Unit 4: Keynesian economics

1. Keynes' objections to classical theory

John Maynard Keynes, writing during the Great Depression of the 1930s, saw that the Classical model had failed. Millions were unemployed, and the economy was *not* automatically returning to full employment.

Keynes's Main Objections:

1. Rejection of Say's Law: Keynes argued that Say's Law ("Supply creates its own demand") was wrong. He famously argued that **Demand creates its own supply**. He showed that savings might *not* automatically equal investment. If people save, that is a "leakage" from the circular flow, and if it isn't matched by an "injection" of investment, aggregate demand will be deficient, leading to a recession.
2. Wages and Prices are *Not* Flexible: Keynes argued that in the real world, wages are **"sticky downwards."** Workers and trade unions will resist wage cuts, even during a recession.
   • Therefore, the Classical "automatic fix" (falling wages) will not work.
3. The "Liquidity Trap": He argued that even if the central bank lowered interest rates to zero, savings might *still* be greater than investment. People might just hoard cash (liquidity) out of fear, and firms won't invest if they have no confidence in future sales.
4. Full Employment is Not Guaranteed: The Classical model said the economy is *always* at full employment. Keynes showed that the economy could get stuck in an **"under-employment equilibrium"**—a stable state with high unemployment.

2. The Keynesian Approach

The Keynesian approach flips the Classical model on its head.

• In the Classical model, Supply is key, and the economy is at full employment.
• In the Keynesian model, Aggregate Demand (AD) is key, and the economy can be at *any* level of employment.

Keynes's Central Idea: The total level of **output (GDP) and employment** in the economy is determined by the level of **Aggregate Demand (AD)**.

• If AD is high, firms will produce more and hire more workers.
• If AD is low (deficient), firms will produce less and fire workers, leading to a recession and unemployment.

3. Keynesian Consumption Function

Keynes argued that the most important component of Aggregate Demand is Consumption (C). He proposed a "fundamental psychological law" to describe how households consume.

C = a + bY

• C = Total Consumption
• a = Autonomous Consumption: The minimum amount of consumption households will do even if their income (Y) is zero (by borrowing or using savings). This is the C-intercept.
• Y = Total Income (specifically, disposable income)
• b = Marginal Propensity to Consume (MPC): The fraction of each *additional* dollar of income that is spent on consumption.
  • MPC = (Change in C) / (Change in Y)
  • Keynes argued that 0 < MPC < 1 (e.g., if MPC = 0.8, you will spend 80 cents of every new dollar you get and save 20 cents).

4. Saving, Investment Functions

Saving Function (S)

Saving is simply the part of income that is *not* consumed.
Y = C + S => S = Y - C

We can derive the saving function from the consumption function:
S = Y - (a + bY)
S = Y - a - bY

S = -a + (1 - b)Y

• -a = Autonomous Dissaving: The amount you must borrow or take from savings when income is zero.
• (1 - b) = Marginal Propensity to Save (MPS): The fraction of each *additional* dollar of income that is saved.
  • MPS = (Change in S) / (Change in Y)

Investment Function (I)

Keynes argued that Investment (spending by firms on capital) is the most unstable part of AD. He treated it as **autonomous (independent) of income**.

I = I₀

This means investment is a fixed amount (e.g., 100 billion) determined by business confidence ("animal spirits") and the interest rate, not by the current level of GDP.

5. Basics of Aggregate Demand and Aggregate Supply

This is the main framework for the Keynesian model.

Aggregate Demand (AD)

AD is the total planned spending in the economy. In a simple two-sector model (households and firms):

AD = C + I
AD = (a + bY) + I₀

The AD curve is upward sloping because as Income (Y) rises, Consumption (C) also rises.

Aggregate Supply (AS)

In the Keynesian model, the AS curve is a 45-degree line.
This line represents all points where **Total Spending (AD) = Total Income/Output (Y)**.
It's a graphical representation of the equilibrium condition (Y = AD).

6. The Principle of Effective Demand

Principle of Effective Demand: The equilibrium level of income and employment in the economy is determined by the point where **Aggregate Demand (AD) equals Aggregate Supply (AS)**.

This intersection point is the "effective demand."

• If AD > AS (Spending > Output): Firms' inventories will fall, so they will hire more workers and produce more, causing Y to rise.
• If AD < AS (Spending < Output): Firms' inventories will pile up, so they will fire workers and produce less, causing Y to fall.
• Equilibrium is only reached when AD = AS.

7. Income Determination in a Simple two Sector Model

This is the process of finding the equilibrium income (Y) using algebra. There are two identical methods:

Method 1: AD = AS (Aggregate Demand = Aggregate Supply)

1. Start with the equilibrium condition: Y = AD
2. Substitute the equations for AD: Y = C + I
3. Substitute the functions: Y = (a + bY) + I₀
4. Solve for Y:
   Y - bY = a + I₀
   Y(1 - b) = a + I₀
   

   Y* = [ 1 / (1 - b) ] * (a + I₀)

Method 2: S = I (Leakages = Injections)

1. Start with the equilibrium condition: S = I
2. Substitute the functions: -a + (1 - b)Y = I₀
3. Solve for Y:
   (1 - b)Y = a + I₀
   

   Y* = [ 1 / (1 - b) ] * (a + I₀)

Both methods give the exact same result.

8. Investment Multiplier

The multiplier is one of Keynes's most important concepts. It explains why a small change in spending can have a much larger effect on national income.

The Multiplier (k): The ratio of the change in equilibrium income (ΔY) to the initial change in autonomous spending (e.g., ΔI) that caused it.
k = ΔY / ΔI

From our equilibrium equation, we found the multiplier (k) is:

k = 1 / (1 - b) = 1 / (1 - MPC)
k = 1 / MPS

How it Works:

• Example: Assume MPC = 0.8 (so MPS = 0.2)
• Multiplier (k) = 1 / (1 - 0.8) = 1 / 0.2 = 5
• Scenario: The government or a firm invests100 in building a new road (ΔI = 100).
• Round 1: The100 is paid as income to workers.
• Round 2: The workers spend 80% of it (MPC=0.8), so they spend 80. This becomes income for a shopkeeper.
• Round 3: The shopkeeper spends 80% of that80, which is 64. This becomes income for someone else.
• Result: The initial100 injection of spending leads to a total increase in income of 100 +80 + 64 + ... which will eventually sum to 500.
• ΔY = k * ΔI => 500 = 5 *100

9. Keynesian theory of demand for money

Keynes's theory of money demand is called the **Liquidity Preference Theory**. He asked: Why do people *prefer* to hold *liquid* assets (like cash) instead of interest-bearing assets (like bonds)?

He gave three motives for demanding (holding) money:

1. Transaction Motive (L_T):
   • Holding money for day-to-day purchases (food, rent, bus fare).
   • This depends positively on the level of Income (Y). (More income = more transactions).
2. Precautionary Motive (L_P):
   • Holding money for unforeseen emergencies (medical bills, car repairs).
   • This also depends positively on the level of Income (Y).
3. Speculative Motive (L_S):
   • This was Keynes's big innovation.
   • Holding money as a financial asset, to "speculate" on the future of the interest rate (i).
   • There is an inverse relationship between the interest rate and bond prices.
   • If i is high: You expect it to fall. You buy bonds (money demand is low).
   • If i is low: You expect it to rise. You sell your bonds and hold cash (money demand is high), to avoid the capital loss when bond prices fall.

Total Money Demand (M_D) = L(Y, i)
(M_D depends positively on Income and negatively on the Interest Rate)