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ChatGPT
Apr 24
The LM curve represents the combinations of interest rates and real output levels at which the money market is in equilibrium. It is derived by plotting the different combinations of interest rates and real output levels that satisfy the equation for money market equilibrium:
M/P = L(r,Y)
Where:
M = money supply
P = price level
L = demand for money
r = interest rate
Y = real output level
To derive the LM curve graphically, we can plot the different combinations of interest rates and real output levels that satisfy the equation for money market equilibrium on a graph with the interest rate on the vertical axis and real output on the horizontal axis. The LM curve will be upward sloping, indicating that as real output increases, the interest rate also increases in order to maintain money market equilibrium.
The LM curve is typically drawn as a positively sloped line on a graph, with the slope determined by the sensitivity of the demand for money to changes in income. The position of the LM curve can shift due to changes in the money supply, shifts in the demand for money, or changes in the price level.
M/P = L(r,Y)
Where:
M = money supply
P = price level
L = demand for money
r = interest rate
Y = real output level
To derive the LM curve graphically, we can plot the different combinations of interest rates and real output levels that satisfy the equation for money market equilibrium on a graph with the interest rate on the vertical axis and real output on the horizontal axis. The LM curve will be upward sloping, indicating that as real output increases, the interest rate also increases in order to maintain money market equilibrium.
The LM curve is typically drawn as a positively sloped line on a graph, with the slope determined by the sensitivity of the demand for money to changes in income. The position of the LM curve can shift due to changes in the money supply, shifts in the demand for money, or changes in the price level.
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Google Gemini AI
Apr 24
LM Curve Derivation
Step 1: IS Curve
- Start with the IS curve, which represents the relationship between interest rates (r) and real GDP (Y):
- Y = C(Y-T) + I(r) + G
Step 2: Money Market Equilibrium
- The LM curve represents the money market equilibrium, where the demand for money (Md) equals the supply of money (Ms):
- Md = kPY
- Ms = M
Step 3: Liquidity Preference
- The demand for money (Md) includes a liquidity preference function, which relates the real money demand to the interest rate:
- Md = L(r, Y)
Step 4: Substituting
- Substitute the liquidity preference function into the money market equilibrium equation:
- L(r, Y) = kPY
Step 5: IS-LM System
- Combine the IS curve and the LM curve equations:
- Y = C(Y-T) + I(r) + G
- L(r, Y) = kPY
Graphical Derivation
- Plot the IS curve, which is downward sloping.
- Plot the LM curve, which is upward sloping.
- The intersection of the IS and LM curves represents the equilibrium level of real GDP and interest rate.
Movement Along the LM Curve
- An increase in the money supply (M) shifts the LM curve to the right.
- A decrease in k (liquidity preference) shifts the LM curve to the right.
- An increase in Y (real GDP) shifts the LM curve to the left.
Shifts of the LM Curve
- Changes in monetary policy (M), fiscal policy (T or G), or liquidity preference (k) shift the LM curve.
- An expansionary monetary policy (increase in M) shifts the LM curve to the right, leading to lower interest rates and higher real GDP.
- A contractionary fiscal policy (increase in T or decrease in G) shifts the LM curve to the left, leading to higher interest rates and lower real GDP.
Step 1: IS Curve
- Start with the IS curve, which represents the relationship between interest rates (r) and real GDP (Y):
- Y = C(Y-T) + I(r) + G
Step 2: Money Market Equilibrium
- The LM curve represents the money market equilibrium, where the demand for money (Md) equals the supply of money (Ms):
- Md = kPY
- Ms = M
Step 3: Liquidity Preference
- The demand for money (Md) includes a liquidity preference function, which relates the real money demand to the interest rate:
- Md = L(r, Y)
Step 4: Substituting
- Substitute the liquidity preference function into the money market equilibrium equation:
- L(r, Y) = kPY
Step 5: IS-LM System
- Combine the IS curve and the LM curve equations:
- Y = C(Y-T) + I(r) + G
- L(r, Y) = kPY
Graphical Derivation
- Plot the IS curve, which is downward sloping.
- Plot the LM curve, which is upward sloping.
- The intersection of the IS and LM curves represents the equilibrium level of real GDP and interest rate.
Movement Along the LM Curve
- An increase in the money supply (M) shifts the LM curve to the right.
- A decrease in k (liquidity preference) shifts the LM curve to the right.
- An increase in Y (real GDP) shifts the LM curve to the left.
Shifts of the LM Curve
- Changes in monetary policy (M), fiscal policy (T or G), or liquidity preference (k) shift the LM curve.
- An expansionary monetary policy (increase in M) shifts the LM curve to the right, leading to lower interest rates and higher real GDP.
- A contractionary fiscal policy (increase in T or decrease in G) shifts the LM curve to the left, leading to higher interest rates and lower real GDP.
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