Money. 1 What is money? Spring functions of money: Store of value Unit of account Medium of exchange

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1 Money Spring What is money? 3 functions of money: Store of value Unit of account Medium of exchange Whether something is money is not always so clear: Physical bills and coins Balances on checking accounts Balances on savings accounts Other financial investments (stocks, bonds, etc.) Gold Foreign currency Cigarettes Objects used as money need to be Easy to carry Hard to counterfeit Easily divisible (Sargent and Velde: The Big Broblem of Small Change ) Historically: Commodity money (e.g. gold) 1

2 ECON 52, Spring THE BANKING SYSTEM AND MONEY SUPPLY Paper money backed by gold or silver Fiat money Fiat money as A social convention Encouraged by the legal system ( legal tender ) Different measures of the quantity of money in the economy or money supply Monetary base M0 M1 M2 Physical Currency Physical Currency Physical Currency Physical Currency Central Bank Reserves Demand deposits Demand deposits Savings deposits Some mutual funds ( money market ) 2 The banking system and money supply An Example 1. Ann has $1 in physical currency 2. Ann deposits $1 in a Bank 3. The Bank lends Bob $1 and gives him the loan in physical currency What has happened? (See slides) What is M0 at each stage? What is M1 at each stage? Distinction between money and wealth Reserve requirements Legally, if a bank receives $1 in deposits it cannot make a loan of $1 Reserve requirements: for each dollar of deposits the bank must keep ρ in reserves (deposits in the central bank) ρ varies by country and by type of deposit. Range: ρ = 0 to ρ = 0.3 approx. Historically even higher 2

3 ECON 52, Spring THE BANKING SYSTEM AND MONEY SUPPLY Two purposes of reserve requirements: Make (almost) sure that the bank can always meet withdrawals Give the central bank control over the money multiplier (see below) Bank earns interest on loans but (traditionally) not on reserves Banks usually want to have as little reserves as they can, so they just have ρd Therefore bank balance sheet is typically: Assets Reserves: ρd Loans and bonds: (1 ρ) d Liabilities Deposits: d Recently: Interest rates are very low, so opportunity cost of having reserves is very low In US, Central Bank has started paying interest on reserves. How central banks adjust the money supply Buy bonds from banks. Pay with reserves. The central bank is creating reserves. Also known as printing money even though it does not involve printing money. Suppose the central bank creates reserves to buy bonds. See slides Overall, the increase in the money supply is: Monetary base M1 ρ The Central Bank controls the monetary base directly and M1 and other measures of the money supply indirectly. The money multiplier is m = 1 ρ Multiplier measures how much M1 increases per unit of increase in the monetary base. What if borrowers don t just keep the money in deposits? Transactions with each other but always paying in deposits: calculation is not affected 3

4 ECON 52, Spring NOMINAL AND REAL INTEREST RATES Take out physical cash: need to adjust calculation What if banks keep excess reserves? Then the money multiplier becomes smaller See graph of excess reserves and monetary aggregates. 3 Nominal and Real interest rates Notation: p t : price level in period t i t+1 : nominal interest rate between t and t + 1 π t+1 : rate of inflation between period t and period t + 1, i.e. p t+1 p t 1 + π t+1 Suppose you make a loan of 1 dollar at a nominal interest rate of i t+1 You give up: 1 p t You get 1 + i t+1 dollars at t + 1 You can buy 1+i t+1 p t+1 goods at t + 1 Overall, for each good you get goods at t that you could have consumed if you didn t make the loan 1 + r t+1 1+i t+1 p t+1 1 p t = (1 + i t+1 ) p t p t+1 = 1 + i t π t+1 Therefore the real interest rate is r t+1 = 1 + i t π t+1 1 i t+1 π t+1 Sometimes know as the Fisher equation (for Irving Fisher) Note that until t+1 you don t really know what the real interest rate is, because there might be uncertainty about p t+1. Expectations of p t+1 (or equivalently, expectation of π t+1 are extremely important) 4

