Macroeconomics マクロ経済学

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1 Macroeconomics マクロ経済学
Chap.15　The Supply of and Demand for Money 第15章　貨幣の供給と需要

2 Modern age is a monetary economy
Modern age is a monetary economy. ⇒ All transactions are intermediated by money. ⇒ The flow of money should also be analyzed from the aspects of both supply and demand. First of all, what are the functions and kinds of money? How is money supplied? How is performed the creation of derived deposits from primary deposits? What kind of holding motives the demand for money is based on? ... Monetary theory of the Classical school is the quantity theory of money, and Keynes's theory is the liquidity preference theory. Cambridge cash balance equation is located in the middle. How can we explain the supply of and demand for money, and their equilibrium? How is the interest rate determined by the quantity theory of money, the loanable fund theory, and the liquidity preference theory, respectively? 現代は貨幣経済⇒すべての取引は貨幣が媒介 　　　　　　　⇒貨幣の流れも、供給と需要の双方の側面から分析する必要 先ず貨幣の機能と種類とは何か、 貨幣の供給がどのように行われるか、 本源的預金から派生的な預金がどのように信用創造されるのか、 貨幣の需要がどのような保有動機に基づいて行われるのか、 …古典派の貨幣理論は貨幣数量説、ケインズのそれは流動性選好説 　中間にケンブリッジの現金残高方程式 貨幣の需要と供給、およびそれらの均衡をどう解明するのか 貨幣数量説、貸付資金説、流動性選好説で利子率がどのように決定されるのか

3 １．The Functions & Kinds of Money 貨幣の機能と種類
Modern economy = "Indirect exchange or monetary economy" "buying goods with money and buying money with goods“(Clower pointed out) Basic characteristics necessary for becoming money ⇒ General acceptability that everyone will respond to an exchange (1) Divisibility to divide value finely (2) Transportability that can carry great value with a small amount (or portability), (3) Durability that can save value without wearing it The fundamental functions of money ⇒ (1) Measure of value to measure value finely before transactions 　　(2) Means of exchange to intermediate indirect exchange 　　(3) Store of value that can carry value to the future 現代の経済＝（クラウワーが指摘）「財で貨幣を買い、貨幣で財を買う」間接交換すなわち貨幣経済（monetary economy） 　貨幣となるために必要な基本的性質 ⇒誰もが交換に応じてくれる一般的受容性（general acceptability） (1)　価値を細かく分割できる分割可能性（divisibility） (2)　少量で大きな価値を運べる運搬可能性（transportability）携帯可能性（portability）、 (3)　価値を減耗せずに保存できる耐久性（durability） 貨幣の本源的機能 ⇒(1) 交換に先立って価値を細かく測定できる価値尺度（measure of value） (2) 間接交換を仲立ちする交換手段（means of exchange） (3) 価値を将来へ持ち越すことができる価値貯蔵手段（store of value）

4 １B．The Functions & Kinds of Money 貨幣の機能と種類
Modern money =Modern currency in the sense of circulating money ⇒ divided into narrow money and broad money The former is called M1 (Money 1), which consists of cash currency and deposit currency( = demand deposits). Cash currency =Legal tender(=government coins = coins such as 1 yen, 5 yen, 10 yen, 50 yen, 100 yen, 500 yen) + Central Bank Note(=paper money = 1000 yen, 5000 yen, yen, etc.). Legal tender in Japan is the money that the government has its issuing right, issues only to the Bank of Japan, and the Bank has its circulation right to the public. Central bank notes in Japan are the money that the Bank of Japan (Nippon Ginko) has its issuing right, issues and circulates to the public. The government, Ministry of Finance, purchases coins that had issued to the Bank already and sells coinsets to the public as a set. 現代の貨幣（money）＝流通する貨幣という意味で通貨（currency） 狭義貨幣（narrow money）と広義貨幣（broad money）とに大別 前者はM1（Money 1）、現金通貨（cash currency）と預金通貨（deposit currency）＝要求払預金（demand deposits）とから構成 現金通貨＝1円、5円、10円、50円、100円、500円などの硬貨（coins）＝法定貨幣（legal tender）＋1000円、5000円、10000円などの紙幣（paper money）＝中央銀行券（central bank note） 日本では法定貨幣は政府が日本銀行に対して発行する発行権、日本銀行が公衆に対して流通させる流通権。 中央銀行券は日本銀行（Nippon Ginko, the Bank of Japan）が公衆に対して発行する発行権と流通させる流通権。 コインセットは、政府が日本銀行に対して発行した硬貨から、コインセットの分を政府が日本銀行から購入し、それをセットにして公衆へ販売。

