The Modern Approach to Aggregate Demand The Demand for Money and the LM Curve

Learning Objectives Understand how people choose how much money to demand. Learn how money demand changes when interest rates and income change. Understand how money supply and money demand interact to determine the equilibrium rate of interest. Learn how changes in money supply and money demand change the equilibrium rate of interest.

Learning Objectives Learn how to use the money demand function and the money supply function to graphically and algebraically derive the LM curve. Learn how changes in money demand and money supply shift the LM curve.

The Money Market Interest rates are determined through the interaction of money demand and money supply.

Money Demand The Theory of Liquidity Preference –Assumptions: Assets can be divided into two types: –Assets that pay interest, bonds. –Assets that do not pay interest, money.

The Theory of Liquidity Preference According to the theory of liquidity preference, people are willing to hold money because it is readily accepted in exchange for goods and services. –The relationship between liquidity and the interest rate is inverse. As an asset’s liquidity increases, its rate of return falls.

Household Budget Constraint Households hold their wealth as money or bonds.  W = M + P B B Households accumulate real wealth by saving.  /\W/P = S = Y – C Household income is divided into two parts: the income from owning bonds and labor income.  Y = i(P B B/P) + (w/P)L

Household Budget Constraint If a household were to transfer its entire portfolio to bonds, it would maximize income. Therefore, maximum income equals the household’s accumulation of bonds plus its labor income.  Y MAX = i(P B B/P) + (w/P)L

Household Budget Constraint A household that transfers its entire portfolio to bonds sacrifices the convenience of using money in transactions. When the household chooses to hold some of its wealth as money, it loses the income it could have received on those balances. Therefore, its budget constraint is:  Y = Y MAX – i(M/P)

Household Budget Constraint According to the budget constraint, households choose how much income to earn and how much money to hold. As individuals transfer their wealth from money to bonds, they increase their income, but simultaneously decrease their liquidity.

Demand for Money: Utility People choose to hold money because it yields utility. Utility is gained by the interaction of the income received by households and the real balances held to facilitate transactions. We measure that utility or value in units of commodities called real money balances where real money balances equal M D /P.

Money Demand and Interest Rates Money balances confer utility on individuals. But, according to the law of diminishing utility, the utility gained from holding an extra unit of money decreases as the household holds an increasingly larger portion of its wealth in cash. The household chooses how much money to hold by equating the marginal utility of holding money to its marginal cost, the interest rate.

Money Demand and Interest Rates The interest rate, i, is the cost of holding money. –As i rises, the opportunity cost of holding money rises and people hold less. –As i falls, the opportunity cost of holding money falls and people hold more.

Money Demand and Interest Rates i M D /P 0 As the interest rate falls from i 1 to i 2, the household reallocates its portfolio from bonds to money. Money demand increases from (M/P) 1 to (M/P) 2 i1i1 i2i2 (M/P) 1 (M/P) 2 MD

Money Demand and Income A household attains a higher level of utility if it receives a higher income. Liquidity increases the utility of any given income, but as income increases, the household must hold more cash to generate the same level of utility. Therefore, the demand for money increases as income increase.

Money Demand and Income People hold money to make transactions. –Higher levels of income are associated with more transactions. Money demand increases. –Lower levels of income are associated with fewer transactions. Money demand decreases.

Money Demand: Shifts i Money Increases in income mean the household needs more money for transactions. Money demand shifts to the right from MD(Y 2 ) to MD(Y 3 ). Decreases in income mean the household needs less money for transactions. Money demand shifts to the left from MD(Y 2 ) to MD(Y 1 ). 0 MD(Y 2 ) MD(Y 3 ) MD(Y 1 )

Derivation of the Money Demand Function U = (Y – i(M/P)) (M/P) h  U/  (M/P) = (M/P) h (– i) + (Y – i(M/P)) h(M/P) h-1 (Y – i(M/P))(M/P) h (Y – i(M/P))(M/P) h  U/  (M/P) = – i/Y + h/(M/P) = 0 i/Y – h/(M/P) = 0 i/Y = h/(M/P) i(M/P) = hY (M D /P) = (h/i)Y

Other Money Demand Shifters Price Level –An increase in the price level increases money demand because the number of dollars needed for transactions rises. Inflationary Expectations –Higher expected inflation means a decrease in the purchasing power of money; thereby, decreasing demand.

Other Money Demand Shifters Risk –Higher risk of alternative assets increases money demand. Liquidity of Alternative Assets –Higher liquidity increases the attractiveness of alternative assets and decreases money demand. Payments Technology –As the efficiency of payments technology increases, money demand decreases.

