Unit 4: Financial Sector

Students will examine the financial sector and explain how monetary policy is implemented and transmitted through the banking system.

Money & Financial Assets

Functions and Properties of Money

Money is any asset that serves as a medium of exchange, a unit of account, and a store of value. The medium of exchange function enables transactions without barter, the unit of account provides a common pricing yardstick, and the store of value allows intertemporal purchasing power. All three functions define “money” for AP Macroeconomics.
Effective money exhibits standard properties: acceptability, portability, durability, uniformity, divisibility, and limited supply. These properties support the three functions by making exchange reliable and calculation precise. The curriculum treats stability of the purchasing power of money as desirable in this context.
Liquidity is the ease with which an asset can be used to make transactions without loss of value. Currency and checkable deposits are highly liquid and therefore counted in narrow money. Less liquid assets require conversion before use as a medium of exchange.
Money is a stock variable distinct from income and wealth. Income is a flow earned over time, while wealth is the value of accumulated assets at a point in time. Confusing these terms leads to incorrect statements about the money supply.
The opportunity cost of holding money is the nominal interest rate \(i\) foregone on alternative interest-bearing assets. Higher \(i\) raises the cost of holding idle balances and affects money demand in Unit 4’s money market. This cost concept is part of the academic treatment of monetary choice.

Types of Money

Commodity money has intrinsic value independent of its monetary use. Its value arises from the material itself, such as a metal with consumption or industrial uses. The curriculum emphasizes that intrinsic value is not required for money to function.
Commodity-backed money is redeemable for a commodity at a fixed rate. The monetary instrument is a claim on the commodity rather than the commodity itself. Redemption promises anchor its value under the specified regime.
Fiat money has value by government decree and general acceptability. It is not redeemable for a commodity and relies on institutional credibility and controlled supply. Modern monetary systems use fiat money as the unit of account.
Near-money consists of highly liquid financial assets that are not directly usable as a medium of exchange. Examples include savings deposits, small time deposits, and retail money market mutual fund shares. These assets enter broader money measures but not the narrowest aggregate.
Currency refers to notes and coins in circulation outside banks, while demand deposits are checkable balances at depository institutions. Both function as money when they are directly usable for transactions. The course treats travelers’ checks within narrow money when specified.

Money Aggregates and the Monetary Base

The monetary base \(MB\) equals currency in circulation plus bank reserves at the central bank. Reserves include required and excess reserves held as vault cash or at the central bank. \(MB\) is sometimes called high-powered money because it underlies deposit creation.
\(M1\) includes currency in circulation, demand deposits, and other checkable deposits. These components are immediately spendable and therefore highly liquid. \(M1\) is the narrow measure of the money supply used for transactions.
\(M2\) equals \(M1\) plus savings deposits, small time deposits, and retail money market deposit or mutual fund balances. \(M2\) adds near-monies that are easily converted into transaction balances. \(M2\) is a broader measure that captures additional liquid assets.
The relationship between \(MB\) and the money supply depends on the reserve ratio and currency-deposit behavior. Multiple deposit creation links reserves to deposits through bank lending subject to required reserves. Currency drains and excess reserves reduce the expansion relative to the simple multiplier.
Credit cards are not part of the money supply because they are liabilities that create loans, not money balances. Stocks and bonds are financial assets but are excluded from \(M1\) and \(M2\) unless held in covered near-money forms. Proper classification prevents double counting across categories.

Financial Assets: Definitions, Risk, and Liquidity

Financial assets are claims on future income or payments, including bonds, stocks, and loans. Their valuation depends on expected payments and the discount rate. The curriculum treats these assets as alternatives to money balances.
Expected return summarizes the average payoff, while risk summarizes variability around that payoff. A higher required return compensates for higher risk in comparative statements. AP questions use this tradeoff qualitatively rather than with advanced statistics.
Liquidity ranks assets by how quickly and reliably they can be used for transactions at stable value. Money is most liquid, while long-term and specialized claims are less liquid. Liquidity preference underlies the downward-sloping money demand with respect to \(i\).
Maturity is the time until final payment on a debt asset, and default risk is the likelihood a borrower fails to pay as promised. Longer maturity generally increases price sensitivity to interest rate changes. Higher default risk requires a higher yield to compensate holders.
Diversification spreads idiosyncratic risk across many independent assets. Diversification reduces asset-specific variability but does not eliminate aggregate or systemic risk. The curriculum distinguishes between diversifiable and non-diversifiable components at a conceptual level.

Time Value, Interest Rates, and Bonds

The nominal interest rate \(i\) is the stated rate on financial contracts, and the real interest rate satisfies \( r \approx i - \pi^{e} \). The approximation uses expected inflation \( \pi^{e} \) for ex-ante comparisons. This Fisher relationship is part of the Unit 4 core notation.
Future value and present value connect payments across time. The formulas are \( FV = PV(1+i)^{n} \) and \( PV = \frac{FV}{(1+i)^{n}} \). Discounting applies the appropriate interest rate to translate future sums into current equivalents.
A bond is a debt instrument that promises specified payments such as coupons and principal at maturity. The price of a bond equals the present value of its promised cash flows discounted at the market interest rate. A zero-coupon bond’s price is \( P = \frac{F}{(1+i)^{n}} \) where \(F\) is face value.
Bond prices and market interest rates move inversely by the discounting relation. When \(i\) rises, discount factors fall and present values decrease, so prices decline. When \(i\) falls, discount factors rise and present values increase, so prices rise.
Price sensitivity to interest rates increases with longer maturity and decreases with higher coupon rates. This property is referred to as interest rate risk in bond valuation. AP Macroeconomics requires the directional comparison rather than full duration calculus.

