Lecture 16 - IS and LM curves (CLOSED SO NO NX)

Question 1

Consumption and investment formula (diff from normal)

Answer 1

C=a+b(Y-T)

a is fixed parameter representing minimum consumption.

I=d-fr
d is fixed parameter of max amount of investment with 0 borrowing costs.
f is interest rate sensitivity of investment (how much firms respond to r)

Question 2

Put into Y function.

Answer 2

Y=a+d+G-bT /(1-b) - f/(1-b)r for the X axis
So split up fr from the others.

SLOPE
-f/(1-b) r
X intercept
a+d+G-bT/1-b

To find y intercept rearrange Y function to make r subject

Question 3

What shifts IS

2. What is the size of shift determined by for G* and T*

Answer 3

Changes in G* or T*
Increased IS = increase in G* and fall in T*

2. The MPC b (multiplier effect)

G* size determined by 1/ (1-b)
T* size determined by -b/ (1-b)

Question 4

Example of a multiplier effect (an increase in G)

Answer 4

an increase in G* raises income and household then increase consumption raising income level further.

Question 5

What determines the SLOPE of the IS

Answer 5

The slope is
-f/(1-b)

an increase in f or b makes IS flatter.
(f is investment sensitivity to r and b is MPC)

Question 6

Recall Demand for money formula

Answer 6

Md/P =L(Y)=kY

Question 7

This is transaction demand for money, we can now add an asset demand for money.

What do we also have to assume?

Answer 7

Md/P = L(Y,i)
Md/P=ky - lr

Md/P = L(Y,i) where Y (income) increases, demand for money increases so we hold more, and if nominal interest rate (i) increases, cost of holding money increases thus we demand less.

We assume under fixed prices, expected inflation and inflation is therefore 0 so i=r. I.e money market influences real interest rate in short run.

Question 8

So how do we show this negative relationship graphically between demand for money and interest rates (where i=r under fixed prices in SR)

Answer 8

downward sloping demand for RMB curve. labelled L(r)

Question 9

Scenario: impact of increase in income on money market and LM curve

Answer 9

Increase in RMB demand. Shifts L(r) upwards, increasing r.

Why? In order to increase holdings of money, households sell bonds. So price of bonds fall, and interest rises (r=B/Pb. Pb falls, r increases.)

Continues until demand for money=supply of money

LM curve - captures this by a movement along the LM curve to a higher interest rate, and higher Y (since income/output Y has increased)

Question 10

Scenario 2:
A fall in money supply on the MM and LM curve

Answer 10

Shift left in supply. R increases. Why?

Individuals have to sell bonds since not enough money in the economy, Pb falls, so r increases at any Y

LM curve - r increases at any Y, so a shift upwards.

Question 11

Compare a fall of money supply in the long run vs short run on the nominal interest rates

Answer 11

short run - r increases (shown last slide) and i=r since no inflation so i (nominal as asked increases)

long run - nominal interest rate i falls. Use QTOM
With flexible prices, if Ms falls, inflation falls (M=λP), i falls since inflation lower. (using fisher i=r+πe)

Question 12

LM curve algebra - how do we find the slope and intercept

Answer 12

Md/P = kY - lr
Ms/P= kY - lr
Where k is income sensitivity to demand, l is interest rate sensitivity to demand.

Rearrange to find Y
Y= Ms/P/k + l/k r

Here we can see an increase Ms/P or a fall in k shifts LM curve right.

Slope is k/l Y after rearranging to make r subject, so a fall in k or increase in l flattens the slope.

Question 13

What is k and I in money demand equation

Answer 13

k is income sensitivity of money demand.
(If high, money demand increases a lot when income rises)

Makes sense as if k high, we demand a lot of money as income rises)
Y=M/kP , we demand a lot of money, so don’t spend, so output falls.

I is interest rate sensitivity of money demand.