Aggregate Demand and Money Demand

Aggregate Demand

Aggregate demand in a closed economy comprises demand from consumers, investors, and the government.

Consumer Demand

Consumer demand (C) depends on income and the marginal propensity to consume:

$C = c<em>0 + c</em>1(1 - \tau)Y + TT$

Where:

• $c_0$ is autonomous consumption.
• $(1 - \tau)Y + TT$ is disposable income (total income (Y) plus government transfers (TT) minus taxes ($\tau$)).
• $c_1 \in [0,1]$ is the marginal propensity to consume.
• $s = 1 - c_1 \in [0,1]$ is the marginal propensity to save.
• $Y$ is total production.

Investment Demand

Investment (I) depends on the interest rate and output:

$I = I<em>0 - b \times i + I</em>1 \times Y$

Where:

• $I_0$ is the autonomous component of investment.
• b > 0 is the sensitivity of investments to the interest rate ($i$).
• I_1 > 0 is the sensitivity of investment to output ($Y$).

Government Demand

Government demand (G) is government consumption of goods. The government budget is:

$B = \tau \times Y - TT - G$

This is known as the primary budget.

Aggregate Demand Equation

$Z = C + I + G$

$Z = c<em>0 + c</em>1(1 - \tau)Y + TT + I<em>0 - b \times i + I</em>1 \times Y + G$

In equilibrium, total demand equals supply ($Y$):

$Y = A + c<em>1(1 - \tau)Y + I</em>1 \times Y - b \times i$

Where $A$ is the autonomous component of aggregate demand.

Solving for $Y$ gives the IS curve:

$Y = \frac{1}{1 - c<em>1(1 - \tau) - I</em>1} (A - b \times i)$

Keynesian Multiplier

The term \frac{1}{1 - c1(1 - \tau) - I1} > 0 is the Keynesian multiplier ($m$).

• The tax rate ($\tau$) reduces the multiplier.
• The propensity to consume ($c_1$) increases the multiplier.
• The sensitivity of investments to income ($I_1$) increases the multiplier.

Savings and Investment

In a closed economy, savings equals investment:

$S = Y - C - \tau Y$

$I = S + (\tau Y - G)$

Government net borrowing can displace private investments.

Money Demand

Monetary Aggregates

• M0: Currency in circulation.
• M1: M0 + traveler's checks, demand deposits, and other checkable deposits.
• M2: M1 +