5 １C．The Functions & Kinds of Money 貨幣の機能と種類
Total amount of money that the central bank supplies in the market = total cash circulation of central bank notes and legal tender held by the public in the market and total central bank deposits (at central bank current account) = monetary base MB, base money BM = high powered money HM (by Friedman’s definition) = currency for settlements & credit creation, it does not include earning assets ( excess reserves with positive interest rate) As of the end of 2011, MB ≒118 trillion yen, issued balance of Bank of Japan Notes ≒ 82 trillion yen, circulation balance of legal money ≒ 5 trillion yen, BOJ‘s current account deposits NC ≒ 32 trillion yen, cash held by the public ≒ ≒86 trillion yen As of February 2017, MB ≒ 431 trillion yen , issued balance of Bank of Japan Notes≒ 99 trillion yen, circulation balance of legal money ≒5 trillion yen, BOJ’s current account deposit NC ≒ 327 trillion yen, cash held by the public ≒ ≒ 104 trillion yen 中央銀行が市中に供給している貨幣の合計＝市中保有の中央銀行券と法定貨幣を合わせた現金流通高、および中央銀行預け金（中央銀行当座預金）の合計＝マネタリ・ベースMB（monetary base）、ベースマネーBM（base money）＝フリードマンはハイパワードマネーHM（high powered money: 高出力貨幣）信用創造をするパワーの元となる決済用通貨であり, 収益資産(付利をした超過準備)は含まない 2011 年末現在、MB＝約118兆円、日銀券発行残高＝約82兆円、貨幣流通高＝約5兆円、日銀当座預金NC＝約32兆円、市中保有現金＝118-32=約86兆円 2017 年2月現在、MB＝約431兆円、日銀券発行残高＝約99兆円、貨幣流通高＝約5兆円、日銀当座預金NC＝約327兆円、市中保有現金＝ =約104兆円

6 １D．The Functions & Kinds of Money 貨幣の機能と種類
Central bank's balance sheet Assets = central bank’s lending, outstanding securities holdings, foreign exchange reserves Liability = cash currency (coin + central bank note), central bank current account Deposit currency = demand deposits withdrawable according to demand = ordinary deposit, current deposit, notice deposit, separate deposit Daily little transactions ⇒ cash, Transaction with large amount ⇒ Transfer of deposit and check payment, the leading role of money is deposit currency Narrow money M1 (Money 1) = cash currency + deposit currency Broad money M2 (Money 2) = M1 + time deposits Time deposits = time deposits, due date time deposit, accumulating time deposits etc. You can withdraw time deposits at maturity date or withdraw it before the maturity date, and use it for payments⇒Time deposits have high liquidity next to cash and demand deposits. 中央銀行のバランスシート（balance sheet: 貸借対照表） 資産＝中央銀行貸出、証券保有残高、外貨準備高 負債＝現金通貨（硬貨＋中央銀行券）、中央銀行当座預金 預金通貨＝要求に応じて引き出しができる要求払預金＝普通預金、当座預金、通知預金、別段預金 日常の少額の取引⇒現金、金額の大きな取引⇒預金の振込や小切手支払い、貨幣の主役は預金通貨 狭義貨幣M1 （Money 1） ＝現金通貨＋預金通貨 広義貨幣M2（Money 2）＝M1＋定期性預金（time deposits） 定期性預金＝定期預金、期日指定定期預金、積立定期預金など 満期時に引き出しするか、満期前でも解約すれば、支払いに充てる⇒現金や要求払預金に次ぐ貨幣＝近似貨幣（near money）、準通貨（quasi-currency）

7 １E．The Functions & Kinds of Money 貨幣の機能と種類
Liquidity is easiness to convert to cash. Time deposits have high liquidity next to demand deposits.⇒near money or quasi-currency. General account that combines ordinary deposits and time deposits ⇒if the balance of ordinary deposits become zero, 90% of time deposits can be used for payments at a higher interest rate than time deposits. = Overdraft；OD As of the end of 2011, cash currency ≒78 trillion yen, deposit currency ≒ 450 trillion yen, ≒ six times, M1 ≒ 528 trillion yen, quasi-currency ≒ 553 trillion yen + negotiable time deposit about 31 trillion yen ≒ 584 trillion yen , M2 ≒ 807 trillion yen, M1 excluding NC ≒496 trillion yen, M2 excluding NC ≒ 775 trillion yen As of January 2017, cash currency ≒ 95 trillion yen, deposit currency ≒ 598 trillion yen, ≒ 6 times, M1 ≒ 693 trillion yen, quasi-currency ≒ 561 trillion yen + negotiable time deposit about 32 trillion yen ≒ 593 trillion yen, M2 ≒ 961 trillion yen, M1 excluding NC ≒ 366 trillion yen (26% decrease from 2011), M2 excluding NC ≒ 634 trillion yen (18% decrease from 2011) 満期時に引き出しするか、満期前でも解約すれば、支払いに充てる⇒現金や要求払預金に次ぐ貨幣＝近似貨幣（near money）、準通貨（quasi-currency） 現金への換金の容易性を流動性（liquidity）、定期性預金は要求払預金に次いで流動性が高い。 普通預金と定期預金をセットにした総合口座⇒普通預金残高がゼロになっても定期預金残高の90％まで支払いに充てることができる当座貸越（overdraft） 2011年末現在、現金通貨＝約78兆円、預金通貨＝約450兆円、約6倍、 M1＝528兆円、準通貨＝約553兆円＋譲渡性定期預金約31兆円＝584兆円、M2＝807兆円、NC除くM1＝約496兆円、NC除くM2＝約775兆円 2017 年1月現在、現金通貨＝約95兆円、預金通貨＝約598兆円、約6倍、M1＝693兆円、準通貨＝約561兆円＋譲渡性定期預金約32兆円＝593兆円、 M2＝961兆円、 NC除くM1＝約366兆円（2011年より26％減少）、NC除くM2＝約634兆円（2011年より18％減少）

