www.lancaster.ac.uk/postgrad/alia10/econ102.html
a.ali11@lancaster.ac.uk


 In class we’ll look at Q2, Q3, Q4, Q6 and Q7.
 Please make sure you review all of problems on your own and ask if you have any questions.
 If you’re unsure of any solutions here, please see Chapter 23 in your textbook – it provides detailed explanations and examples.

nd


Suppose a household spends €1,680 evenly over the week. What is the household’s demand for money as measured by its average money holding per day?
The average daily demand for money is €1,680 / 7 days, so €240 per day.
For a more complex example of the average daily demand, see Example 23.2 in your book.

Draw a diagram to illustrate what might happen to the demand for money curve if the economy experiences a decline in real GDP.
Here is our diagram for the Money Demand Curve (See Fig. 23.1 and 23.2 in your book):
The money demand curve shows the relationship between the aggregate quantity of money demanded (M) and the nominal interest rate (i)
The money demand curve is downward sloping because an increase in the nominal interest rate increases the opportunity cost of holding money, which reduces the quantity of money demanded.

Draw a diagram to illustrate what might happen to the demand for money curve if the economy experiences a decline in real GDP.
A fall in real income reduces the demand for money at any interest rate as people need less money to buy goods and services.
So the money demand curve (MD) shifts to the left.
In Summary, things that might cause the money demand curve to shift are:
 Changes in Real Income (Real GDP)
 Changes in the Price level
 Changes to the cost or benefit of holding money. Examples of these would be technological and financial advances.
Note: Please see your book for a more complete summary.

Here is a summary of the notation and some of the relationships we use:
CUR = currency in circulation with the non-bank public
RES = bank reserves
D = bank deposits rr = the banks’ desired reserve-deposit ratio = bank reserves ÷ deposits = RES ÷ D cr = the public’s currency-deposit ratio = currency held by the non-bank public ÷ deposits =
CUR ÷ D
ΔM = change in money supply =
1+𝑐𝑟
M = the money supply = CUR + D = 𝑐𝑟+𝑟𝑟
1+𝑐𝑟
∆𝐻 𝑐𝑟+𝑟𝑟
𝐻
1+𝑐𝑟
The money multiplier = 𝑐𝑟+𝑟𝑟
H = the monetary base = bank reserves + currency held by the non-bank public = CUR + RES
CUR = crD
RES = rrD

Suppose that the banking sector currently holds 100 in currency reserves, 700 in loans and
800 in deposits (all in € million).
What would you predict the final money supply to be if all money is held as bank deposits and the banks’ desired reserve to deposit ratio is 5 per cent (0.05)?
We are given RES = 100, D = 800, loans are 700. We are told that M = D. So, in the initial
1 scenario described, M = 800 and 𝑟𝑟 = = 0.125 = 12.5% .
8
We want to find out, what will M equal if rr = 0.05?
1+𝑐𝑟
We know that money supply is: M = 𝐻 𝑐𝑟+𝑟𝑟
Also, because all money is held as bank deposits, that means that cr = 0 and CUR = 0, so we can re-write our equation for money supply as:
1
M = 𝑅𝐸𝑆 𝑟𝑟
1
M = €100 𝑚𝑖𝑙𝑙𝑖𝑜𝑛
0.05
M = €2,000 𝑚𝑖𝑙𝑙𝑖𝑜𝑛
So, in this problem we can see that if the reserve ratio is decreased, holding all else constant, then Money Supply will increase.

In a particular economy the monetary base is €300. If the banks’ desired reserve–deposit ratio is 0.15 and the public hold 5 per cent of deposits in currency, find (a) deposits held by the public and (b) the money supply.
cr = 0.05
To summarize, we know: H = €300
And we want to find D and M.
rr = 0.15
We know that H is:
Because CUR = cr*D and RES = rr*D, we can re-write this as:
𝐻 = 𝐶𝑈𝑅 + 𝑅𝐸𝑆
𝐻 = 𝑐𝑟 + 𝑟𝑟 × 𝐷
So we can re-arrange this relationship to solve for D:
𝐻
D = 𝑐𝑟+𝑟𝑟
So, now we can plug in and solve:
D =
€300
0.05+0.15
D =
€300
0.2
D = €1,500

In a particular economy the monetary base is €300. If the banks’ desired reserve–deposit ratio is 0.15 and the public hold 5 per cent of deposits in currency, find the money supply.
cr = 0.05
To summarize, we know: H = €300
In part (a) we found:
In part (b) we want to find M.
D = €1,500
We know that M is:
We can plug in and solve for M: rr = 0.15
M =
1+𝑐𝑟 𝑐𝑟+𝑟𝑟
𝐻
M =
1+0.05
0.05+0.15
€300
M =
1.05
0.20
€300
M = €1,575