5 ECON 52, Spring MONEY DEMAND 4 Money demand Why do people hold money? Opportunity cost: money doesn t pay interest, other assets do Benefit of holding money: double coincidence of wants problem A simple model of money demand (Baumol-Tobin) There are two kinds of assets money (M1) interest-paying assets (stocks, bonds, etc.) Money is necessary to make transactions (you cannot use interest-bearing assets for these) Households consume c in a period (a month or a quarter, maybe). This is a real (as opposed to nominal) amount. The price level is p Therefore households spend pc in nominal terms pc is not spent all at once: households spend a little bit each day within the period Therefore the household doesn t need to have pc in money all at once Household can go to the bank as many times as it wants during the period Each time it goes to the bank, it transfers enough assets into money to pay for expenses until it goes to the bank again. We call this withdrawing money, but it can mean a transfer from savings to checking as well as taking out physical cash. There is a cost F of going to the bank. Bank fees Mental cost of dealing with the issue. F is a real cost, so if the price level is p, the nominal cost is pf If the household goes to the bank once, it has to withdraw pc at the beginning of the period. Then it draws down the balance, so on average it holds M = pc 2 5

6 ECON 52, Spring MONEY DEMAND If the household goes to the bank N times, it withdraws pc N M = pc 2N. Draw graph. each time. On average it holds The household tries to minimize the costs associated with managing money: Cost of going to the bank. Minimized by few visits to the bank, high money holdings. Foregone interest from holding money rather than other assets. Minimized by many visits to the bank, low money holdings. Mathematically: i is the interest rate: min N pc pf N + i 2N FOC: Nominal or real? Why? pf ipc 2 N 2 = 0 ic N = 2F and therefore M = pc 2N = pc ic 2 2F cf = p 2i Alternatively M cf p = 2i The quantity M p is known as real money balances. It is an answer to the question: how many goods would the household be able to buy with the amount of money it holds? 6

7 ECON 52, Spring EQUILIBRIUM IN THE MONEY MARKET Interpretation of the role of c, F and i Generalization Inspired by the Baumol-Tobin model, we can write a more general money-demand function as: M p = md (Y, i) Having Y or c doesn t matter very much: different ways of measuring number of transactions i matters because it is the opportunity cost of holding money Don t fixate of the exact function that arises from the Baumol-Tobin model but on the main economic forces it illustrates Plot the money-demand function. What happens if GDP increases The cost of going to the bank increases 5 Equilibrium in the money market Central bank decides the supply of money directly controls the monetary base understands that the banking system will generate a multiplier Households choose how much money to hold, according to their money demand In equilibrium, supply must equal demand: M = m D (Y, i) p In this equation, M is exogenous. Controlled by the central bank Y, i and p endogenous Suppose the central bank adjusts the money supply. How does the economy adjust? Increasing prices? 7

8 ECON 52, Spring THE CLASSICAL VIEW Increasing GDP? Lower nominal interest rates? If so, do real interest rates also fall? Recall that real interest rates are r t+1 = i t+1 π t+1? 6 The Classical view Complete separation of the real economy from the monetary economy (the classical dichotomy ) The real variables (in particular, Y t and r t+1 ) depend only on real parameters and shocks (technology, preferences, etc.), as in the Neoclassical/RBC model What happens in our money market equilibrium if there is an unexpected permanent increase in M? M t = m D (Y t, i t+1 ) p t Y is not affected (depends on real preferences and technology) r t+1 is not affected (depends on real preferences and technology) Conjecture: p t+1 and p t rise by exactly the same amount If conjecture is true π t+1 is not affected [Careful about the timing: one thing is inflation between t and t + 1 and another is inflation between t 1 and t] Therefore if conjecture is true i t+1 = r t+1 + π t+1 is not affected Therefore if conjecture is true, p t increases one-for-one with M t Which confirms the conjecture Conclusion: prices rise immediately in the same proportion as M Conclusion: one necessary ingredient for the classical view to hold is that prices must be flexible. One main distinction between neoclassical/rbc models vs. Keynesian/New Keynesian models: are prices flexible? 8