8 ２．Supply of Money 貨幣の供給 Gold standard system ⇒ The government or central bank supplies money to the market according to a certain amount of gold reserve Paper money standard, managed currency system ⇒ The central bank supplies money to the market at discretion regardless of gold reserve （１）　Central bank’s lending policy⇒to lend at official discount rate, to supply cash by discounting qualified bill at official discount rate ⇒ Central bank supplies money accommodatively＝Endogenous money supply Open market operation= to supply cash through buying operation of securities⇒ to collect cash by selling operation of securities, ⇒ central bank supplies money actively. ＝Exogenous money supply 金本位制⇒政府あるいは中央銀行は一定量の金準備に応じて貨幣を市中へ供給 紙幣本位制（paper money standard）、管理通貨制（managed currency system） ⇒中央銀行は金準備に関係なく裁量的に貨幣を市中へ供給 （１）中央銀行の貸出政策（lending policy）、公定歩合で貸出、適格手形を公定割引歩合で割り引いて現金を供給⇒中央銀行が受動的（accommodative）に供給 　内生的な貨幣供給（endogenous money supply） （２）公開市場操作（open market operation）、買いオペレーションで現金供給 　売りオペレーションで現金回収、⇒中央銀行が能動的（active）、 　外生的な貨幣供給（exogenous money supply）

9 ２B．Supply of Money 貨幣の供給
(3) Operations of deposit reserve ratio; Lowering deposit reserve ratio decreases deposit reserve and increases cash circulation . Increasing deposit reserve ratio increases deposit reserve and reduce cash circulation. ⇒ Exogenous money supply (4) Operations of selling or buying foreign exchange in the foreign exchange market; When a central bank sells yen and buys dollar exchange at the Ministry of Finance account (MOF account) in response to the government‘s order, yen depreciates, and supply of yen increases. If you sell dollar exchange and buy yen, yen appreciates, supply of yen decreases. ⇒ Active, exogenous money supply ∴ A mixture of exogenous and endogenous parts　for the foreign exchange rates. Money supply by lending policy and discount rate operation ⇒ Increases or decreases base money Money supply through operations of deposit reserve ratio and selling and buying operations of foreign exchanges ⇒ Increases or decreases the cash circulation in the market through changing cash reserve at central bank account while keeping the base money unchanged （３）預金準備率操作（operations of reserve ratio）、預金準備率を引き下げると預金準備が減って現金流通高が増。預金準備率を引き上げると預金準備が増えて現金流通高が減。⇒外生的な貨幣供給 （４）外国為替市場での為替売買操作（operations of selling or buying foreign exchange）、政府の指示を受けて中央銀行が財務省勘定（Ministry of Finance account: MOF勘定）で円を売ってドル為替を買えば円安、円の供給が増。 ドル為替を売って円を買えば円高、円の供給が減⇒能動的、外生的な貨幣供給 　∴外為相場については、外生的な部分と内生的な部分とが混在 貸出政策と公定歩合操作による貨幣供給⇒ベースマネーを増減させる 預金準備率操作と為替売買操作による貨幣供給⇒ベースマネーを不変に保ちつつ、中央銀行預け金を増減させて、市中の現金流通高を変化

10 ３．Money Multiplier 貨幣乗数
Money that the central bank supplies in the market = high-powered money H = base money, monetary base = cash　currency in the market C + central bank current account CA (exclude excess reserve as earning assets) ⇒generates the narrow money M1 = cash currency C +deposit currency D ⇒ generates the broad money M2 = M1 + time deposit TD (quasi-currency) If the cash deposit ratio is cd, the deposit reserve ratio is rd, and the quasi-currency / deposit currency ratio is td, 　M1/H＝(C＋D)/(C＋CA)＝(C/D＋1)/(C/D＋CA/D)＝(cd＋1)/(cd＋rd) 　　M2/H＝(C＋D＋TD)/(C＋CA)＝(C/D＋1＋TD/D)/(C/D＋CA/D) 　　　　　＝(cd＋1＋td)/(cd＋rd) 中央銀行が市中に供給する貨幣＝ハイパワードマネーH＝マネタリベース＝市中の現金通貨C＋中央銀行当座預金CA（収益資産としての超過準備を除く）⇒現金通貨C＋預金通貨Dの総計の狭義貨幣M1を生む ⇒M1＋定期性預金TD（準通貨）の総計の広義貨幣M2を生む 現金・預金比率をcd、預金準備率をrd、準通貨・預金通貨比率をtdとおくと、 　　M1/H＝(C＋D)/(C＋CA)＝(C/D＋1)/(C/D＋CA/D)＝(cd＋1)/(cd＋rd)

