2 Today’s Outline Week 19 worksheet – Money Markets: 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.If you didn’t receive your 2nd exam, please collect it at the end of class.Exam 3 will be available some time after Easter holidays.
3 Question 1Suppose 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.
4 Question 2Draw 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 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.
5 Question 2Draw 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 levelChanges 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.
6 Money Supply NotationHere is a summary of the notation and some of the relationships we use:CUR = currency in circulation with the non-bank publicRES = bank reservesD = bank depositsrr = the banks’ desired reserve-deposit ratio = bank reserves ÷ deposits = RES ÷ Dcr = the public’s currency-deposit ratio = currency held by the non-bank public ÷ deposits = CUR ÷ DM = the money supply = CUR + D = 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 𝐻ΔM = change in money supply = 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 ∆𝐻The money multiplier = 1+𝑐𝑟 𝑐𝑟+𝑟𝑟H = the monetary base = bank reserves + currency held by the non-bank public = CUR + RESCUR = crDRES = rrDNote: This notation and the derivations of equations can be found in Chapter 23 of your textbook.
7 Question 3Suppose 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 scenario described, M = 800 and 𝑟𝑟= 1 8 =0.125=12.5%.We want to find out, what will M equal if rr = 0.05?We know that money supply is: M= 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 𝐻Also, 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:M= 1 𝑟𝑟 𝑅𝐸𝑆M= €100 𝑚𝑖𝑙𝑙𝑖𝑜𝑛M=€2,000 𝑚𝑖𝑙𝑙𝑖𝑜𝑛So, in this problem we can see that if the reserve ratio is decreased, holding all else constant, then Money Supply will increase.
8 Question 4(a)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.To summarize, we know: H = €300 rr = cr = 0.05And we want to find D and M.We know that H is: 𝐻=𝐶𝑈𝑅+𝑅𝐸𝑆𝐻= 𝑐𝑟+𝑟𝑟 ×𝐷So we can re-arrange this relationship to solve for D:D= 𝐻 𝑐𝑟+𝑟𝑟So, now we can plug in and solve:D= €D= €D=€1,500Because CUR = cr*D and RES = rr*D, we can re-write this as:
9 Question 4(b)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.To summarize, we know: H = €300 rr = cr = 0.05In part (a) we found: D = €1,500In part (b) we want to find M.We know that M is: M= 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 𝐻We can plug in and solve for M: M= €300M= €300M=€1,575
10 Question 5The 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 = 0.2We want to find ΔM if ΔRES = €10.The money supply is: M= 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 𝐻So the change in money supply, ΔM, due to a change in the monetary base, ΔH is:∆M= 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 ∆𝐻To calculate the ΔM, we first need to derive the public’s currency-deposit ratio cr.We know that: CUR=cr∗DWe can re-arrange to solve for cr: cr= 𝐶𝑈𝑅 𝐷But we need to find D to be able to use this.We can calculate D by re-arraning: RES = rr DD = RES / rrThough RES is unknown, we can derive it from H = CUR + RES.Rearranging this equation gives RES = H – CURRES = €1,000 – €500 = €500So D = RES / rr = €500 / 0.2 = €2,500And cr = CUR/D = €500 / €2,500 = 0.2Now we have cr and rr, so we can use the equation for ΔM.Note: There was a typo in the initial wording of this problem on the worksheet. It has been corrected here.
11 Question 5The 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 CUR = €500 rr = ΔRES = €10In the Previous slide, we found:D = €2, cr = 0.2Now we have all of the values to plug into the money supply change equation:∆M= 1+𝑐𝑟 𝑐𝑟+𝑟𝑟 ∆𝐻∆M= €10∆M= 3 €10 =€30So ΔM = €30 if ΔRES = €10.Now, we want to find the money multiplier.m𝑜𝑛𝑒𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟= 1+𝑐𝑟 𝑐𝑟+𝑟𝑟m𝑜𝑛𝑒𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟=3
12 Question 6(a)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 = MD19,600 = 20,000 – 8,000ii = (20,000 – 19,600)/8,000i = 0.05So the equilibrium interest rate is 5%.
13 Question 6(b)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 = 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 = MDMS = 20,000 – 8,000iMS = 20,000 – 8,000(0.06)MS = 19,520So, ΔM = 19,600 – 19,520 = -80. Money Supply has decreased by 80.
14 Question 6(b) alternative method 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 ΔiΔM = -8,000 * 0.01ΔM = -80So the central bank would have to reduce the money supply by 80.
15 Question 7Use 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.(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).Note: this is similar to Figure 23.4 in your book.
16 Next Class Week 20 Worksheet - IS-LM Model Chapter 24 in the TextbookLast tutorial session before Easter break!