of Money

The Equilibrium Interest Rate (Figure 3)


Numerical Illustration

• L=0.25Y-12.5r

• Ms=400

• A) Find r* if Y=2000

• B) What happens to r when Y increases by 100? Illustrate with money market diagrams

• C) Find the new r*

• D) What happens to r* when Ms increases to 450?


Solution

Md=0.25Y-12.5r

Ms=400

At Equilibrium

Md=Ms

0.25𝑌 − 12.5𝑟 = 400

0.25𝑌 − 400 = 12.5𝑟0.25𝑌

12.5-400

12.5=

12.5𝑟

12.5

𝑟∗ = 0.02𝑌 − 32

a) If Y=2000𝑟∗ = 0.02 2000 − 32𝑟∗ = 40 − 32𝑟∗ = 8

b) When Y increases by 100

∆Y=100

From the money market equilibrium𝑟∗ = 0.02𝑌 − 32𝑑𝑟

𝑑𝑌= 0.02

𝑑𝑟 = 0.02 × 𝑑𝑌𝑑𝑌 = 100𝑑𝑟 = 0.02 × 100𝑑𝑟 = 2

• from the above we realize that when Y increases by 100, r increases by 2.


Solution

• From the diagram, anincrease in Y by 100 willshift the money demandcurve to the right fromMd(2000) to Md(2100). thiscauses interest rate to risefrom 8 to 10.


Solution

c) From part b above, when Y increases by 100, interest rate increases by 2, that is𝑑𝑟 = 2Therefore the new 𝑟∗ is

𝑟∗ = 𝑜𝑙𝑑 𝑟∗ + 𝑑𝑟𝑟∗ = 8 + 2𝑟∗ = 10

𝑁𝑒𝑤 𝑟∗ = 10

d) When Ms increases to 450∆Ms=𝑀𝑠2-𝑀𝑠1∆𝑀𝑠 = 450 − 400∆𝑀𝑠 = 50

From the money market equilibrium

𝑟 =0.25

12.5𝑌 −

1

12.5(𝑀𝑠 =

400)𝑑𝑟

𝑑𝑀𝑠= −

1

12.5= −0.08

𝑑𝑟=−0.08×𝑑𝑀𝑠𝑑𝑀𝑠 = 50𝑑𝑟=−0.08 × 50𝑑𝑟=−4

from the above we realize that when Ms increases to 450, interest rate decreases by 4.


Solution

• Therefore new 𝑟∗ is

𝑟∗ = 8 − 4

𝑟∗ = 4

• From the diagram below, an increase in money supply from 400 to 450 shifts the money supply curve to the right. This leads to a decrease in interest rate


As already indicated, the level of the interest rate is based on the

level of both money supply and demand.

o A change in the policy-determined interest rate (the prime

rate in Ghana) requires the money supply to change. This

is because interest rate cannot be determined in isolation

since it is the result of the interaction between money

demand and supply.

o In figure 4 below, the initial money supply is shown by the

vertical line Ms0, and the demand for money is shown by

the negatively sloped curve Md.

o The initial equilibrium is at E0, with corresponding interest

rate of interest i0.

Interest Rates and Money Supply Changes


Interest Rates and Money Supply Changes (Figure 4)

Quantity of Money

MD

i1

E0

M1

i0

M0

MS

E1


If monetary authorities choose to lower the interest rate from i0to i1 as shown in figure 4. In order to achieve this they mustgenerate an increase in the money supply, from Ms

0 to Ms1.

The new equilibrium given the money demand function is at E1.

Starting at E1, with Ms1 and i1, it can be seen that a decrease in

the money supply to Ms0 would be required to achieve an

increase in the interest rate from i1 to i0.

Interest Rates and Money Supply Changes


Money, The Interest Rate and Output

• Goods market The market in which goods and services

are exchanged and where equilibrium level of aggregate

output is determined. Recall the Keynesian cross

diagram: Y=C+I+G in equilibrium.

• Money market The market where financial instruments

are exchanged and in which the equilibrium level of the

interest rate is determined. Recall the money market

equilibrium condition: Ms=Md


The Link between the Goods and Money Markets

• There are two key links between the goods market and the

money market:

• Link 1: Income and the Demand for Money

– Income, which is determined in the goods market, hasconsiderable influence on the demand for money in the moneymarket (as already discussed).

• Link 2: Planned Investment Spending and the Interest

Rate:

– The interest rate which is determined in the money market,

has significant effects on planned investment in the goods

market


The Link between the Goods and Money Markets


Investment, The Interest Rate, and The Goods Market

When the interest rate falls,

planned investment rises.

When the interest rate rises,

planned investment falls.

FIGURE 5 Planned Investment Schedule

A reduction in the rate of interest increases desiredinvestment expenditure.

From figure 6 below, initial equilibrium is at E0, with a quantityof money M0 (shown by the vertical money supply curve Ms

0),an interest rate of i0 (point A in part (ii)).

The monetary authorities then lower the interest rate to i1 (byincreasing the money supply to M1), this increases investmentexpenditure from l0 to l1 (point B).

Similarly, a policy-induced rise in the interest rate from i0 to i1is accompanied by a fall in the money stock from M1 to M0

and leads investment to fall by Δl from l1 to l0.

The Effect of Changes in the Interest Rate Investment Spending


Quantity of Money

(i). Money Demand and Supply

MD

i1

E0

M1

i0

MS0

M0

MS1

E1

i0

i1

I0 I1

A

B

ID

0 0

Investment expenditure

(ii). The investment demand function

The Effect of Changes in the Interest Rate on Investment Spending (Figure 6)

I


Changes in the interest rate cause shifts in the

aggregate expenditure and aggregate demand

functions due to the effects on investment.

A fall in the interest rate increased desired investment

expenditure by Δl.

Here, in part (i) the aggregate expenditure function

shifts up by Δl, from AE0 to AE1.

At the fixed price level P0, equilibrium GDP rises from

Y0 to Y1, shifting the aggregate demand curve

horizontally from AD0 to AD1 in part (ii) of figure 8.

The Effects of Changes in the Interest Rate on Aggregate Demand


The Effects of Changes in the Interest Rate on Aggregate Demand (Figure 7)

Real GDP 0

45o

AE0E0

Y0

(i). Shift in Aggregate Expenditure

AE = Y

Real GDP

(ii). Shift in Aggregate Demand

Y0

P0

AD1

E0

I


Real GDP 0

45o

AE0

Y1

E0

Y0

AE1E1

I

AE = Y

Real GDP

Y0

AD0

P0

AD1

E1E0

Y1

The Effects of Changes in the Interest Rate on Aggregate Demand (Figure 8)

(i). Shift in Aggregate Expenditure

(ii). Shift in Aggregate Demand


Sample Questions

1. Write out the money demand function and explain thedeterminants of the demand for money.

2. How does a change in the interest rate change the quantity ofmoney demanded? Illustrate this using the demand for moneycurve.

3. What will be the implication of increased consumer credits onmoney demand.


session 9 money market equilibrium - … · college of education school of continuing and distance...

Documents