11 ３B．Money Multiplier 貨幣乗数
Magnification of how much money the high-powered money H produces = multiplier (money multiplier). Power means a power to create money through credit creation.(M. Feedman) Cash deposit ratio cd decreases, deposit reserve ratio rd falls, quasi-currency / deposit currency ratio td rises, ⇒ money multiplier becomes large At the end of 2011, cash currency = about 78 trillion yen, deposit currency = about 450 trillion yen, quasi-currency = about 553 trillion yen, monetary base = about 125 trillion yen M1／H＝(78＋450)／125＝4.2 M2／H＝(78＋450＋553)／125＝8.6 ハイパワードマネーHがどれだけの貨幣を生み出すかの倍率＝貨幣乗数（money multiplier）powerとは貨幣を信用創造で造る力である（M.　Freedman） 　現金・預金比率cdが下がる、預金準備率rdが下がる、準通貨・預金通貨比率tdが上がる、⇒貨幣乗数は大きくなる 　2011年末現在、現金通貨＝約78兆円、預金通貨＝約450兆円、準通貨＝約553兆円、マネタリーベース＝約125兆円⇒ 　　M1／H＝(78＋450)／125＝4.2 　　M2／H＝(78＋450＋553)／125＝8.6

12 ４．Credit Creation of Deposit Currency 預金通貨の信用創造
Transmission path or circulation path of the money supply From the central bank to commercial banks ⇒ companies (business corporations), financial institutions such as securities companies and insurance companies ⇒ households ⇒ to purchase goods and services, so that money is paid to companies, financial institutions, nonprofit corporations. ⇒Households and companies deposit money into the commercial banks as deposits, and the deposits are used for payment as deposit currency. Deposits made by companies’ and households’ depositing cash into banks = primary deposits Deposits except deposit reserves (cash reserves) are again lent to companies and households. Rate of deposit reserve against deposits = rate of deposit reserve 貨幣供給の波及経路、流通経路 中央銀行から市中銀行⇒企業（事業法人）、証券会社や保険会社等の金融機関⇒家計⇒財貨やサービスの購入に充てるので、企業や金融機関、非営利法人へとその貨幣が流通、企業や家計は市中銀行へ貨幣を預金として預け入れ、その預金が預金通貨として支払いに充当。 企業や家計が銀行へ現金を預け入れて作る預金＝本源的預金（primary deposits） 預金準備（deposit reserve、現金準備）の部分を除いて、企業や家計に貸出 預金に対する預金準備の割合＝預金準備率（rate of deposit reserve）

13 ４B．Credit Creation of Deposit Currency 預金通貨の信用創造
Loans are initially implemented in the form of deposits at the same bank’s account ⇒ those derived from primary deposits through lending = derivative deposits ⇒ Lending further to companies and households, except for the deposit reserves of derivative deposits The primary deposit is D, the deposit reserve ratio is R, then the process of increasing deposits is D＋D (1－R)＋D (1－R )2＋D (1－R )3＋　……　＝D ／(1－(1－R ))＝D ／R ⇒ Infinite Equal Proportion Series with the first term being D and the common ratio being (1 - R) ⇒ the total sum is D ／R Phillips formula in response to discoverer C. A. Phillips＝Credit creation, 　　 1 / R ＝credit creation multiplier Ratio of loan among deposits=L ⇒ common ratio is L(1－R), deposit retention rate=S ⇒ common ratio is SL(1－R) ∴ credit creation multiplier = 1／(1－SL(1－R))　＜1／R 貸出は、当初は同じ銀行の口座の預金という形で実行⇒本源的預金から貸出を通じて派生的に作られたもの＝派生的預金（derivative deposits） ⇒派生的預金のうち預金準備の部分を除いて、企業や家計にさらに貸出 本源的預金をD、預金準備率をR、預金が増えていくプロセスは、 　　D＋D (1－R)＋D (1－R )2＋D (1－R )3＋　……　＝D ／(1－(1－R ))＝D ／R ⇒初項がDで公比が(1－R )の無限等比級数⇒その合計はD ／R 発見者フィリップス（C. A. Phillips）に因んでフィリップスの公式（Phillips formula） 信用創造（credit creation）、倍数1／R を信用創造乗数（credit creation multiplier） 貸出に回る割合をL⇒公比はL(1－R)、預金滞留率をS⇒公比はSL(1－R) ∴信用創造乗数＝1／(1－SL(1－R))　＜1／R

14 ４C．Credit Creation of Deposit Currency 預金通貨の信用創造
 Numerical example: primary deposit is 10 trillion yen, deposit reserve ratio is 1.2% ⇒ ( ) + 10 ( ) ( ) = 10 / 0.012= 10 * 83.3 = 833 Ultimately, deposit currency of 833 trillion yen, which is 83.3 times of 10 trillion yen, is created＝credit creation Ratio of loan among deposits=L = 0.98, the deposit retention rate S = 0.95 ⇒10 / ( * 0.98 ( )) = 10 / ( ) = 10 / = 10 * = Credit creation multiplier is times ≒ 13 times Present deposit reserve ratio of the Bank of Japan: 0.05 to 1.2% according to the amount of deposits in the case of time deposits, in case of demand deposits etc. R is 0.1 to 1.3% depending on deposit amount. However, the reserve ratio has not been changed since As of the end of 2011, the cash currency is about 78 trillion yen, the total of demand deposits and time deposits is about 1034 trillion yen, assuming that all of the cash currencies become primary deposits, the credit creation multiplier of the deposit currency is 1034 / 78 = 13.3 ≒ 13 times 数値例：本源的預金が10 兆円、預金準備率が1.2％ ⇒10＋10(1－0.012) ＋10(1－0.012)2＋10(1－0.012)3＋……　＝10／0.012＝10×83.3＝833 最終的には10兆円の83.3倍の833兆円の預金通貨が創造 貸出に回る割合をL＝0.98、預金滞留率をS＝0.95 ⇒10／(1－0.95×0.98(1－0.012))＝10／(1－0.9198)＝10／0.0802＝10×12.47＝124.7 信用創造乗数は12.47倍≒13倍 日本銀行の現在の預金準備率；定期性預金の場合は預金額に応じて0.05～1.2％、要求払預金などの場合はそれより高く預金額に応じて0.1～1.3％。ただし1991年から準備率は変更されていない。2011年末現在の現金通貨は約78兆円、要求払預金と定期性預金の合計は約1034兆円、現金通貨のすべてが本源的預金になると仮定した場合、預金通貨の信用創造乗数は1034／78＝13.3 ≒13倍

