Chapter 5 ~ IS-LM model
Z = C (Y – T) + I + G (Consumption + Investment + Government spending) C = C (Y – T)
As Y = Z -> Y = C (Y – T) + I + G
Investments depend mostly on;
- The level of sales; higher sales, higher investment and vice versa
- The interest rate; higher interest rates, lower investment and vice versa
Therefore, in the new model (IS-LM) I = I (Y, i)
Y = C (Y – T) + I (Y, i) + G = IS-relation with respect for interest rate changes.
Consumption and investment relations are not linear, an increase in output leads to a less than one-
for-one increase in demand -> Demand curve is flatter than a 45-degree line and not a line, but curve.
A higher interest rate leads to lower investment and lower demand, therefore if interest increases,
the demand curve shifts downward.
IS-relation: on the goods market, production Y is equal to the demand for goods Z.
IS-curve: relation between the interest rate and output (downward-sloping curve).
Changes in Taxes or Government spending will shift the IS-curve.
If Taxes increase, the IS-curve moves to the left -> for the same interest rate a lower output.
If Government spending increases, the IS-curve moves to the right -> same interest rate and higher Y
M = $ Y L (i) with M = nominal money stock with the central bank as controlling M directly
Right side is the demand for money, a function of nominal income and nominal interest rate.
Increase in Y leads to an increase in demand of money, increase in i leads to decrease in demand.
However, this does not take into account real money, real income and interest rates, this is the case in
the equation M / P = Y L(i) with P = price level this is the LM relation.
In a graph, the supply of money is (in the short run) given and unchangeable (a vertical line), the
demand of money decreases when the interest rate increases (with a given level of Y).
An increase in income leads to an increase in the interest rate;
Income increase -> money demand increase, however money supply is given. The interest rate must
go up until demand and supply are equal again.
LM-curve: relation between output and the interest rate (upward-sloping curve).
Changes in nominal supply of money and price level will lead to change the real supply of money.
An increase in the (real) money supply leads to a decrease in the interest rate -> the LM-curve shifts
downwards.
Note: the lecture approaches the LM-curve as a horizontal line, because the central bank can set a
interest rate in order to reach their goals (for the economy).
The IS- and LM-relation together determine output and interest rate in a model. The IS-curve
corresponds to (equilibrium in) the goods market, the LM-curve corresponds to (equilibrium in) the
financial market. There can only be 1 overall equilibrium point at the time (in the short run).
, Fiscal contraction or consolidation: increasing taxes or decrease in government spendings to reduce
the government’s budget deficit. Fiscal expansion: increase in deficit (vice versa). To determine the
effect(s) of this change you go through 3 steps.
1. Determine how the given change affects the equilibrium of the goods and/or financial
market; how does it shift the IS- and/or LM-curve? (graphically)
2. Characterize the effects of these shifts on the intersection of the IS- and LM-curves, what
does the change doe to equilibrium output and corresponding interest rate? (graphically)
3. Describe the effects in words.
In the short run, a reduction of the budget deficit may or may not (unknown) decrease investment.
Monetary expansion: increase in money supply vs. Monetary contraction or tightening.
A monetary expansion is more investment-friendly than a fiscal expansion, as you know for sure that
investment goes up.
In practice, the 2 policies are often used together in a monetary-fiscal policy mix or short; policy mix.
Sometimes they’re used in the same directions, but they can also be set up in opposite directions.
Changes in the economy do not work through in the equilibrium right on the spot, it takes time, in
the IS-LM model this dynamics are neglected, but you can describe them in words;
- Consumers need to take some time to adjust their consumption to new disposable income
- Firms need some time to adjust their investments following a change in their sales or a
change in interest rate
- Firms need some time to adjust production following a change in their sales.
How much time exactly is needed in a case can only be determined by looking at data and using
econometrics.
Fisher equation
1+i
1+r = e r ≈ i – π^e r = real interest rate i = nominal interest rate
1+ π
You can integrate this in the IS-LM model; Y = C (Y – T) + I (Y, i – π^e + x) + G and LM = i
The expected inflation = π^e risk premium = x
Or switch i (nominal interest rate) for r (real interest rate), but the central bank does not
communicate with a real interest rate, they aim for this but try to reach that rate through regulating
the nominal interest rate.
Borrowing rate: r + x (for consumers and firms)
If i = 0 and π^e > 0 r < 0 and π^e < 0 r > 0
Monetary limits ->
Credibility and Zero lower bound: the nominal interest rate cannot go far below 0, because people
will go tend to hold cash with only a small negative return.
