The IS-LM model describes equilibrium in two markets and together determines general equilibrium in the economy. (See pgs. 713-723 in Mankiw 2 nd Ed.)
IS stands for Investment and Savings.
The IS curve shows the relationship between the interest rate (r) and level of income
(Y) in the goods market. This relationship is an inverse relationship, so the IS curve is downward sloping.
Shifts in the IS curve are due to changes in fiscal policy (i.e. it will shift to the right if
Government expenditure increases, Taxes decrease, Investment increases
(sometimes we could say business outlook becomes more optimistic, that is something that leads to an increase in I), and increases in autonomous
Consumption, and vice versa).
LM stands for Liquidity and Money.
The LM curve shows all points where the money market is in equilibrium (M
D given a combination of the rate of interest and national income.
= M
S
)
The LM curve is upward-sloping, showing that an increase in income is associated with an increase in interest rate, and vice-versa.
Shifts in the LM curve are due to changes in monetary policy (i.e. increase in M
S shifts LM to the right, and vice versa).

Question 3(a)
You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: M
D
= 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; and the real money supply is £850 billion.
Find the equations of i) the IS curve and ii) the LM curve.
The IS curve
The LM curve

Question 3(a)
You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: M
D
= 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; and the real money supply is £850 billion.
Find the equations of the IS curve
In the product market, equilibrium occurs when Y = C + I and so:
C = 100 + 0.75Y
I = 500 -10r
Note: The coefficient on r is negative here because the lower the interst rate, the cheaper it is to invest, so investment will increase.
There is an inverse relationship between the two.
We can plug these in to Y = C + I
Y = 100 + 0.75Y + 500 – 10r
0.25Y = 600 -10r
Y = 2400 – 40r This is equation of the IS curve.

Question 3(a)
You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: M
D
= 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; the real money supply is £850 billion.
Find the equations of the LM curve.
In the money market, equilibrium occurs when M
D
= M
S and so:
M
D
= M
S
0.5Y – 15r = 850
0.5Y = 850 + 15r
Y = 1700 + 30r This is the equation of the LM curve.

Question 3(b)
In part (a) we found:
IS curve: Y = 2400 – 40r
LM curve: Y =1700 + 30r
What are the equilibrium income and rate of interest in the economy given the information above?
To find the equilibrium, set IS equal to LM:
IS = LM
2400 – 40r = 1700 + 30r
70r = 700 r = 10% This is the equilibrium interest rate.
To find the equilibrium income, we can plug this value of r into either expression for
Y and obtain Y = £2,000 billion.

Question 3(c)
If autonomous investment increases by £35 billion, what will be the new equilibrium income and interest rate? What will be consumption and investment? What is the value of the multiplier?
Autonomous investment is now £535 billion, so I = 535 – 10r.
This is just like part (a). First, we’ll find the equations of the IS curve
In the product market, equilibrium occurs when Y = C + I and so:
C = 100 + 0.75Y
I = 535 -10r
We can plug these in to Y = C + I
Y = 100 + 0.75Y + 535 – 10r
0.25Y = 635 -10r
Y = 2540 – 40r This is equation of the IS curve.
(note: it shifts to the right from before)

IS curve shifts right increases Y and i

Question 3(c)
If autonomous investment increases by £35 billion, what will be the new equilibrium income and interest rate? What will be consumption and investment?
The LM curve is still the same as in part(a):
LM =1700 + 30r
So setting the new IS curve = LM, we get:
2540 – 40r = 1700 + 30r
Solving we get:
70r = 840
So, r = 12% and Y = £2,060 billion
To find consumption and investment, we can plug in r and Y into our equations for C and I:
C = 100 + 0.75Y
C = 100 + 0.75*(2060 billion)
C = £1,645 billion
I = 535 -10r
I = 535 -10*12
I = £415 billion

Question 3(c)
If autonomous investment increases by £35 billion, what is the value of the multiplier?
The multiplier is: Multiplier = (change in Y)/(change in I)
= (2,060-2000)/35
= 60/35
= 1.714 (4sf)
This multiplier, which takes account of the effect of the interest rate change associated with the extra investment, is sometimes called the interest-variable multiplier.

Question 3(d)
Suppose the interest rate had not changed when autonomous investment increased, what would consumption, investment, and planned expenditure have been? What is the value of the multiplier in this case?
If r remained at 10% then I = 535 – 10*(10) = £435 billion
Y = £2,140 billion from the IS equation.
C = £1,705 billion
The value of the multiplier is now 140/35 = 4.
This multiplier is the interest-constant multiplier. When we previously derived values for the multiplier it was this we obtained. Note that 1/(1 – MPC) in the economy equals 4, which confirms the value calculated using changes in Y and I.
Introducing the money markets into the model, as the answers to c) and d) show, reduces the value of the multiplier. This is another complication to add to those caused by permanent income and life-cycle considerations. It is not easy being an economic policy-maker.