15 ５．Motives to Hold Money and Demand for Money 貨幣の保有動機と需要
In the monetary economy money mediates all transactions ⇒ Money demand based on transactions motive. T, the price is P,⇒ the transaction amount is PT, Money demand MD is MD＝PT． The transaction of final product Y except for the transaction of intermediate goods, its price is P, ⇒the nominal final product is PY, the money demand is MD＝PY . Money demand as a function of PT or PY = money demand function Needs to hold money for unexpected payments⇒　precautionary motive ⇒ It is determined according to the size of transaction amount and nominal income ⇒ MD＝PT、MD＝PY　 Adam Smith and other classicalists ⇒ emphasize on the fundamental function of money such as measure of value and means of exchange ⇒ emphasis on transactions motive and precautionary motivation Figure Money demand by transactions motive　　 貨幣経済ではすべての取引を貨幣が媒介⇒取引動機 （transactions motive）に基づく貨幣需要。取引量をT、 その価格をP、取引金額はPT、⇒貨幣需要MDは、MD＝PT 中間財の取引を除いて最終生産物Yの取引、その価格をP、 ⇒名目の最終生産物はPY、貨幣需要は、MD＝PY 貨幣需要をPTやPYなどの関数＝貨幣需要関数 （money demand function） 不測の支払いに備えて、貨幣を保有しておく必要⇒ 予備的動機（precautionary motive）⇒取引額や名目所得 の大きさに応じて決まる⇒MD＝PT、MD＝PY　　　 アダム・スミスなどの古典派⇒価値尺度や交換手段という貨幣 の本源的機能を重視⇒取引動機や予備的動機を重視 15-1図　取引動機による貨幣需要

16 ５B．Motives to Hold Money and Demand for Money貨幣の保有動機と需要
Keynes also focuses on the fundamental function of store of value, the view of purchasing assets to obtain future profits ⇒ Money demand based on speculative motive Interest rate i or the rate of return rises ⇒ Asset holdings are advantageous, purchasing assets by reducing money holdings　　　　　MD＝L(i)　　L’(i)＜0 Keynes proposed the liquidity preference theory that “interest is a reward for releasing liquidity”, liquidity preference function L(i) Profits from holding assets = capital gain (＝profit due to a rise of price) + interest income Especially asset holding aiming at capital gain is called speculation Figure Money demand by speculative motive ケインズは価値貯蔵手段という本源的機能も着目、将来の収益 を得るために資産を購入するという観点⇒投機的動機 （speculative motive）に基づく貨幣需要 利子率iないし収益率が上昇⇒資産保有が有利、貨幣保有を 減らして資産購入　　MD＝L(i)　　L’(i)＜0 ケインズは「利子は流動性を手放すことに対する報酬である」 という流動性選好説（liquidity preference theory）、流動性 選好関数（liquidity preference function） 資産保有による利益＝値上がり益である資本利得 （capital gain）＋利子所得（interest income） 前者を狙う資産保有を特に投機（speculation） 図　投機的動機による貨幣需要

17 ５C．Motives to Hold Money and Demand for Money 貨幣の保有動機と需要
Money demand shown by Keynes' liquidity preference function focuses on interest income ⇒ it is better to say asset motive rather than speculative motive. ⇒ Money demand based on transactions and precautionary motives depends on nominal income PY, money demand based on speculative motive depends on interest rate i ⇒　 MD＝L(PY, i)　　 L’(Y)>0, L’(i)＜0 Divide by P to show real value, k is a constant⇒MD／P＝kY＋L(i)＝m1＋m2　L’(i)＜0 The part of kY = m1 on the right side is money holding based on transactions and precautionary motives as shown in figure15-1, part of L(i) ＝m2 is money holding based on speculative motive as shown in figure15-2. ⇒ Keynes called the former as the active balance, the latter as the idle balance. ケインズの流動性選好関数で表される貨幣需要は利子所得を主眼⇒投機的動機というよりむしろ資産動機（asset motive）と呼ぶ方がよい 　⇒取引動機や予備的動機に基づく貨幣需要が名目所得PYに依存、投機的動機に基づく貨幣需要が利子率iに依存 MD＝L(PY, i)　　 L’(Y)>0, L’(i)＜0 物価Pで除して実質値で表し、kを定数　　MD／P＝kY＋L(i)＝m1＋m2　　L’(i)＜0 右辺のkY＝m1の部分は15-1図のように取引動機と予備的動機に基づく貨幣保有、L(i) ＝m2の部分は15-2図のように投機的動機に基づく貨幣保有 ⇒ケインズは前者を活動残高（active balance）、後者を遊休残高（idle balance）