Banking & Money Creation

Bank Balance Sheets and T-Accounts

A bank’s balance sheet records assets, liabilities, and bank capital with the identity \( \text{Assets} = \text{Liabilities} + \text{Capital} \). Major assets include reserves, loans, and securities, while major liabilities include checkable deposits. Bank capital represents owners’ equity that absorbs losses.
Reserves consist of vault cash and deposits at the central bank, and they are used to meet withdrawals and legal requirements. Loans are earning assets created by extending credit to borrowers. Securities are marketable claims held by the bank as part of its asset portfolio.
Checkable deposits are the bank’s liabilities because the bank owes depositors on demand. Time deposits are also liabilities but are less liquid and may have different regulatory treatment. Borrowings from other institutions or the central bank are additional liabilities.
T-accounts summarize changes by listing only the affected items rather than the entire balance sheet. Each recorded operation preserves the accounting identity by posting equal debits and credits. This tool is used to trace money creation and reserve changes.
Solvency refers to having positive capital after marking assets and liabilities to their values. Liquidity refers to having sufficient reserves or liquid assets to meet withdrawals and settlements. A solvent bank can still face liquidity strain if reserves are inadequate.

Required Reserves, Reserve Ratio, and Excess Reserves

The required reserve ratio is \( rr \), a policy parameter applied to reservable deposits. Required reserves satisfy \( RR = rr \cdot D \) where \( D \) is checkable deposits. This condition must hold each maintenance period.
Total reserves \( R \) equal required reserves plus excess reserves, so \( R = RR + ER \). Excess reserves satisfy \( ER = R - RR \). Excess reserves are the portion available for new lending subject to prudence and regulation.
Reserves are held as vault cash and as balances at the central bank. Only specified deposit categories are reservable for the calculation of \( RR \). Nonreservable liabilities are excluded from the base.
When deposits change, required reserves change by \( rr \) times the deposit change. A rise in deposits raises \( RR \) and reduces \( ER \) one-for-one unless reserves also rise. A fall in deposits lowers \( RR \) and mechanically increases \( ER \) if total reserves are unchanged.
If \( ER \) is zero, the bank is fully loaned up relative to its requirement. If \( ER \) is positive, the bank has lending capacity consistent with its risk and policy constraints. If \( ER \) is negative, the bank must obtain reserves or reduce reservable liabilities.

Multiple Deposit Creation and the Simple Money Multiplier

When banks lend excess reserves and recipients redeposit funds, deposits and required reserves expand across institutions. The process of repeat lending and redepositing is called multiple deposit creation. It links an initial reserve injection to a larger change in deposits.
Under the simple assumptions of no currency drain and no excess reserves, the deposit multiplier is \( m_D = \frac{1}{rr} \). The total change in checkable deposits is \( \Delta D = m_D \cdot \Delta R \). Here \( \Delta R \) denotes the initial change in banking system reserves.
Loans create deposits at issuance and destroy deposits when they are repaid. Interest flows affect income statements but not the multiplier identity directly. The expansion is bounded by the required reserve condition.
Changes in reserves that are not deposited in banks do not generate the full multiplier. Currency leakage removes funds from the redeposit cycle and reduces \( \Delta D \). Holding excess reserves also reduces the effective propagation.
The simple multiplier is a theoretical upper bound given the stated assumptions. Any deviation from the assumptions lowers realized deposit expansion. AP analysis uses the stated formula when those assumptions are declared.

Monetary Base, Money Supply, and Currency–Deposit Behavior

The monetary base is \( MB = C + R \) where \( C \) is currency in circulation and \( R \) is bank reserves. The narrow money supply is \( M1 = C + D \). These identities separate outside money from deposit money.
The currency–deposit ratio is \( c \equiv \frac{C}{D} \). A higher \( c \) implies that a larger share of transaction balances is held as currency. This reduces the portion available to support deposits.
With currency drain, the money multiplier becomes \( m_M = \frac{1 + c}{rr + c} \) under zero excess reserves. The total change in \( M1 \) is \( \Delta M1 = m_M \cdot \Delta MB \). The denominator collects marginal leakages from reserves and currency holding.
A rise in \( rr \) increases the denominator and lowers \( m_M \). A rise in \( c \) also increases the denominator and lowers \( m_M \). The comparative statics identify factors that contract or expand money creation.
Distinguish \( MB \) control from \( M1 \) outcomes because the multiplier can vary with behavior. Given \( MB \), changes in \( rr \) and \( c \) alter the mapping to \( M1 \). This separation is used in curriculum diagrams of money creation.

Constraints and Leakages in Deposit Expansion

Excess reserve holdings represent a voluntary or regulatory leakage relative to the simple model. When banks increase \( ER \), fewer new loans are created per unit of reserves. The effective multiplier declines accordingly.
Currency drain is a public portfolio choice that redirects funds from deposits to cash. When redeposits are lower, successive rounds of required reserves and lending are curtailed. The effective multiplier again falls below \( \frac{1}{rr} \).
Loan demand can be a constraint on deposit expansion at a given interest rate and underwriting standard. If creditworthy borrowers are scarce, reserves may remain unused as \( ER \). In that case, deposit growth is smaller than the simple prediction.
Capital adequacy requirements impose a separate constraint from reserves. If losses reduce capital, asset growth is limited until capital is restored. This restricts balance sheet expansion even when reserves are available.
Asset valuation changes can alter measured capital and thereby constrain lending. Securities and loan write-downs reduce capital and permissible asset size. These effects are distinct from the reserve requirement mechanism.

