Week 5
Page 1: Title Slide
Output in the Short Run: The Money Market
Valerio Pieroni
Date: 1/19
Page 2: Objectives
Continuation of the IS-LM model development.
Key Questions:
What occurs in the money market in the short run?
How does monetary policy influence interest rates?
How to derive the LM curve, representing equilibrium in the money market?
Page 3: Long Run Money Market Review
Long run dynamics: Prices are flexible, adjusting for equilibrium in the money market.
Quantity Equation:
MY = PV
Implication of money supply increase:
M ↑ => P ↑ (given V is constant, Y is by economic fundamentals).
Connection between money supply changes and nominal interest rate via Fisher Equation:
↑P, ↑π => ↑i
i = r + π
Page 4: Short Run Money Market Equilibrium
In the short run, given fixed prices, a variable must adjust to restore equilibrium.
The variable: real interest rate.
Equilibrium condition in the short run:
[ \frac{M}{P} \equiv D_m = L(Y, i) \quad \text{where} \quad \frac{\partial L}{\partial Y} > 0, \frac{\partial L}{\partial r} < 0 ]
Page 5: Interest Rate Adjustments
Focus on how interest rates adjust to maintain equilibrium in the money market.
Introduction of the Theory of Liquidity Preference.
Page 6: Theory of Liquidity Preference - Assumptions
Assumption 1: Two assets in economy:
Money: Non-interest bearing, used for transactions.
Bonds: Interest-bearing, not for transactions (e.g., Treasury bills).
Rate of return on bonds:
r = (PF - PI) / PI
Relationship: Higher initial price (PI) => lower rate of return.
Page 7: Theory of Liquidity Preference - Continued Assumptions
Assumption 2: Money supply is exogenous and controlled by the Central Bank.
Assumption 3: Real money demand expressed as:
[ \frac{M}{P} \equiv D_m = L(Y, r) ]
Implication: The portfolio adjustments by individuals affect interest rates, restoring equilibrium.
Page 8: Equilibrium in Liquidity Preference
Money market equilibrium equates the supply and demand:
[ \frac{M}{P} = L(Y, r) ]
Page 9: Equilibrium in Liquidity Preference - Further Details
Continuation of discussing equilibrium conditions (content not detailed).
Page 10: Increase in Money Supply
Central bank increases money supply:
[ \frac{M}{P}^S \uparrow ] => Excess Supply
Results in M/P > L(Y, r): Individuals prefer to hold cash.
They buy bonds, leading to increased demand and thus a rise in bond prices.
Higher bond prices = lower rates (r) => demand for liquidity increases.
Until equilibrium is restored: [ \frac{M}{P} = L(Y, r) ]
Page 11: Increase in Money Supply - Further Explanation
Additional discussion on subsequent effects due to increased money supply (content not detailed).
Page 12: Central Bank and Interest Rates
Central Bank alters the real interest rate by modifying the money supply via monetary policy.
Actions:
Increase real interest rate => Decrease money supply.
Decrease real interest rate => Increase money supply.
Central banks primarily set nominal interest rates, which adjust real rates due to price rigidities.
Page 13: Decrease in Money Supply
Concepts related to the impacts and adjustments of a decrease in money supply (content not detailed).
Page 14: Short Run vs Long Run
Differences in theories predicting relationships between M and i:
Short Run:
Decrease in M => Excess demand for cash => Selling of T-Bills => Decrease in PI => Increase in r (and i).
Long Run:
Decrease in M => Decrease in P (Quantity theory) => Decrease in i (via Fisher equation).
Page 15: The LM Curve
Definition: Each point on LM curve combines Y and r for money market equilibrium.
Preparation for graphical derivation of the LM curve.
Page 16: Derivation of the LM Curve
Steps for deriving the LM curve graphically (details not specified).
Page 17: Graphical LM Curve Derivation (Continued)
Implicit depiction of money market equilibrium through demand function dependent on Y and r.
Example demand function:
L(Y, r) = kY - hr
Rearranged form:
[ Y = \frac{1}{k} \left( \frac{M}{P} + \frac{h}{k} r \right) ]
Resulting equation for LM curve:
[ r = \frac{k}{h} Y - \frac{1}{h} \frac{M}{P} ]
Page 18: Position of the LM Curve
Each point in the LM curve indicates a money market and financial market equilibrium.
LM curve shifts in response to monetary policy changes:
Increase in money supply (mS) shifts curve right.
Decrease in money supply shifts curve left.
Change in output: ( \Delta Y = \frac{1}{k} \Delta m = \beta \Delta m )
Page 19: Slope of the LM Curve
The LM curve shows an upward slope in (Y, r) space:
Implications:
Increase in Y leads to increased money demand (mD), decreased bond demand (BD), and increased r.
Mathematical relationship for the slope:
LM curve: [ r = \frac{k}{h} Y - \frac{1}{hm} ]
Derivative: [ \frac{dr}{dY} = \frac{k}{h} > 0 ]
Coefficients k and h indicate money demand sensitivity and impact on the LM slope.