18 ６．Quantity Theory of Money 貨幣数量説
Adam Smith and other classicalists ⇒ emphasize on measure of value and means of exchange ⇒ emphasize on transactions motive and precautionary motive ⇒ Money demand MD is a function of nominal transaction amount PT or nominal income PY. MD＝PT　　or　　MD＝PY M is the circulation amount of money, V is the circulation velocity, ⇒the money supply MS is its product, MS＝MV The equilibrium in the money market is achieved when the supply and the demand are equal, MS＝MD, MV＝PT　or MV＝PY These are Fisher's exchange equations formulated by Irving Fisher, the former V is transactions velocity, the latter V is income velocity, Replacing the equation with respect to P ⇒ P＝MV／T　or　P＝MV／Y アダム・スミスなどの古典派⇒価値尺度や交換手段を重視⇒取引動機や予備的動機を重視⇒貨幣需要MDは、名目取引額PTないし名目所得PYの関数,　MD＝PT　　ないし　　MD＝PY 貨幣の流通高をM、流通速度をV、⇒貨幣供給MSはその積として、MS＝MV 貨幣市場の均衡は、MS＝MDと供給と需要が均等の時に達成、MV＝PT　　ないし　　MV＝PY アーヴィング・フィッシャー（Irving Fisher）が定式化、フィッシャーの交換方程式（Fisher’s exchange equation）、前者のVを取引流通速度（transactions velocity）、後者のVを所得流通速度（income velocity） 物価Pについて整理⇒　P＝MV／T　　ないし　　P＝MV／Y

19 ６B．Quantity Theory of Money 貨幣数量説
Circulation velocity V is a given exogenous variable determined by social payment practices and payment schemes. Physical transaction volume T and real income Y are determined by the activities of the real economy ⇒ Therefore, if the monetary authority gives the circulation amount of money M, the price P is determined. ⇒ The quantity theory of money Circulation velocity V, physical transaction amount T, real income Y, etc. are determined by the real sector of the economy, and the circulation amount of money M and price P are determined by the monetary sector of the economy = the classical dichotomy Money does not affect the real sector of the economy, but simply decides the price P which is a nominal value.⇒ neutrality of money, veil theory of money 流通速度Vは社会の支払慣行や支払制度によって決まる所与の外生変数 物的な取引量Tや実質所得Yは実物経済の活動により決まる ⇒金融当局が貨幣流通量Mを与えれば、物価Pが決定⇒貨幣数量説（quantity theory of money） 流通速度V、物的な取引量T、実質所得Yなどは実物経済で決まり、貨幣流通量Mや物価Pは貨幣部門で決まる二分法＝古典派の二分法（classical dichotomy） 貨幣は実質経済量には影響を与えず、単に名目値である物価Pを決める ⇒貨幣の中立性（neutrality of money）、貨幣ヴェール観（veil theory of money）

20 ６C．Quantity Theory of Money 貨幣数量説
Source of the quantity theory of money= French doctor, economist François Quesney In " Tableau economique, Economic Table" in 1758, the circulation of money in the economy is compared to the circulation of blood in the human body. Blood circulates the human body, sends nutrition and oxygen to each tissue, and discharges waste products and carbon dioxide from each organization. In a healthy human body the amount of blood maintains a moderate proportion of body weight, 1/13, 8%. If too much or too little blood, it will cause harmful influence. It is important to maintain the optimum quantity of blood. Similarly, money circulates the economy to smoothly promote various transactions, in a healthy economy, the amount of money is maintained at a moderate proportion, if it is too much, inflation and bubbles occur, if too little deflation, to cause harmful effects. ⇒ It is important to maintain the optimal quantity of money. 貨幣数量説の淵源＝フランスの医師・経済学者ケネー（François Quesney） 1758年に『経済表』、経済における貨幣の循環を人体における血液の循環に例え 血液は人体を循環して栄養や酸素を各組織に送る、老廃物や二酸化炭素を各組織から搬出。健康な人体では血液の量は体重の適度の割合1/13、8％を維持、多すぎても少なすぎても有害な影響。血液の最適量を維持することが重要 同様に、貨幣は経済を循環してさまざまな取引を円滑に促進、健全な経済では貨幣量は適度の割合を維持、多すぎればインフレやバブルを起こし、少なすぎればデフレ、有害な影響、⇒貨幣の最適量を維持することが重要