Reserve Changes and Balance-Sheet Responses

An increase in system reserves raises \( ER \) for banks that were at requirement. With unchanged \( rr \), the increase in \( ER \) provides capacity for additional loans. New loans expand deposits and required reserves in subsequent rounds.
A decrease in system reserves lowers \( ER \) for banks that were at requirement. If \( ER \) becomes insufficient, banks must reduce loans, sell assets, or obtain reserves. Deposits contract and required reserves fall with the contraction.
Changes in \( rr \) alter \( RR \) at each deposit level through \( RR = rr \cdot D \). A higher \( rr \) raises required reserves and reduces lending capacity at any \( R \). A lower \( rr \) reduces required reserves and increases lending capacity at any \( R \).
Shifts in the public’s currency preference change \( C \) relative to \( D \). A higher currency–deposit ratio reduces deposits supported by a given \( MB \). A lower currency–deposit ratio increases deposits supported by a given \( MB \).
These balance-sheet relations are accounting statements within the banking system. They connect reserve quantities and behavioral ratios to deposit magnitudes. The curriculum employs them to explain money creation under stated assumptions.

Money Market (MS–MD)

Model Definition and Axes

The money market relates the nominal interest rate \(i\) to the quantity of money \(M\) demanded and supplied. The vertical axis shows \(i\) and the horizontal axis shows the nominal quantity of money. The model is used with a fixed aggregate price level for short-run analysis.
The nominal money stock is typically measured by \(M1\) or \(M2\) as specified in a problem. Real money balances are defined as \(M/P\) and are used to express demand in real terms. Many presentations summarize money demand as \( \frac{M^d}{P} = L(i, Y) \).
Money demand is drawn as a downward-sloping curve in \(i\)–\(M\) space. Money supply is drawn as a vertical line when set by policy at a given moment. Equilibrium occurs at the intersection that determines \(i^{*}\) and the corresponding quantity of money.
Movements along money demand are caused by changes in \(i\). Shifts of money demand are caused by non–interest-rate determinants such as income and price level. Shifts of money supply are caused by policy changes that alter the chosen money quantity.
The ceteris paribus condition holds non–interest determinants fixed when tracing a single curve. The diagram is comparative static and not a time path. Labels must specify which aggregate \(M\) is graphed and which determinants are held constant.

Money Demand (MD): Theory and Shape

Money demand is the desired holding of monetary assets for transactions, precautionary, and speculative purposes. The opportunity cost of holding money is the nominal interest rate \(i\) on nonmoney assets. A higher \(i\) increases the cost of holding money and reduces the quantity demanded.
Transactions demand is positively related to nominal spending needs. For a given price level, higher real income \(Y\) increases the volume of transactions. This shifts money demand to the right at every \(i\).
Precautionary demand reflects holdings for unforeseen timing differences in receipts and payments. Greater uncertainty in cash flows raises desired money balances. This shifts money demand to the right conditional on other determinants.
Speculative demand reflects portfolio choices between money and interest-bearing assets. When bond yields are expected to rise, holders prefer money to avoid price risk in bonds. This raises money demand at each current \(i\).
The standard functional statement is \( \frac{M^d}{P} = L(i, Y) \) with \( \partial L/\partial i < 0 \) and \( \partial L/\partial Y > 0 \). In nominal terms, a higher price level \(P\) scales nominal money demand proportionally if real demand is unchanged. Graphically, nominal money demand shifts right when \(P\) rises at given \(i\) and \(Y\).

Determinants (Shifters) of Money Demand

Price level \(P\) shifts nominal money demand by changing the dollar value needed for the same real balances. A rise in \(P\) increases nominal \(M^d\) proportionally at each \(i\). A fall in \(P\) decreases nominal \(M^d\) proportionally at each \(i\).
Real output \(Y\) shifts real money demand through transactions volume. Higher \(Y\) increases desired real balances \(M^d/P\) and shifts nominal \(M^d\) right. Lower \(Y\) reduces desired real balances and shifts nominal \(M^d\) left.
Payment technology and financial innovation affect the need to hold money. Improved transaction methods reduce desired balances for a given \(Y\) and \(i\). This shifts money demand left in either real or nominal form.
Expectations about interest rates influence speculative demand. Anticipated higher future rates increase current preference for money to avoid bond price declines. This shifts money demand right at each current \(i\).
Institutional or regulatory changes that alter access to transactions balances can shift demand. For example, changes that broaden checkable access raise measured money demand. Changes that restrict access lower measured money demand at given fundamentals.

Money Supply (MS): Policy, Tools, and Shape

In the model, money supply is taken as a policy-determined quantity independent of \(i\) at a moment. It is drawn as a vertical line at the chosen nominal money stock. The central bank selects this level using its instruments.
Open market operations change reserves and deposits through asset purchases and sales. An open market purchase increases reserves and shifts money supply right. An open market sale decreases reserves and shifts money supply left.
The required reserve ratio \(rr\) affects deposit creation for a given monetary base. A lower \(rr\) raises the money supply by supporting a higher deposit expansion. A higher \(rr\) lowers the money supply by restricting deposit expansion.
The discount rate sets terms for borrowing reserves from the central bank. Easier discount policy raises reserves and shifts money supply right. Tighter discount policy lowers reserves and shifts money supply left.
Interest on reserves alters banks’ willingness to hold reserves relative to lending. A higher rate on reserves reduces deposit creation and lowers the effective money supply. A lower rate on reserves raises deposit creation and increases the effective money supply.

Equilibrium Nominal Interest Rate and Comparative Statics

Equilibrium occurs where money supply equals money demand at \(i^{*}\). At that point, the planned quantity of money held equals the quantity provided. The diagram identifies \(i^{*}\) on the vertical axis and the corresponding \(M\) on the horizontal axis.
An increase in money supply shifts the vertical MS line right. The new intersection occurs at a lower \(i\) with a higher quantity of money. A decrease in money supply shifts MS left and raises \(i\).
An increase in money demand shifts MD right. The new intersection occurs at a higher \(i\) with the same MS. A decrease in money demand shifts MD left and lowers \(i\).
Simultaneous shifts require identifying the net effect on the intersection. If MS and MD both increase, the interest rate outcome depends on relative magnitudes. If MS increases while MD decreases, the interest rate falls unambiguously.
These comparative statics hold with the assumption of a fixed price level for the diagram. When the price level changes, nominal money demand shifts proportionally if real demand is unchanged. The supply curve remains vertical at the policy-set nominal quantity.

