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2) (10 points) In Lecture 7 we assumed that banks hold only reserves and loans as assets for simplicity. Now suppose that banks use a: fraction of their deposits to buy treasuries. Derive the money multiplier as a function of x, currency-deposit ratio 0dr, and actual reserve ratio a7". How does an increase in x affect money multiplier, monetary base, and money supply? 1 What is Money? Money is the economic term for assets that are widely used and accepted as payment. Not cash, wealth, or income. Historically, the forms of money have been very different: from shells to gold to cigarettes (Eastern Europe and German Prisoners Of War camps). Most prices are measured in units of money, so understanding the role of money is important to under- standing inflation. 2 Three Functions of Money i) Medium of exchange: money permits trade of goods and services at lower cost (in terms of time and effort). ii) Unit of account: money is the basic unit for measuring economic value. iii) Store of Value: money is a way of storing wealth. 3 Measures of Money The distinction between monetary and non-monetary assets is controversial. There are two main official measures of money stock, called monetary aggregates: i) M1 : the most narrow definition, includes mainly currencies and balances held in checking accounts. ii) M2: includes everything in MI plus other "money like" components like saving deposits. 4 Money Supply Money supply (MS) is the amount of money available in an economy. Money supply (MS) is affected by Central Banks, depository institutions (banks), the public (households and firms).5 Role of Banks in the Monetary System Balance sheet of a bank is simply as follows: Table 5.1: Balance Sheet of a Bank Assets Liablhties Loam (L) Deposits (D) Reserves (R) Deposits (D) is the amount borrowed from the public. Loans (L) is the amount issued as loans, Reserves (R) is the amount deposited into bank but aren't loaned to the public. Simply, R = D 7 L1 You can simply think reserves as the cash held in the banking system. In reality, balance sheets of banks are more complicated than this as they typically have other liabilities and assets, but let's keep it simple. 5.1 Why do Banks Hold Reserves? Holding reserves is not a protable business. By issuing loans, banks can generate more returns. They hold reserves for two reasons mainly: 1) Central Bank (CB) requires them to hold at least a fraction of their deposits as reserves This fraction is called the required reserve ratio (rr). Therefore, 13% = g 2 rr. Required reserve ratio (rr) varies across countries, but it is typically around 0.15. In reality, CB keeps these reserves for the bank. So, if you deposit 100058 to Bank A in Country X today (assume rr = 0.1 in Country A), then Bank A will transfer 1000 an rr = 1000 s 0,1 = 1000 to the CB of Country X as reserves today, Moreover, CB doesn't pay any interest to Bank A for keeping required reserves. Bank A can issue loans with the remaining 900$. Value of loans Bank A or any bank in Country X cannot exceed 90 percent of the deposits they hold if rr = 01. Lets denote actual raerve ratio of a bank with or = %. Notice that bank can hold actual reserve ratio more than the level that is required by CB, i.e., or can be strictly greater than rr. 2) Banks hold reserves for their liquidity needs. Everyday some people withdraw cash from their deposits, banks usually pay them with the new deposits. But there might be days when cash withdrawals are more than the new deposits. Banks can pay them with the extra reserves if they hold any. That is the second main reason to hold reserves. Having said that, there are other ways that banks can meet their liquidity needs. First one is borrowing from other banks in the interbank market, where banks borrow/ lend to each other at an interest rate (this interest rate is called federal funds rate in the US, and it is the main policy target of the Fed aka Central Bank of the US). The interest rate in the interbank market is determined by the supply and demand with no involvement of CB. For example, if many banks want to borrow but only a few wants to lend, interest rate will go up in the interbank market The other nancing option is to borrow from the CB at an interest rate that is asked by CB (this is what we call discount window borrowing, we will come to this later.) 52 Money Creation by Banks Although banks don't print paper money, they do create money. Let's see how they do it. First, lets make two strong assumptions (which we will relax later): A1: The public doesn't hold cash, they put all their money on bank deposits. A2: Banks hold only required reserves, that is or = r1: Suppose that the public (households and rms) initially has 10003 paper currency and required reserve ratio rr is equal to 01 Due to assumption A1, they will deposit this into banks. Step 1: Thus, Deposits increase by 1000$. Then, by assumption A2, bank will exactly put 10 percent of this into reserves because ar : 011, thus Reserves increase by 100$. Banks issue loans with the remaining 900$. The person or entity who gets this 900$, will buy goods/services from a seller. And thus 900$ will go to deposit account of seller because by assumption Al the public doesn't hold any cash For example, if this is a mortgage loan for a house, this 900$ will go to the deposit account of the person who sells this house. Step 2: Thus, Deposits increase by 900$ Then, by assumption A2, bank will exactly put 10 percent of this into reserves, thus Reserves increase by 903;. Banks issue loans with the remaining 810$. Step 3: Thus, Deposits increase by 810$. Then, by assumption A2, bank will exactly put 10 percent of this into reserves, thus Reserves increase by 81$. Banks issue loans with the remaining 729$, This will continue for innite number of steps Notice that deposits in each step increases by 90 percent of the increase in the previous step. So, total deposits in the economy is equal to D =1000+900 +810+ = 1000[1+ 0.9 + 081 + 0472 + ..] =1ooo[1+(17 rr)+(17 ")2 +(17 \")3 + ] = 1000i TT _ 1000 = 10000 M In the fourth step above, I used the innite geometric series formula: 1+1+12+13+uu = if 1