Macroeconomics — Chapter 6: Foundations of the Combined Model

🔗 The integrated IS-LM model:

So far, we studied two markets separately:

The goods market:
Determines output Y. Equilibrium condition: Y = AD = C + I + G.

The money market:
Determines the interest rate r. Equilibrium condition: M/P = L(r, Y).

The integrated model:
Connects the two markets. Y and r are determined simultaneously, and a change in one market affects the other.

🔄 The shared variables:

1. Output (Y):
In the goods market, Y is determined by equilibrium. In the money market, Y affects money demand: when Y rises, L rises.

2. Interest rate (r):
In the money market, r is determined by equilibrium. In the goods market, r affects investment and consumption: r ↑ → I ↓, C ↓.

This interaction creates the circular connection in the integrated model.

📈 Effect of an increase in Y on the money market:

1. Y rises, so there are more transactions in the economy.
2. More transactions require more money.
3. Money demand rises: L(r, Y) increases.
4. Money supply is fixed by the central bank.
5. Excess demand for money is created.
6. The interest rate rises until a new equilibrium is reached.

In the graph, the money demand curve shifts to the right and the equilibrium interest rate rises.

📉 Effect of an increase in r on the goods market:

1. Investment (I):
r ↑ means financing becomes more expensive, so investment becomes less worthwhile and I decreases.

2. Consumption (C):
r ↑ makes saving more attractive and borrowing more expensive, so C decreases.

3. Aggregate demand:
AD = C + I + G. When C and I fall, AD falls.

4. Output:
Y falls. This is why a rise in interest rates cools down the economy.

⚖️ Integrated equilibrium:

Two conditions must hold at the same time:

1. Goods market:
Y = AD = C(Y,r) + I(Y,r) + G

2. Money market:
M/P = L(Y,r)

This is a system of two equations with two unknowns: Y and r. The solution gives the equilibrium values Y* and r*.

At this point, there is no pressure for change in either market.

🏛️ Fiscal policy:

Who carries it out? The government, usually through the Ministry of Finance.

Tools:

1. Public spending (G):
G ↑ is expansionary policy. G ↓ is contractionary policy.

2. Taxes (T):
T ↓ is expansionary policy because disposable income rises. T ↑ is contractionary policy.

Effect:
Fiscal policy directly affects the goods market through aggregate demand AD, and indirectly affects the money market through Y.

🏦 Monetary policy:

Who carries it out? The central bank.

Tools:

1. Money supply (M):
Buying bonds increases M. Selling bonds decreases M.

2. Reserve requirement:
Lower reserves increase M. Higher reserves decrease M.

3. Policy interest rate:
Lower interest is expansionary. Higher interest is contractionary.

Effect:
Monetary policy directly affects the money market and indirectly affects the goods market through investment and consumption.

📊 The key difference:

Economy with unemployment (Y < Y_F):
There are unused resources. Production can increase. Therefore, AD ↑ leads to Y ↑, while P remains relatively stable.

Economy at full employment (Y = Y_F):
All resources are used. Production cannot increase much. Therefore, AD ↑ leads mainly to P ↑, meaning inflation, while Y remains fixed.

The same policy can have different results depending on the state of the economy.

🔄 The full transmission mechanism:

Step 1 — goods market:
G↑ → AD↑ → Y↑. Higher government spending increases aggregate demand and output.

Step 2 — transition to the money market:
Y↑ means more transactions, so money demand L rises.

Step 3 — money market:
L↑ with fixed money supply creates excess demand for money, so r↑.

Step 4 — back to the goods market:
r↑ reduces I and C, partially offsetting the increase in Y.

📋 Expansionary fiscal policy:

Goal:
To increase aggregate demand AD and output Y.

Tools:

1. Increasing G:
More government spending directly increases AD.

2. Decreasing T:
Lower taxes increase disposable income, which raises consumption C and therefore AD.

When is it used?
During unemployment or recession, when the goal is to stimulate the economy.

In the integrated model under unemployment: Y rises, r rises, and I falls partly because of the higher interest rate.