Money Market vs. Loanable Funds: Distinctions

The money market uses nominal interest \(i\) with axes \(i\) and \(M\). The loanable funds market uses real interest \(r\) with axes \(r\) and the quantity of funds. The two diagrams answer different questions within the curriculum.
Money demand reflects a portfolio choice between money and nonmoney assets. Loanable funds demand reflects planned investment borrowing at various real rates. The determinants and slopes differ across the two models.
Money supply is policy-set and vertical at a point in time. Loanable funds supply is upward sloping, reflecting saving behavior and capital flows. Government budget position affects loanable funds supply through public saving.
The Fisher relationship connects nominal and real rates as \( r \approx i - \pi^{e} \). A change in expected inflation alters the mapping between the two markets. This mapping allows consistent interest-rate statements across diagrams.
Problems specify which market to use by the variables and curves mentioned. References to money, \(M\), and the nominal interest rate indicate the money market. References to saving, investment, and the real interest rate indicate loanable funds.

Central Bank & Monetary Policy

Central Bank Roles and Objectives

The central bank conducts monetary policy to influence the money supply and the nominal interest rate. Standard objectives include price stability and output near potential \(Y^{*}\). Institutional tasks also include lender-of-last-resort, payment-system oversight, and prudential supervision at curriculum scope.
Policy independence supports credibility by separating short-run political pressures from instrument choices. The curriculum treats independence as facilitating consistent achievement of stated goals. Accountability is represented by public goals and transparent communication.
Price stability means a low and predictable inflation rate measured by a broad index. Output stabilization means reducing deviations of \(Y\) from \(Y^{*}\) without altering \(Y^{*}\) itself. These goals are complementary in the long run within the model used.
The central bank’s balance sheet records assets such as securities and liabilities such as currency and reserves. Changes in these items alter the monetary base \(MB = C + R\). This linkage connects operating actions to the banking system’s reserve position.
Policy analysis distinguishes goals, targets, instruments, and indicators. Goals are ends like low inflation, targets are variables the bank aims to control, instruments are tools it can directly adjust, and indicators are observed measures used to infer conditions. This taxonomy organizes the framework for the unit.

Policy Instruments and Operating Targets

Open market operations adjust reserves by buying or selling securities. An open market purchase increases \(R\) and shifts money supply right in the money market diagram. An open market sale does the opposite by decreasing \(R\).
The required reserve ratio \(rr\) sets the minimum fraction of reservable deposits held as reserves. Lower \(rr\) raises deposit creation capacity and higher \(rr\) lowers it. The parameter enters the money multiplier conditions in the banking section.
The discount rate governs the terms at which banks can borrow reserves from the central bank. Easier discount policy increases available reserves and tighter policy decreases them. This instrument supports the operating framework but is not the primary tool in the curriculum.
Interest on reserves influences banks’ willingness to hold reserves versus extend loans. A higher rate on reserves increases the attractiveness of reserves and restrains deposit expansion. A lower rate on reserves reduces the attractiveness and supports expansion.
The operating target is presented as the short-run nominal policy rate in this unit. Adjustments to reserves are chosen to achieve the target rate in the money market. The federal funds rate is the canonical reference for the target at AP depth.

Open Market Operations and the Monetary Base

The monetary base \(MB\) equals currency in circulation plus bank reserves at the central bank. An open market purchase raises \(MB\) by increasing \(R\) and may increase \(C\) through currency issuance. An open market sale lowers \(MB\) by decreasing \(R\) and may reduce \(C\) when currency is returned.
With a given currency–deposit ratio and reserve ratio, changes in \(MB\) map to changes in the money supply. The mapping is summarized by the money multiplier derived in the banking section. Deviations such as excess reserves and currency drain reduce the realized change in money.
On the central bank’s balance sheet, a purchase increases securities on the asset side and reserves on the liability side. A sale decreases securities and reserves in the corresponding entries. These accounting relations implement the change in \(MB\).
When policy targets an interest rate, reserve supply is varied as needed to sustain that rate. The money stock adjusts endogenously to the demand for reserves at the target. When policy targets a money stock, the interest rate becomes the endogenous outcome.
Curriculum diagrams may show either a vertical money supply at a chosen level or a supply adjusted to hit a rate target. Both representations are consistent with the stated operating objective. The choice of diagram follows the variable emphasized in the question.

Money Market Implementation and Interest Rate Targeting

In the money market, money supply \(MS\) is drawn vertical at the policy-controlled nominal quantity. Money demand \(MD\) is downward sloping in the nominal interest rate \(i\). Their intersection determines the market rate \(i^{*}\).
To lower \(i\), policy shifts \(MS\) right via an increase in reserves. To raise \(i\), policy shifts \(MS\) left via a decrease in reserves. These movements are comparative-static statements for the diagram.
Under interest-rate targeting, the central bank offsets exogenous money-demand shifts to maintain \(i^{*}\). A rightward shift of \(MD\) is met with a rightward adjustment of \(MS\) to keep the intersection at the target. A leftward shift is met with a leftward adjustment accordingly.
The real money balances identity \( M/P \) links nominal \(M\) and the aggregate price level. For given \(P\), a change in nominal \(M\) changes real balances one-for-one. For changing \(P\), nominal \(M\) must adjust to maintain a real-balance objective.
The Fisher relation \( r \approx i - \pi^{e} \) connects nominal and real rates for comparative statements. At a given expected inflation \(\pi^{e}\), a lower \(i\) implies a lower real rate \(r\). This mapping is used to link the money market to spending components in the AD identity.