21 ７．Cambridge Quantity Theory of Cash Balance ケンブリッジの現金残高数量説
Cambridge School, Marshall ⇒ Prices is P. People demand money to keep a fixed proportion k of nominal income PY and a certain proportion h of nominal property PA as immediate purchasing power. ⇒ Nominal money demand function is MD＝kPY＋hPA In the form of real money demand, MD／P＝kY＋hA Since Marshall’s numerical example is k = 0.1 (one tenth), h = 0.02 (1/50), income PY = wheat 5 million quarter, property PA = wheat 25 million quarter, so money demand is, MD = 0.1 × 5 million × 25 million = 500, ,000 = 1 million (quarter) Given the money supply M, in equilibrium, M＝kPY＋hPA　or M／P＝kY＋hA In the case of mismatch between supply and demand, prices P and coefficients k and h fluctuate　to adjust the mismatch. ⇒ the way of thinking that prices P adjust is the quantity theory of money, it is called the quantity theory of cash balance However, the way of thinking that the coefficients k and h change is a unique idea different from the quantity theory of money. ケンブリッジ学派のマーシャル⇒物価をP、名目所得PYの一定割合kと名目財産PAの一定割合hを即時の購買力として保有するように、貨幣を需要する　⇒名目貨幣需要関数MDは、　MD＝kPY＋hPA、　　実質貨幣需要の形では、　MD／P＝kY＋hA マーシャルは数値例ではk＝0.1（10分の1）、h＝0.02（50分の1）、所得PY=小麦500万クォーター、財産PA＝小麦2500万クォーターとしたので、貨幣需要は、 　　MD＝0.1×500万＋0.02×2500万＝50万＋50万＝100万（クォーター） 貨幣供給量Mが与えられると均衡では、M＝kPY＋hPA　ないしM／P＝kY＋hA 需給不一致の場合は、物価Pや係数のkやhが変動して調整　⇒物価Pが調整するのは貨幣数量説の考え方、現金残高数量説（quantity theory of cash balance） しかし係数のkやhが変化するのは、貨幣数量説とは異なる独自の考え方

22 ７B．Cambridge Quantity Theory of Cash Balance ケンブリッジの現金残高数量説
Pigou, a disciple of Marshall, expressed the total assets measured by wheat as Y ⇒ M＝kPY　or M／P＝kY They are called Cambridge equation of exchange, cash balance equation Rewrite it to obtain k＝M／PY ＝percentage of money holdings against nominal income PY ＝ Marshallian k ⇒ One indicator to judge whether the relationship between money supply and real economy is appropriate If we set k＝1／V, we obtain MV＝PY . It matches Fischer's exchange equation, it is one form of the quantity theory of money, but it is different in that k is considered variable. ⇒ Therefore Cambridge exchange equation, while drawing on the flow of the quantity theory of money, played a role of the bridge that leads to Keynes' liquidity preference theory. マーシャル門下のピグーは小麦で測った全資力をまとめてY ⇒　M＝kPY　　あるいは　　M／P＝kY ケンブリッジの交換方程式（Cambridge equation of exchange）、現金残高方程式（cash balance equation）という。書き換えて、　k＝M／PY 名目所得PYのうち貨幣で保有する割合、マーシャルのk（Marshallian k） ⇒貨幣供給と実体経済との関係が適正であるかどうかを判断する一つの指標 　　k＝1／Vとおけば、　MV＝PY フィッシャーの交換方程式に一致、貨幣数量説を変形、kを可変と見る点で異なる。 ⇒よってケンブリッジの交換方程式は、貨幣数量説の流れを汲みながらも、実はケインズの流動性選好説へとつながる橋渡しの役割

23 ８．Liquidity Preference Theory 流動性選好説
Keynes paid attention to the part hPA that is held as money among property PA in Marshallian money demand function, and considered that it is demanded in response to interest rate i on the basis of speculative motive. Equilibrium conditions of real money supply and demand divided by prices P, 　 M／P＝kY＋L(i)　　L’(i)＜0 kY = activity balance based on transactions and precautionary motives Liquidity preference function L (i) = idle balance based on speculative motives. Interest rate i, rate of return rise⇒ asset holdings become advantageous, sell money to buy assets, ∴ L’(i)＜ behind it there is a view of money that emphasizes store of value to carry value to the future Demand for money based on speculative motive is variable according to economic situation, state of interest rate. ケインズ⇒マーシャルの貨幣需要関数で財産PAのうち貨幣 で保有する部分hPAに着目、これが投機的動機に基づき 利子率iに反応して需要される 物価Pで除した実質貨幣需給の均衡条件、 　　M／P＝kY＋L(i)　　L’(i)＜0 kY＝取引動機や予備的動機に基づく活動残高、 流動性選好関数L(i)＝投機的動機に基づく遊休残高。利子率i・ 収益率が上昇⇒資産保有が有利となり貨幣を手放して資産の購入、 　∴L’(i)＜0…その背後には、価値を将来に持ち越す価値貯蔵 機能も重視した貨幣観 投機的動機に基づく貨幣需要＝景気局面や利子率に応じて異なる