Money Supply The supply of real money balances is defined as the ratio of nominal money balances and the price level, M S /P. –where M is the nominal money supply and P is the price level.

Money Supply –The real money supply is assumed to be fixed in supply and invariant with respect to the interest rate. The money supply is assumed to be an exogenous variable determined by the central bank. The price level is also assumed to be exogenous as well as fixed in the short run.

The Money Market i MoneyMS MD The equilibrium rate of interest is determined by the intersection of money demand and money supply. Money supply is vertical because MS does not vary with the interest rate. Money demand slopes down because the opportunity cost of holding money rises and falls with interest rates. i* 0

Money Supply: Shifts i MoneyMS 1 MS 2 MS 3 MD A decrease in the money supply shifts MS to the left from MS 2 to MS 2, increasing the equilibrium interest rate. An increase in the money supply shifts MS to the right from MS 2 to MS 3, decreasing the equilibrium interest rate. i1i1 i2i2 ieie 0

Monetary Policy Transmission Mechanism –The increase in the money supply increases liquidity in the portfolios of individuals. Money supply is now greater than money demand at the current rate of interest. –People rebalance their portfolios by using the excess liquidity to buy other assets such as bonds. –As the price of bonds rises, interest rates fall.

Equilibrium in the Keynesian Model Unlike the classical model, in the Keynesian model, changes in the money supply result in changes in the interest rate. In the classical model, the price level adjusts immediately to restore the equality between money demand and money supply. In the Keynesian model, prices are slow to adjust because of rigidities in the system. Income is also slow to adjust, so interest rates must adjust to restore equilibrium.

Evidence for the Modern Theory The introduction of interest rates as a determinant of money demand means that changes in interest rates will change the velocity of money. Data collected over the period 1890 to 2000 (see text) demonstrate that velocity is not a constant, and that it has closely paralleled the interest rate as predicted by the theory.

The LM Schedule The LM schedule plots every income and nominal interest rate (Y, i) combination that results in equilibrium in the money market. –The LM schedule is an equilibrium schedule. At every point on an LM schedule, money demand just equals money supply.

The LM Schedule: Derivation i MoneyM S /P MD(Y 1 ) i1i1 i2i2 MD(Y 2 ) E1E1 E2E2 E2E2 E1E1 LM Y 1 Y 2 Y i 00

The LM Schedule: Derivation At point E 1, money demand equals money supply –The equilibrium interest rate and level of income are i 1 and Y 1. –This combination is one point on the LM schedule. Let Y rise to Y 2.

The LM Schedule: Derivation At the point E 2, money demand equals money supply –The equilibrium interest rate and level of income now are i 2 and Y 2. –This combination is another point on the LM schedule.

LM Derivation: Algebra Quantity of money demanded equals the quantity supplied.  M D = M S where M S = M, an exogenously determined quantity of money. Money demand equals:  M D /P = h/iY Solve for i:  M D /P = h/iY = P(h/i)Y = M = h/i = M/PY =  i/h = PY/M = i = (hP/M)Y

The LM Schedule: A Decrease in the Nominal Money Supply i MoneyM 1 /P MD i1i1 i2i2 E1E1 E2E2 E2E2 E1E1 LM 1 Y 1 Y i M 2 /P LM 2 00

A Decrease in the Money Supply At the point E 1, money demand equals money supply. –The equilibrium interest rate and level of income are i 1 and Y 1 respectively. Let the nominal money supply decrease, causing the interest rate to rise to i 2. Income is still Y 1. Equilibrium now occurs at the point E 2. The point E 2 lies on LM 2 because it represents equilibrium in the money market when Y = Y 1 and i = i 2.

The LM Schedule: An Increase in the Money Demand i MoneyM S /P MD(Y 1 ) i1i1 i2i2 E1E1 E2E2 E2E2 E1E1 LM 1 Y 1 Y i LM 2 MD(Y 2 ) 00

An Increase in Money Demand At the point E 1, there is equilibrium in the money market. –The equilibrium interest rate and level of income are i 1 and Y 1 respectively. Let money demand increase. Y is still Y 1. Equilibrium now occurs at E 2, where r is i 2 and Y is Y 1. The point E 2 lies on LM 2 because it represents equilibrium in the money market when Y is Y 1 and i is i 2.

Other LM Shifters A change in the price level –If the price level rises (falls), the real money supply falls (rises). Any factor that changes money demand –Changes in wealth, the risk of alternative assets, the liquidity of other assets, inflationary expectations, etc.