Transmission to AD–AS (Short Run and Long Run)

Expansionary monetary policy increases \(MS\), lowers \(i\), and increases interest-sensitive components of planned expenditure at a given price level. Aggregate demand shifts right in the AD–AS model. Short-run equilibrium shows higher \(Y\) and higher \(P\) with upward-sloping SRAS.
Contractionary monetary policy decreases \(MS\), raises \(i\), and reduces interest-sensitive components of planned expenditure at a given price level. Aggregate demand shifts left in the AD–AS model. Short-run equilibrium shows lower \(Y\) and lower \(P\) with upward-sloping SRAS.
In the long run, nominal wages and input prices adjust to the aggregate price level. Pure demand-driven monetary changes leave real output at \(Y^{*}\) with a different \(P\). This statement is the long-run neutrality of money in the model.
With a recessionary gap, expansionary policy moves \(Y\) toward \(Y^{*}\) by shifting AD right. With an inflationary gap, contractionary policy moves \(Y\) toward \(Y^{*}\) by shifting AD left. The LRAS position anchors potential output for classification.
Policy transmission thus consists of the sequence reserve change \(\rightarrow\) money and interest \(\rightarrow\) components of spending \(\rightarrow\) AD \(\rightarrow\) \(Y,P\). Each arrow denotes a model linkage stated elsewhere in the unit. The sequence is comparative-static and not a time path.

Policy Lags, Constraints, and Considerations

Recognition lag is the time to identify deviations of \(Y\) from \(Y^{*}\). Implementation lag is the time to execute operating changes. Transmission lag is the time for interest-rate changes to affect planned spending.
Interest sensitivity of spending affects the magnitude of AD shifts from a given change in \(i\). Lower sensitivity implies smaller shifts for the same interest-rate movement. Higher sensitivity implies larger shifts under the same conditions.
At very low nominal interest rates, additional increases in \(MS\) may have limited effect on \(i\). This limits the movement along money demand in the standard diagram. The concept is presented as a constraint within the model without requiring extensions.
When proportional taxes and imports are present, the induced change in \(Y\) from a given AD shift is smaller. This follows from the leakage-adjusted multipliers presented earlier. Monetary policy effects pass through those same multipliers in AD–AS.
Stability of expected inflation \(\pi^{e}\) affects the mapping between nominal and real rates. If \(\pi^{e}\) changes, the same nominal \(i\) implies a different real \(r\). This consideration alters the strength of the transmission to planned expenditure.

Loanable Funds Market

Model Definition and Axes

The loanable funds market relates the real interest rate \(r\) to the quantity of funds saved and invested. The vertical axis shows \(r\) and the horizontal axis shows the quantity of loanable funds. Equilibrium occurs where the supply of saving equals the demand for investment funds.
The price of funds in this model is the real interest rate rather than the nominal rate. All quantities are real, so units are in inflation-adjusted purchasing power. This distinction separates the loanable funds diagram from the money market diagram.
Supply represents planned saving available to lend at each \(r\). Demand represents planned real investment and other borrowing at each \(r\). The model is static and holds noninterest determinants fixed along a given curve.
A higher \(r\) raises the opportunity cost of current consumption and increases the quantity of saving. A higher \(r\) also raises the cost of borrowing and decreases the quantity of investment demanded. These opposing movements generate upward-sloping supply and downward-sloping demand.
Comparative statics analyze shifts of either curve due to nonprice determinants. Movements along a curve result only from changes in \(r\). Curve labeling must specify “Real interest rate” and “Quantity of loanable funds” for clarity.

Supply of Loanable Funds (Saving)

Supply is composed of private saving, public saving, and net foreign saving consistent with the model’s scope. Private saving depends on disposable income, preferences for saving, and intertemporal considerations. Public saving equals \(T - G - TR\) and can be positive or negative.
The supply curve slopes upward because a higher \(r\) increases the quantity of funds households are willing to supply. This is represented as a movement along the existing supply curve. The slope reflects the responsiveness of saving to \(r\).
Rightward shifts of supply occur when factors raise saving at each \(r\). Examples include higher disposable income allocated to saving or policies that increase public saving. Leftward shifts occur when saving falls at each \(r\).
Foreign capital inflow is recorded as additional funds available to lend domestically. Such inflow shifts the supply curve to the right at each \(r\). Foreign capital outflow shifts the supply curve to the left at each \(r\).
In this framework, changes in expected inflation do not shift the real supply curve by themselves. The curve is defined in real terms and is indexed by real returns. Any re-indexing to nominal terms is handled by the Fisher relationship separately.

Demand for Loanable Funds (Investment)

Demand for loanable funds reflects planned real investment and other real borrowing at each \(r\). Firms compare the real cost of funds to expected real returns on capital projects. Government borrowing can also be represented on the demand side in this model.
The demand curve slopes downward because a higher \(r\) reduces the quantity of investment that yields an acceptable real return. This is represented as a movement along the existing demand curve. The slope reflects the responsiveness of investment to \(r\).
Rightward shifts of demand occur when expected profitability of investment rises at each \(r\). Technological improvements or lower effective taxes on capital can produce such shifts in the diagram. Leftward shifts occur when expected profitability falls at each \(r\).
Autonomous increases in government borrowing shift the demand curve to the right at each \(r\). Autonomous decreases in government borrowing shift the demand curve to the left at each \(r\). These statements classify fiscal positions within the loanable funds framework.
Input cost changes that alter expected net returns on capital can shift the demand curve. Higher noninterest costs reduce the set of projects with net positive returns and shift demand left. Lower noninterest costs expand the set and shift demand right.