24 ８B．Liquidity Preference Theory 流動性選好説
Full employment ⇒ Y is constant at full employment national income YF . increases or decreases in the money supply MS lower or raise the interest rate i. 　M／P does not change, money demand does not respond to interest rate i. Due to L’(i)＝dL／di＝0, the interest elasticity (dL/L)／(di/i) is zero. ⇒ As shown in the figure 15-2, the liquidity preference curve is vertical, at the supply-demand equilibrium, M／P＝kY,　L’(i)＝0, k is also constant. This corresponds to the classical quantity theory of money. Depression ⇒ as shown in the figure 15-2, interest rate i sticks to the lower limit, liquidity trap.⇒ If the Bank increases or decreases the money supply MS, M / P increases or decreases, the interest rate i does not change ⇒ Money demand reacts infinitely to the interest rate i, L’(i)＝dL／di＝－∞. Therefore, interest elasticity as shown in the figure 15-2, the liquidity preference curve is horizontal and in the supply-demand equilibrium, M／P＝kY＋L(i)　L’(i)＝－∞ 完全雇用⇒Yは完全雇用国民所得YFで一定、貨幣供給MSを増減すると、 利子率iは低下・上昇、M／Pは不変、貨幣需要は利子率iに対して反応 しない。　L’(i)＝dL／di＝0ゆえ利子弾力性(dL/L)／(di/i)がゼロ ⇒15-2図のように流動性選好曲線は垂直、需給均衡では、 M／P＝kY,　L’(i)＝0, 　kも一定で,古典派の貨幣数量説と一致。 不況⇒15-2図のように利子率iは下限に張り付き流動性の罠 （liquidity trap）⇒貨幣供給MSを増減すると、M／Pは増減、利子率iは 不変⇒貨幣需要は利子率iに対して無限に反応、L’(i)＝dL／di＝－∞ ゆえに利子弾力性(dL/L)／(di/i)も－∞⇒ 15-2図のように流動性選好 曲線は水平、需給均衡では、　M／P＝kY＋L(i)　　L’(i)＝－∞

25 ８C．Liquidity Preference Theory 流動性選好説
Underemployment between the two ⇒ when increasing / decreasing the money supply, M / P increases or decreases, interest rate i falls / rises ⇒ Money demand responds within a finite range to the interest rate i. Because L’(i)＝dL／di＜0, the interest elasticity (dL/L)／(di/i) is also minus. ⇒ As shown in the figure15-2, the liquidity preference curve is mildly downward sloping. At the supply and demand equilibrium, M／P＝kY＋L(i)　　L’(i)＜0 “Liquidity preference theory ” advocated by Keynes in “General Theory of Employment, Interest and Money ”(1936) considered not only transactions and precautionary motives but also speculative motive.∴ “general theory” of money and interest. It analyzes not only full employment targeted by classical school but also depression and underemployment to which Keynes was facing. ∴ "general theory ” of employment. 両者の間の不完全雇用⇒貨幣供給MSを増減すると、M／Pは増減、利子率iは低下・上昇⇒貨幣需要は利子率iに対して有限の範囲内で反応、L’(i)＝dL／di＜0ゆえ利子弾力性(dL/L)／(di/i)もマイナス ⇒15-2図のように流動性選好曲線は緩やかな右下がり曲線、 需給均衡では、M／P＝kY＋L(i)　　L’(i)＜0 ケインズが『雇用、利子および貨幣の『一般理論』（1936年）が提唱した流動性選好説 ⇒取引動機や予備的動機だけでなく、投機的動機も考慮∴貨幣と利子の「一般理論」、 古典派が分析対象とした完全雇用だけでなく、ケインズが直面した大不況も中間である不完全雇用も包摂するので雇用の「一般理論」

26 ９．Inventory Approach 在庫アプローチ
Baumor and Tobin analyzed money demand by applying inventory control theory. Under the monthly salary system, income Y yen is paid to a worker at the beginning of the month, the worker equally expends Y for 1 month ⇒ initially holds the full monthly salary in the form of deposits or bonds, interest income is earned at the interest rate i , the amount that is shifted from deposits or bonds to cash each time is C yen, the cost required for cashing is b yen. ⇒ The average balance of holding money is C/2, the average holdings of deposits or bonds is Y/2－C/2, the number of shifting is n＝Y/C The net income R, which is the interest income minus the shift cost, R＝(Y/2－C/2)i－(Y/C)b ボーモルやトービン＝在庫管理論を応用して貨幣需要を分析。 月給制で、月初にY円の収入、それを1ヶ月間均等に支出⇒当初は月給の全額を預金あるいは債券で保有、利子率iで利子所得、毎回預金あるいは債券から現金にシフトする金額をC円、現金化に要する費用をb。 ⇒貨幣の平均保有残高はC/2、預金ないし債券の平均保有残高はY/2－C/2、シフト回数はn＝Y/C 利子所得からシフト費用を引いた純収入Rは、 　　R＝(Y/2－C/2)i－(Y/C)b

27 ９B．在庫アプローチ Inventory Approach
　　dR/dC＝－i/2＋Yb/C2＝0,　　∴　C*＝ √2Yb/i 最適な平均貨幣保有残高、平均貨幣需要MDは、　MD＝C*/2＝ √Yb/2i 　貨幣需要は所得Yの増加関数、利子率iの減少関数 　所得Yが2倍になっても、貨幣需要は √2倍 …貨幣需要の在庫アプローチ（inventory approach） 　一般型の均衡条件式は、　M＝L(Y, i) , L’(Y)＞0, L’(i)＜0 ⇒流動性選好説と同様に、所得Yに正に依存、利子率iに負に依存 To maximize net revenue, differentiate it with respect to the shift amount C to equalize to zero, 　dR/dC＝－i/2＋Yb/C2＝0,　　∴　C*＝ √2Yb/I The optimal average balance of money holdings, average money demand MD is MD＝C*/2＝ √Yb/2i Money demand is an increasing function of income Y, decreasing function of interest rate i Even if income Y doubles, money demand √ 2 times ... inventory approach to money demand Equilibrium condition of general type is M＝L(Y, i) , L’(Y)＞0, L’(i)＜0 ⇒ Likewise to the liquidity preference theory, it depends positively on income Y, depends negatively on interest rate i.