Z = C (Y – T) + I + G (Consumption + Investment + Government spending) C = C (Y – T)
As Y = Z -> Y = C (Y – T) + I + G
Investments depend mostly on;
- The level of sales; higher sales, higher investment and vice versa
- The interest rate; higher interest rates, lower investment and vice versa
Therefore, in the new model (IS-LM) I = I (Y, i)
Y = C (Y – T) + I (Y, i) + G = IS-relation with respect for interest rate changes.
Consumption and investment relations are not linear, an increase in output leads to a less than one-
for-one increase in demand -> Demand curve is flatter than a 45-degree line and not a line, but curve.
A higher interest rate leads to lower investment and lower demand, therefore if interest increases,
the demand curve shifts downward.
IS-relation: on the goods market, production Y is equal to the demand for goods Z.
IS-curve: relation between the interest rate and output (downward-sloping curve).
Changes in Taxes or Government spending will shift the IS-curve.
If Taxes increase, the IS-curve moves to the left -> for the same interest rate a lower output.
If Government spending increases, the IS-curve moves to the right -> same interest rate and higher Y
M = $ Y L (i) with M = nominal money stock with the central bank as controlling M directly
Right side is the demand for money, a function of nominal income and nominal interest rate.
Increase in Y leads to an increase in demand of money, increase in i leads to decrease in demand.
However, this does not take into account real money, real income and interest rates, this is the case in
the equation M / P = Y L(i) with P = price level this is the LM relation.
In a graph, the supply of money is (in the short run) given and unchangeable (a vertical line), the
demand of money decreases when the interest rate increases (with a given level of Y).
An increase in income leads to an increase in the interest rate;
Income increase -> money demand increase, however money supply is given. The interest rate must
go up until demand and supply are equal again.
LM-curve: relation between output and the interest rate (upward-sloping curve).
Changes in nominal supply of money and price level will lead to change the real supply of money.
An increase in the (real) money supply leads to a decrease in the interest rate -> the LM-curve shifts
downwards.
Note: the lecture approaches the LM-curve as a horizontal line, because the central bank can set a
interest rate in order to reach their goals (for the economy).
The IS- and LM-relation together determine output and interest rate in a model. The IS-curve
corresponds to (equilibrium in) the goods market, the LM-curve corresponds to (equilibrium in) the
financial market. There can only be 1 overall equilibrium point at the time (in the short run).
, Fiscal contraction or consolidation: increasing taxes or decrease in government spendings to reduce
the government’s budget deficit. Fiscal expansion: increase in deficit (vice versa). To determine the
effect(s) of this change you go through 3 steps.
1. Determine how the given change affects the equilibrium of the goods and/or financial
market; how does it shift the IS- and/or LM-curve? (graphically)
2. Characterize the effects of these shifts on the intersection of the IS- and LM-curves, what
does the change doe to equilibrium output and corresponding interest rate? (graphically)
3. Describe the effects in words.
In the short run, a reduction of the budget deficit may or may not (unknown) decrease investment.
Monetary expansion: increase in money supply vs. Monetary contraction or tightening.
A monetary expansion is more investment-friendly than a fiscal expansion, as you know for sure that
investment goes up.
In practice, the 2 policies are often used together in a monetary-fiscal policy mix or short; policy mix.
Sometimes they’re used in the same directions, but they can also be set up in opposite directions.
Changes in the economy do not work through in the equilibrium right on the spot, it takes time, in
the IS-LM model this dynamics are neglected, but you can describe them in words;
- Consumers need to take some time to adjust their consumption to new disposable income
- Firms need some time to adjust their investments following a change in their sales or a
change in interest rate
- Firms need some time to adjust production following a change in their sales.
How much time exactly is needed in a case can only be determined by looking at data and using
econometrics.
Fisher equation
1+i
1+r = e r ≈ i – π^e r = real interest rate i = nominal interest rate
1+ π
You can integrate this in the IS-LM model; Y = C (Y – T) + I (Y, i – π^e + x) + G and LM = i
The expected inflation = π^e risk premium = x
Or switch i (nominal interest rate) for r (real interest rate), but the central bank does not
communicate with a real interest rate, they aim for this but try to reach that rate through regulating
the nominal interest rate.
Borrowing rate: r + x (for consumers and firms)
If i = 0 and π^e > 0 r < 0 and π^e < 0 r > 0
Monetary limits ->
Credibility and Zero lower bound: the nominal interest rate cannot go far below 0, because people
will go tend to hold cash with only a small negative return.