Equilibrium, Shifts, and Outcomes

Equilibrium real interest \(r^{*}\) and quantity \(Q^{*}\) occur at the intersection of supply and demand. At \(r^{*}\), planned saving equals planned real investment. The diagram identifies this point with standard axis labels.
A rightward shift of demand raises \(r\) and increases the equilibrium quantity of funds. A leftward shift of demand lowers \(r\) and decreases the equilibrium quantity. These results hold with supply held fixed.
A rightward shift of supply lowers \(r\) and increases the equilibrium quantity of funds. A leftward shift of supply raises \(r\) and decreases the equilibrium quantity. These results hold with demand held fixed.
When both curves shift, the change in \(r\) is ambiguous without magnitudes. The change in quantity is also ambiguous without magnitudes. Directional outcomes require identifying which shift dominates.
Equilibrium \(r^{*}\) is the real rate used for consistency across diagrams. The money market uses the nominal rate \(i\) rather than \(r\). The Fisher relationship links the two measures as needed for analysis.

Government Budget Position and Crowding Effects

Public saving equals \(S_{public} = T - G - TR\) and identifies the government’s contribution to funds. A budget deficit corresponds to negative public saving and a budget surplus corresponds to positive public saving. These identities classify fiscal stance in the model.
Representing a deficit as higher borrowing shifts the demand for loanable funds to the right. The new equilibrium features a higher real interest rate and a larger quantity of funds. The label “crowding out” refers to reduced private investment at the higher \(r\).
Representing a surplus as higher public saving shifts the supply of loanable funds to the right. The new equilibrium features a lower real interest rate and a larger quantity of funds. The label “crowding in” refers to increased private investment at the lower \(r\).
Either representation is acceptable if applied consistently within the diagram. The AP treatment commonly places deficits on the demand side and surpluses on the supply side. The directional conclusions for \(r\) and the quantity are the same across representations.
Balanced-budget changes that leave public saving unchanged do not shift the loanable funds curves. Classifying fiscal items therefore requires identifying their effect on borrowing or saving. The diagram records only the net effect at each \(r\).

International Capital Flows

Net capital inflow provides additional funds to domestic borrowers at each \(r\). In the diagram, net inflow shifts the supply of loanable funds to the right. Net capital outflow shifts the supply of loanable funds to the left.
The savings–investment identity links these flows to external balances. One statement is \(S + \text{net inflow} = I\) at the aggregate level. The model records the inflow on the supply side for the comparative statics.
Differentials between domestic and foreign real returns influence the direction of flows. A higher relative domestic real return attracts capital until differentials are reduced by flows. A lower relative domestic real return releases capital until differentials are reduced.
Shifts from international flows change equilibrium \(r\) and the quantity of funds. Rightward supply shifts lower \(r\) and raise the quantity, while leftward supply shifts raise \(r\) and lower the quantity. These are standard outcomes in the diagram.
These statements are expressed in real terms consistent with the axes. Currency valuation mechanics are outside the scope of the single closed-form diagram. The classification focuses only on the supply of funds at each \(r\).

Fisher Relationship and Interest Rate Measures

The Fisher relationship states \( r \approx i - \pi^{e} \) for ex ante comparisons. Here \(r\) is the real interest rate, \(i\) is the nominal interest rate, and \(\pi^{e}\) is expected inflation. This relationship maps nominal to real terms across models.
In the loanable funds market, decisions are indexed by \(r\). In the money market, choices are indexed by \(i\). Consistency requires specifying which rate is referenced in a question.
A change in expected inflation \(\pi^{e}\) alters the nominal rate \(i\) required to maintain a given \(r\). Holding \(r\) fixed, a higher \(\pi^{e}\) implies a higher \(i\) and a lower \(\pi^{e}\) implies a lower \(i\). This re-indexing does not shift real supply or demand by itself.
Shifts of real curves arise from nonprice determinants of saving and investment. Re-indexing via \(\pi^{e}\) operates on measured nominal variables rather than real quantities. The diagram remains anchored to \(r\) on the vertical axis.
When comparing diagrams, label rates explicitly to avoid mixing units. Use \(r\) in loanable funds, use \(i\) in money market, and use \(P\) and \(Y\) in AD–AS. This convention maintains internal consistency across the unit.

Diagram Consistency Across Models

The loanable funds market determines \(r\) given saving and investment determinants. The money market determines \(i\) given money supply and money demand determinants. The AD–AS model determines \(Y\) and \(P\) given aggregate demand and aggregate supply.
Rates are connected by the Fisher relationship \( r \approx i - \pi^{e} \). Statements that transfer between models must convert rates accordingly. This conversion preserves the meaning of “price of funds” across contexts.
Fiscal positions that shift saving or borrowing are represented in the loanable funds diagram. Monetary positions that shift the money stock are represented in the money market diagram. Each model isolates its own comparative statics by construction.
Investment is the component that links \(r\) to aggregate demand in expenditure form. A change in \(r\) alters planned \(I\) in the AD identity at a given price level. The AD–AS diagram then records the implied shift of AD under stated assumptions.
Labeling, axes, and units must match the chosen model for correct interpretation. Mislabeling nominal and real rates leads to inconsistent conclusions. The curriculum requires explicit identification of the diagram used in any analysis.

Money, Inflation, and Quantity Theory

Quantity Equation: Definitions and Identity

The quantity equation is \( M \cdot V = P \cdot Y \), where \(M\) is the money stock, \(V\) is velocity, \(P\) is the aggregate price level, and \(Y\) is real output. The right side \(P \cdot Y\) equals nominal GDP by definition. As written, the equation is an identity that holds for measured aggregates over a period.
Velocity is defined as \( V \equiv \frac{P \cdot Y}{M} \). It measures the average number of times a unit of money is used to purchase final goods and services within the period. Algebraic rearrangement yields \( \frac{M}{P} = \frac{Y}{V} \), which expresses real money balances.
In AP treatment, \(P\) in \(MV=PY\) is aligned with a broad price index such as the GDP deflator. \(Y\) is real GDP, so \(P \cdot Y\) is total nominal spending on final output. \(M\) is a specified aggregate, typically \(M1\) or \(M2\), as the problem states.
The Cambridge cash-balance form writes \( \frac{M}{P} = k \cdot Y \) with \( k \equiv \frac{1}{V} \). This formulation is equivalent to the quantity equation when \(k\) is treated as a parameter. It interprets real money demand as proportional to real income at a given \(k\).
Using the identity requires careful matching of measurement intervals. All variables must refer to the same period to preserve equality. Mixed-period substitutions break the accounting relation and are not permitted.