How is it possible for IS to shift and the interest rate (r) to remain constant?
LM would need to shift right as well.
This can occur due to a shift in money supply:
Ms = Md = (0.5Y) – 15r
Ms = Md = (0.5*2140) – (15*10) = 1070 - 150 = 920 i.e. an increase of 70.
This will lead to a further change in Y.
LM
1

Question 3(e)
Compare your answers to c) and d) to derive the crowding out effect.
Crowding out usually refers to how government investment sometimes is in projects that individuals would have invested in if the government hadn’t made the investment.
In lecture, Coskeran covered the idea of crowding out in the Loanable Funds Model. This question deals with crowding out in the IS-LM model.
In our problem, we have an increase in autonomous investment , which shifts the IS curve out, causing an increase in interest rate. Because total investment is a function of both of these things, I does not increase as much as it would have if r could have been held constant:
I = autonomous investment – 15r
Coskeran’s solution:
From this, we can see the effect from how a rise in interest rates due to increasing autonomous investment has a smaller negative effect on investment, cutting off some of the increase in investment (and income) that would have occurred if the interest rate had not increased.
In this case, the answer to d) tells us that income would have been £2,140 billion if the interest rate had not risen to the 12% rate established in c). Instead, with this higher interest rate income is £2,060 billion. The size of the crowding out effect is the difference between the two income figures, that is £80 billion.

IS Curve is Equilibrium in the Goods Market
To solve for the IS curve set Output (Y) equal to Expenditure
(C+I+G). I is usually a function of interest rate (r).
To the up and right of the IS-curve, output is greater than
Expenditure, while to the bottom and left of the IS-Curve,
Output is less than Expenditure.
To shift the IS curve to the right, we need to increase
Expenditure (usually, I or G).
Likewise, to shift IS to the left, we would need to decrease
Expenditure.

LM Curve is Equilibrium in the Money Market
To solve for the LM-curve set Money Supply (Ms) equal to
Money Demand (Md).
Money Supply is usually constant and Money Demand is usually a function increasing in output (Y) and decreasing in interest rates (r).
To shift the LM curve to the right, we need to increase
Money Supply or decrease
Money Demand (this could be done through increasing interest rates).
Likewise, to shift LM to the left, we would need to decrease Money Supply or increase Money Demand
(again, by using interest rates).

Question 7
In which segment in the diagram above is the supply of money greater than the demand for money in the money market and aggregate demand greater than planned output in the product market?
a) 1 b) 2 c) 3 d) 4

Question 2(a)
The economy is in disequilibrium at points A and B in the diagram above.
For each point, what are the prevailing conditions in i) the money market, and ii) the product market?
At A,
In the money market: the demand for money is greater than the supply
In the product market: planned expenditure is less than planned output
(or planned injections are less than planned withdrawals)
At B,
In the money market: the demand for money is less than the supply
In the product market: planned expenditure is less than planned output, same as A

Question 2(b)
For each point, were income to remain unchanged, what would happen to the interest rate?
This question is just asking, what would happen in the money market at Point A, and at point B?
In A:
In the money market: M
D
> M
S
 r↑
In the product market: planned expenditure < than planned output  inventories ↑  investment ↓  Y↓
For B:
In the money market: M
D
< M
S
 r ↓
In the product market: planned expenditure < than planned output  inventories ↑  investment ↓  Y↓

Question 2(c)
For each point, why is it likely that income will, in fact, change?
Here, we are being asked at each point, due to the disequilibrium, what happens in the goods market?
In A:
In the money market: M
D
> M
S
 r↑
In the product market: planned expenditure < than planned output  inventories ↑  investment ↓  Y↓
For B:
In the money market: M
D
< M
S
 r ↓
In the product market: planned expenditure < than planned output  inventories ↑  investment ↓  Y↓
Coskeran’s solution:
At both A and B conditions in the product market mean that unplanned investment is rising in firms. They will respond to this by cutting output which will cause income to fall.

Question 2(d)
For each point, what must happen to r and Y to bring the economy back into equilibrium?
From A, r will rise and Y will fall.
From B, both r and Y will fall.

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Question 4
A rise in interest rates will increase: a) the speculative demand for money b) the precautionary demand for money c) the transactions demand for money d) none of the above

Question 5
The demand for money represents the idea that there is: a) a negative relationship between the interest rate and the quantity of money demanded.
b) a negative relationship between the price level and the quantity of money demanded.
c) a positive relationship between the interest rate and the quantity of money demanded.
d) a negative relationship between the level of aggregate output and the quantity of money demanded.

Question 6
Aggregate demand in an economy is determined by the following equations:
C = 4 + 0.8Y and I = 180 – 10r where C is consumption expenditure (in billions of pounds), Y is income (in billions of pounds), I is investment expenditure (in billions of pounds), and r is the interest rate expressed as a percentage.
Equilibrium income when r is 10% is: a) £400 billion b) £420 billion c) £180 billion d) Cannot be calculated from the information provided

Question 7
In which segment in the diagram above is the supply of money greater than the demand for money in the money market and aggregate demand greater than planned output in the product market?
a) 1 b) 2 c) 3 d) 4