1. Money, Interest, and Income
Chapter #11

2. Introduction
Money central in determining Y & employment, but absent from last chapter’s model
Interest rates determine aggregate spending  Fed controls money supply in US
Introducing money & monetary policy, to study interaction of goods & assets market
Interest rate on T-bills = payment received by someone who lends to U.S. government
Interest rates: - High just before a recession
- Drop during the recession
- Rise during the recovery
Strong link between money & output growth
IS-LM model is core of short-run macroecon
Maintains spirit & many details from Chapter 10, focused on goods market & fiscal policy
Adds interest rate as additional determinant of AD to previous model & adds monetary policy
Includes goods market & money market, & their link through interest rates & income
Money market & interest rates important for:
Monetary policy works through money market
Expansionary fiscal policy increases interest rate (could offset its expansionary effects)
Interest rate affect composition of I vs C (Higher interest rate lovers I & hence AD)

3. Structure of the IS-LM Model

4. The Goods Market & the IS Curve
IS curve: combinations of i & Y for goods market equilib (planned spending = income)
Derived in two steps: 1. Link between interest rates and investment
2. Link between investment demand and AD
Investment no longer exogenous, but determined by interest % (endogenous)
Investment demand is lower the higher are interest rates
Interest rates are the cost of borrowing money
Increased interest rates raise the price to firms of borrowing for capital equipment  reduce the quantity of investment demand
Investment spending function is specified as:
where b > 0
i = rate of interest
b = responsiveness investment to interest rate
= autonomous investment spending
Negative slope reflects assumption that a reduction in i increases the quantity of I
The position of I schedule is determined by:
The slope, b
If investment is highly responsive to i, the investment schedule is almost flat
If investment responds little to i, the investment schedule is close to vertical
Level of autonomous spending
Increase in shifts the investment schedule out

5. The Interest Rate and AD: The IS Curve
Include new planned investment into AD = C + I + G + NX function of last chapter
↑ in i ↓ AD for a given level of Y
At any level of i, can determine equilibrium level of income & output as in Chapter 10
A change in i will change the equilibrium
Since for any given interest % i1, bi is constant  draw AD function with intercept
Equilibrium income is Y1 at point E1
Plot (i1, Y1) as point E1 on the IS curve
↓ interest i2 shifts AD ↑, w/ new intercept
Equilibrium shifts to point E2, w/ income Y2
Plot (i2, Y2) as another point E2 on IS curve
Applied to all i generates IS curve: Combinations of i & Y at which goods market in equilibrium
Downward sloping IS: i & Y negatively related

6. Slope of IS Curve & Multiplier
IS can also be derived using goods market equilibrium condition:
Steepness of IS curve depends on:
Investment’s sensitive to i (slope b)
If not very sensitive, ∆i causes small ∆AD
Small ∆AD causes small ∆Y  steep IS
Chapter 10 multiplier G = (1 – c(1-t))-1 MPC on solid black AD < dashed AD curve  multiplier larger on dashed AD curves
↓ in i to i2 ↑ AD intercept by = vertical distance
Y ↑ to Y’2 on dashed & Y2 on solid AD
The smaller the investment sensitivity to i & the smaller the multiplier, the steeper the IS
∆Y due to ∆ autonomous spending is

7. The Position of the IS Curve
Two IS curves differ by levels of autonomous spending
Initial AD with and i1  corresponding point E1 on IS curve
If autonomous spending increases to , equilibrium Y increases at i1  point E2, shifting out IS
The change in income as a result from a change in autonomous spending is

8. The Money Market and the LM Curve
LM curve: combinations i & output where MD = MS  money market equilibrium
The LM curve is derived in two steps:
Explain why MD = f(i & income) – theory of real money balance, rather than nominal
Set MD = MS & find combinations of income & i that maintain money market equilibrium
MD is a demand for real money balances (people concerned purchasing power not the # of $ in their pockets) which depends on
Real income: hold $ to pay for purchases, which depend on income
Interest rate: the cost of holding money
The demand for money (or liquidity) is defined as: Demand for real balances sensitivity to Y & i are k & h Demand for real balances implies that for given Y, quantity demanded decreases w/ i (more expensive to keep money, since loss from not investing higher)

9. MS, Money Market Equilibrium & LM Curve
Fed controls nominal MS, M. Real MS is , w/ M &P assumed fixed Combinations of i & Y such that demand for real money balances exactly = available MS Starting at Y1, corresponding demand curve for real balances is L1 (panel (a)) Point E1 in panel (a) is the equilibrium point in the money market Point E1 in panel (b) as a point on money market equilibrium schedule or LM curve If income ↑ to Y2, real money balances is higher at every i  money demand shifts to L2 Interest ↑ to i2 to maintain money market equilibrium at E2 Record E2 in panel (b) as another point on positively slopped LM curve: ↑ in i ↓ demand for real balance. To maintain real money balances = fixed MS, income has to ↑ LM curve can be obtained directly from money market equilibrium: Fixed supply of real balances = = demand for real balances =>

10. Slope & Position of LM Curve
The steeper the LM curve:
The greater the responsiveness of MD to income, as measured by k
The lower the responsiveness of MD to the interest rate, as measured by h
Confirmed this by examining figure below or money market equilibrium
Change in income has a larger effect on i, the larger is k and the smaller is h
Since real MS is constant along LM curve  ∆ in real MS shift LM curve
Initial equilibrium at point E1 w/ interest i1. ↑ in real MS money supply shifts MS curve right
To restore equilibrium at the income level Y1, the i must decrease too
In panel (b), the LM curve shifts right

11. Equilibrium in Goods & Money Market & Changes in Equilibrium Income & Interest
IS & LM summarize conditions that have to be satisfied for goods & money markets equilibrium
Assumptions:
Price level is constant
Firms willing to supply any amount of output demanded at that price (flat AS)
Equilibrium income & interest rate change when either the IS or the LM curve shifts
Effects of an increase in autonomous spending
Shifts IS curve out by G∆I if autonomous investment is the source of increased spending
Resulting change in Y is smaller than change in autonomous spending due to slope of LM curve
Flat SRAS curve

12. Deriving the AD Schedule
AD maps IS-LM equilibrium, holding nominal MS & autonomous spending constant & allowing prices to ∆
Suppose prices increase from P1 to P2
M/P decrease ↓ to M/P2  LM ↓ to LM2
Interest ↑ to i2 output ↓ to Y2, sliding to lower AD
Derive AD equation by substituting LM into IS:
AD summarizes IS-LM relation, relating Y & P for given autonomous spending & nominal MS
Since P is in the denominator, AD is downward sloping
AD depends upon: Autonomous spending & Real money stock
Equilibrium income is:
Higher the higher the level of autonomous spending
Higher the higher the stock of real balances