Velocity Behavior and Money Demand

Velocity is not a structural constant in the short run but may be treated as relatively stable in some comparative exercises. Stability means that \(V\) changes slowly relative to \(M\), \(P\), and \(Y\). The assumption is explicit when deriving inflation from money growth.
Money demand can be summarized as \( \frac{M^d}{P} = L(i, Y) \) with \( \partial L/\partial i < 0 \) and \( \partial L/\partial Y > 0 \). This means desired real balances fall with the nominal interest rate and rise with real income. The quantity-theory special case treats \( L \) as proportional to \(Y\) with a constant coefficient.
When payment technologies or financial practices change, velocity can shift. A higher convenience of nonmoney transactions tends to raise \(V\) by reducing desired real balances at each \(Y\). A lower convenience tends to reduce \(V\) by increasing desired real balances.
In the identity, a rise in \(V\) at given \(M\) raises \(P \cdot Y\) one-for-one. In the money-demand view, a rise in \(V\) corresponds to a fall in \(k\) or a leftward shift in real money demand. Both descriptions are consistent re-statements of the same relationship.
Problems will specify whether to treat \(V\) as fixed or variable. If \(V\) is held fixed, changes in \(M\) map directly to changes in \(P \cdot Y\). If \(V\) varies, the mapping must account for the induced shift in real money demand.

Money Growth, Inflation, and Long-Run Neutrality

Taking growth rates of \( M \cdot V = P \cdot Y \) yields \( \mu + \nu = \pi + g \). Here \( \mu \) is money growth, \( \nu \) is velocity growth, \( \pi \) is inflation, and \( g \) is real GDP growth. This decomposition is arithmetic and holds by construction.
If velocity growth is approximately zero, the relation simplifies to \( \pi \approx \mu - g \). Under this assumption, money growth above real output growth translates into inflation. Money growth equal to real output growth implies roughly stable prices.
Long-run neutrality states that sustained changes in \(M\) affect the price level but not real output \(Y\). In AD–AS, a permanent monetary expansion shifts AD, but wages and prices adjust so the economy returns to \(Y^{*}\). The long-run outcome is a different \(P\) with the same \(Y^{*}\).
Superneutrality strengthens neutrality by asserting that the money growth rate does not affect real variables in the long run. This concept is referenced at the level of comparative statements only. Microfoundations are outside the AP scope.
These long-run statements do not negate short-run effects under sticky prices. Short-run deviations appear because SRAS is upward sloping and input prices adjust with a lag. The curriculum separates these horizons for clarity.

Fisher Effect and Interest Rate Decomposition

The Fisher relationship is \( r \approx i - \pi^{e} \) for ex-ante comparisons. Here \(i\) is the nominal interest rate, \(r\) is the real interest rate, and \( \pi^{e} \) is expected inflation. The expression is an approximation that is adequate at AP precision.
With a given long-run real rate, a higher expected inflation implies a higher nominal interest rate one-for-one. This is called the Fisher effect and aligns nominal contracts with expected price changes. A lower expected inflation implies a lower nominal rate one-for-one.
Ex post, realized real return equals \( i - \pi \) using actual inflation \( \pi \). Differences between \( \pi \) and \( \pi^{e} \) produce gains or losses relative to expected real returns. The AP treatment focuses on the ex-ante relation for model mapping.
The Fisher relation connects the nominal rate used in the money market with the real rate used in loanable funds. A specified \( \pi^{e} \) allows translation between the two diagrams consistently. Without a stated \( \pi^{e} \), only qualitative statements are appropriate.
Higher expected inflation reduces desired real money balances at a given nominal rate through the opportunity-cost channel. This corresponds to a higher velocity in the quantity framework. Consistency requires referencing the same expectation across linked statements.

Real Money Balances, Seigniorage, and Inflation Tax

Real money balances are \( \frac{M}{P} \) and represent the purchasing power of the money stock. A rise in \(P\) holding \(M\) fixed reduces \( \frac{M}{P} \). A rise in \(M\) holding \(P\) fixed increases \( \frac{M}{P} \).
Seigniorage is revenue from money creation and equals \( \frac{\Delta M}{P} \) in real terms for the period. It is also described as \( \pi \cdot \frac{M}{P} \) when money growth finances spending with stable velocity. Both expressions are consistent under the quantity framework.
The inflation tax describes the reduction in real money balances borne by holders when \(P\) rises. The base is \( \frac{M}{P} \) and the “tax rate” is approximately \( \pi \) for small rates. This terminology is accounting language in the curriculum.
As money growth rises, seigniorage revenue initially increases because the base is still large. Beyond some point, higher inflation reduces desired real balances and shrinks the base. The resulting relation is commonly referenced as a Laffer-type shape for seigniorage.
These statements are model summaries and do not alter neutrality conclusions. In the long run, real quantities are determined by resources and technology, not by \(M\). The inflation implications arise from the accounting relation and assumptions on \(V\) and \(Y\).