The initial monetary base is €1,000, of which €500 is currency held by the public. The desired reserve–deposit ratio is 0.2.
Find the increase in money supply associated with increases in bank reserves of €10.
To Summarize: H = €1,000 CUR = €500 rr = 0.2
We want to find ΔM if ΔRES = €10.
1+𝑐𝑟
The money supply is: M = 𝐻 𝑐𝑟+𝑟𝑟
So the change in money supply, ΔM, due to a change in the monetary base, ΔH is:
1+𝑐𝑟
∆M = ∆𝐻 𝑐𝑟+𝑟𝑟
To calculate the ΔM, we first need to derive the public’s currency-deposit ratio cr.
We know that:
We can re-arrange to solve for cr:
CUR = cr ∗ D
𝐶𝑈𝑅 cr =
𝐷
But we need to find D to be able to use this.
We can calculate D by re-arraning: RES = rr D
D = RES / rr
Though RES is unknown, we can derive it from H = CUR + RES.
Rearranging this equation gives RES = H – CUR
RES = €1,000 – €500 = €500
So D = RES / rr = €500 / 0.2 = €2,500
And cr = CUR/D = €500 / €2,500 = 0.2
Now we have cr and rr, so we can use the equation for ΔM.

The initial monetary base is €1,000, of which €500 is currency held by the public. The desired reserve–deposit ratio is 0.2. Find the increase in money supply associated with increases in bank reserves of €10. What is the money multiplier in this economy?
To Summarize: H = €1,000
In the Previous slide, we found:
D = €2,500
CUR = €500 rr = 0.2
ΔRES = €10 cr = 0.2
Now we have all of the values to plug into the money supply change equation:
1+𝑐𝑟
∆M = ∆𝐻 𝑐𝑟+𝑟𝑟
∆M =
1+0.2
0.2+0.2
€10
∆M = 3 €10 = €30
So ΔM = €30 if ΔRES = €10.
Now, we want to find the money multiplier.
1 + 𝑐𝑟 m𝑜𝑛𝑒𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = m𝑜𝑛𝑒𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = 3 𝑐𝑟 + 𝑟𝑟

Suppose the equation of the demand for money curve is MD = 20,000

8,000i.
Find the equilibrium rate of interest if the central bank sets the money supply at 19,600.
In equilibrium MS = MD
19,600 = 20,000 – 8,000i i = (20,000 – 19,600)/8,000 i = 0.05
So the equilibrium interest rate is 5%.

Suppose the equation of the demand for money curve is MD = 20,000

8,000i.
In part (a) we found the equilibrium rate of interest is 5% if money supply is 19,600.
By how much would the central bank have to change the money supply if it wished to increased the equilibrium rate of interest by 1 per cent, or 0.01?
There are two methods we could use to solve this problem. Here’s one way:
If Δi = 0.01, then i = 0.06. We can plug this in for i into the money demand equation and calculate the new equilibrium money supply, as we did in part(a):
MS = MD
MS = 20,000 – 8,000i
MS = 20,000 – 8,000(0.06)
MS = 19,520
So, ΔM = 19,600 – 19,520 = -80. Money Supply has decreased by 80.

Suppose the equation of the demand for money curve is MD = 20,000

8,000i.
In part (a) we found the equilibrium rate of interest is 5% if money supply is 19,600.
By how much would the central bank have to change the money supply if it wished to increased the equilibrium rate of interest by 1 per cent, or 0.01?
Another way we can solve this problem is:
The change in the money supply ΔM is: ΔM = -8,000 Δi
ΔM = -8,000 * 0.01
ΔM = -80
So the central bank would have to reduce the money supply by 80.

Use the money market diagram
(graph 1), to show how the central bank could prevent an increase in the equilibrium rate of interest following a rise in the price level.
Note: this is similar to Figure 23.4 in your book.
(graph 2)
The rise in the price level increases money demand at any given interest rate, so the money demand curve shifts to the right.
If the money supply stays unchanged, then the new equilibrium is at a higher nominal interest rate (economy moves from point E1 to A), i.e. only a higher interest rate will reduce money demand again so that it equals the unchanged money supply.
(graph 3)
But if the central bank raises the money supply, shifting the money supply curve also to the right, then the rise in the nominal interest rate can be prevented (economy moves from point
E1 to E2 instead of to A).


 Chapter 24 in the Textbook