9 ECON 52, Spring THE CLASSICAL VIEW Inflation and money growth Suppose the money supply grows at a constant rate γ: M t+1 = (1 + γ) M t How will prices behave? Conjecture: suppose the real economy is in a steady state. Then p t+1 = (1 + γ) p t Let s verify our conjecture. If the conjecture is true, inflation will be π t+1 = p t+1 p t 1 = γ Nominal interest rates will be i t+1 = r ss + γ Money market equilibrium implies which verifies our conjecture M t = m D (Y ss, r ss + γ) p t M t p t = m D (Y ss, r ss + γ) (constant) Conclusion: inflation is exactly proportional to the rate of growth of the money supply Graphs with evidence Cross country US over time Exercise, what happens if at time t the rate of growth of the money supply increases from γ to γ > γ? 9

10 ECON 52, Spring THE CLASSICAL VIEW Velocity and the Quantity Theory of money Velocity of money : how many times a unit of money is used per unit of time Example: The money supply is $2 At the beginning of the period, Ann and Bob each hold $1 Ann produces an apple and sells it to Bob for $1. Bob produces a banana and sells it to Ann for $1 Ann produces asparagus and sells it to Bob for $1. Bob produces a blueberry and sells it to Ann for $1 Ann produces an apricot and sells it to Bob for $1. Bob produces a blackberry and sells it to Ann for $1 In the example: Nominal GDP is 6 The money supply is 2 Each dollar changes hands 3 times per period In general, we say that M V P Y M is the money supply P is the price level Y is real GDP, so P Y is nominal GDP V is the velocity of money This equation is an identity, not a theory. It holds by definition The quantity theory is the assumption that Y and V are exogenous, or at least do not depend on M Implication: M determines P Does the quantity theory hold in the classical model? Recall: 1. Money market equilibrium M t = m D (Y t, i t+1 ) p t 10

11 ECON 52, Spring SEIGNORAGE 2. Y t and r t+t determined by real factors Velocity will be V t = P t Y t = M t Y t m D (Y t, i t+1 ) Suppose the rate of money growth is high. Then Inflation will be high (π = γ) Nominal interest rates will be high (i = r + π) Money demand will be low (m D (Y, i) is decreasing in i - people go a lot to the bank to avoid the opportunity cost of holding money) Velocity will be high Conclusion: in our model, velocity Does not depend on the level of M Depends on the rate of growth of M 7 Seignorage Historically, seignorage was a fee that the government charged in order to transform raw gold into gold coins Now the term is used to describe the revenue the government obtains due to the ability to issue money People are willing to give up goods in exchange for pieces of paper The government has the ability to produce these pieces of paper Government budget constraint (in nominal terms) B t+1 = p t [G t τ t ] + (1 + i t ) B t [M t+1 M t ] where B t+1 is nominal public debt 11

12 ECON 52, Spring SEIGNORAGE G t is real government spending τ t is real government revenue i t is the nominal interest rate M t is the money supply You can also write this as M t+1 + B t+1 = p t [G t τ t ] + (1 + i t ) B t + M t Interpretation: money is like debt that doesn t pay interest No magic: printing money doesn t create resources Seignorage is like a tax - a tax on what exactly? Historical use of this tax Inflation as a fiscal phenomenon Limits to how much revenue can be raised To collect a lot, you need high growth rate of money supply BUT high γ implies high i and that implies low m D Friedman rule there is no cost to producing money, so there shouldn t be an opportunity cost of holding money policy goal: try to keep the nominal interest equal to 0 (implicitly: don t use this tax!) Since this requires i = r + π π = r so this requires constant deflation! Very low nominal interest rates can also be a symptom of the economy not doing well - we ll come to the liquidity trap 12

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