Interest Rates & Asset Prices

Rate Measures and the Fisher Relationship

The nominal interest rate \(i\) is the stated percentage change in money paid or received over a period. It is used in the money market diagram on the vertical axis. Unless otherwise specified, it is taken as a per-period simple rate in this unit.
The real interest rate \(r\) adjusts the nominal rate for expected inflation. The AP convention uses the Fisher approximation \( r \approx i - \pi^{e} \). Here \( \pi^{e} \) denotes the expected inflation rate for the same period.
Ex post real return uses actual inflation rather than expected inflation. The relation is \( r_{\text{actual}} = i - \pi \). Differences between \( \pi \) and \( \pi^{e} \) create gains or losses relative to expectations.
The Fisher effect states that, for a given expected real rate, the nominal rate moves one-for-one with expected inflation. If \( \pi^{e} \) rises by one percentage point, \( i \) rises by approximately one percentage point. This is a long-run indexing statement rather than a short-run mechanism.
When comparing diagrams, identify which rate is used in each model. Use \(i\) in the money market and use \(r\) in the loanable funds market. Convert between them with \( r \approx i - \pi^{e} \) when required.

Present Value and Discounting

Present value \(PV\) converts future payments into today’s value using a discount rate. The single-payment formula is \( PV = \frac{FV}{(1+i)^{n}} \). The variable \(n\) is the number of periods until the payment is received.
For a stream of payments \( \{CF_t\} \), the valuation is \( PV = \sum_{t=1}^{n} \frac{CF_t}{(1+i)^{t}} \). Each term is discounted by one additional power of \(1+i\). The discount rate indexes time preference and opportunity cost in the model.
Present value moves inversely with the discount rate. If \(i\) increases, \(PV\) decreases holding cash flows and \(n\) fixed. If \(i\) decreases, \(PV\) increases under the same conditions.
Present value also decreases with a longer horizon for a given \(i\). A larger \(n\) places more weight on the discounting denominator. This property is used to compare assets with different maturities.
Asset price equals the present value of its expected cash flows in this unit. The discounting relation is the basis for price–yield results below. No additional microfoundations are required at AP depth.

Bonds: Price, Coupon, and Yield to Maturity

A bond is a debt claim that promises periodic coupons and principal repayment at maturity. The face value is \(F\) and the coupon payment is \(C\) each period. The coupon rate is \( c \equiv \frac{C}{F} \).
The price of a coupon bond is \( P = \sum_{t=1}^{n} \frac{C}{(1+i)^{t}} + \frac{F}{(1+i)^{n}} \). This expression discounts all promised payments at the market interest rate. It applies to level-coupon bonds at AP scope.
Yield to maturity (YTM) is the single discount rate that equates the present value of promised payments to the observed price. Formally, it is the \(i\) that solves the bond pricing equation for a given \(P\). It is an internal-rate-of-return concept for the bond held to maturity.
A zero-coupon bond has no periodic coupons and pays only \(F\) at maturity. Its price is \( P = \frac{F}{(1+i)^{n}} \). This special case makes the price–yield relation transparent.
Classification follows the comparison between coupon rate and yield. If \( c > \text{YTM} \), the bond sells at a premium \( (P>F) \); if \( c < \text{YTM} \), it sells at a discount \( (P

Price–Yield Relation and Interest Rate Risk

Bond prices and market yields move inversely by the discounting formula. When \(i\) rises, each discounted term falls and \(P\) falls. When \(i\) falls, each discounted term rises and \(P\) rises.
For a given coupon and yield change, longer maturity increases price sensitivity. A larger \(n\) means more distant payments that are more heavily affected by discounting. This is the maturity component of interest rate risk at AP depth.
For a given maturity and yield change, lower coupons increase price sensitivity. More of the value arrives at maturity when coupons are smaller. Zero-coupon bonds are the most sensitive among equal-maturity bonds.
The price–yield curve is convex rather than linear. For equal-size yield changes up and down, the absolute price increase from a yield fall exceeds the absolute price decrease from a yield rise. The curriculum requires only recognition of this curvature property.
Required yields differ across bonds due to risk and liquidity differences. Higher default risk or lower liquidity requires a higher yield to compensate holders. Higher required yield implies a lower present value for the same promised payments.

Equity Claims and Basic Valuation Ideas

A stock is an ownership claim on a firm’s residual income and assets. Dividends are discretionary payments to shareholders. There is no contractual maturity for common stock in this unit.
The present value principle applies to equity as the discounted value of expected future dividends and sale price. A higher discount rate lowers the present value holding expectations fixed. A lower discount rate raises the present value under the same expectations.
Equity returns include dividend yield and capital gain or loss. The total return is the sum of these components for the period. This decomposition is a bookkeeping identity at AP scope.
Relative risk and liquidity conditions affect required returns across assets. Higher perceived risk requires a higher expected return to hold the asset. Higher required return lowers price for a given cash-flow expectation by the discounting rule.
Equity differs from bonds by claim priority and payment structure. Bond payments are contractual and senior to equity claims, while dividends are residual. These distinctions explain differing required returns across asset classes.

Rate Changes, Asset Prices, and Model Links

In discounting models, a decrease in the relevant rate raises asset prices by increasing present values. An increase in the relevant rate lowers asset prices by decreasing present values. These statements follow directly from the \(PV\) formulas above.
In the money market, a policy-induced decrease in \(i\) is represented by a rightward shift of \(MS\). For a given expected inflation, this maps to a lower real rate \(r\) by \( r \approx i - \pi^{e} \). Lower \(r\) increases the present value of interest-sensitive assets in comparative statics.
In the loanable funds market, a rightward shift of saving lowers \(r\) and raises the equilibrium quantity. Lower \(r\) increases bond prices by the inverse relation. The same mapping applies to other present-value assets in the unit.
In the AD–AS framework, changes in \(r\) affect the \(I\) component of \(AD\) at a given price level. A lower \(r\) raises planned real investment and shifts \(AD\) right, while a higher \(r\) lowers planned investment and shifts \(AD\) left. These are model connections rather than new valuation rules.
Across diagrams, label axes and rate measures explicitly before making comparisons. Use \(i\) where nominal rates are required and use \(r\) where real rates are required. Convert with the Fisher relation when necessary to maintain consistency.