📋 Expansionary monetary policy:

Goal: To lower the interest rate and encourage investment and consumption.

Tools:

1. Buying bonds from the public:
The central bank pays money, so M increases.

2. Lowering the reserve requirement:
Banks can lend more, so M increases.

3. Lowering the policy interest rate:
It becomes cheaper for banks to borrow, so M increases.

Effect in the integrated model, with unemployment:
M↑ → r↓ → I↑, C↑ → Y↑.

⚡ Crowding-out effect:

Definition:
When the government increases its spending, part of private investment is “crowded out.”

Mechanism:
1. G↑ → AD↑ → Y↑
2. Y↑ → money demand↑ → r↑
3. r↑ → I↓ and C↓
4. Result: G increased, but I decreased.

With unemployment:
The crowding-out is partial. Y still rises, but by less than in the simple multiplier.

At full employment:
The crowding-out is complete. Y does not rise; G increases, while I and C fall by the same amount.

🎯 Effect of G↑ on r and I:

Interest rate (r):
G↑ → Y↑ → money demand↑. With fixed money supply, excess demand for money is created, so r rises.

Investment (I):
r↑ means higher financing costs. Fewer projects are profitable, so I falls.

This is the crowding-out effect: r and I move in opposite directions.

🏦 Effect of M↑ with unemployment:

Step 1 — money market:
M↑ → M/P↑. Money supply rises while demand is initially unchanged, creating excess supply. Therefore r falls.

Step 2 — goods market:
r↓ makes investment cheaper. I↑ and C↑, so AD↑ and Y rises.

Step 3 — feedback:
Y↑ increases money demand, so r rises slightly, but it remains lower than before.

📊 Deflationary gap:

Definition:
A situation in which actual output is lower than full-employment output:
Y < Y_F.

Characteristics:
• There is unemployment
• Resources are unused
• There is no pressure on prices
• Output can increase

Gap size:
Deflationary gap = Y_F - Y.

Policy response:
Expansionary fiscal policy or expansionary monetary policy.

📊 Inflationary gap:

Definition:
A situation in which aggregate demand is higher than full-employment output, but output cannot rise beyond Y_F.

Characteristics:
• The economy is at full employment
• All resources are used
• Excess demand causes prices to rise
• P rises, meaning inflation

Gap size:
Inflationary gap = excess demand = AD - Y_F.

Policy response:
Reduce demand through contractionary fiscal or monetary policy.

🔄 Ways to finance an increase in G:

1. Issuing bonds to the public:
The government borrows from the public. The public gives money and receives bonds. Advantage: taxes do not rise immediately. Disadvantage: the deficit and debt increase.

2. Imposing taxes:
The government collects more from the public. Balanced budget: G↑ = T↑. Advantage: no deficit. Disadvantage: disposable income falls, so C falls.

The financing method affects the results.

⚠️ Factors affecting the crowding-out effect:

The crowding-out effect will be smaller when investment is less sensitive to the interest rate.

Why?
If r rises but I barely decreases, then the increase in government spending is not strongly offset by a decline in private investment.

More generally, crowding out is smaller when I and C are less sensitive to r, when money demand is more sensitive to r, or when money demand is less sensitive to Y.

📐 Detailed solution:

Given:
I = 100 - 50r
Initial r = 0.1
New r = 0.2

Initial investment:
I = 100 - 50 × 0.1 = 100 - 5 = 95

New investment:
I = 100 - 50 × 0.2 = 100 - 10 = 90

Change:
ΔI = 90 - 95 = -5

Investment decreases by 5 units.

🎯 Expansionary fiscal policy under unemployment:

Output (Y): increases, because G↑ raises AD and unused resources can be employed.

Interest rate (r): rises, because Y↑ increases money demand.

Investment (I): falls, because r↑ makes financing more expensive. This is the crowding-out effect.

Price level (P): remains constant, because there are unused resources and no strong pressure on prices.

Under unemployment, Y changes and P remains constant.