ECO403 Final Term Notes and Formulas Preparation Lectures 23-45

Eco403 Macroeconomics Notes And Formulas For Final Term Exam Preparation

LEC 23-45

ENDOGENOUS GROWTH THEORY

Production function for endogenous growth model can be written as: Y = A K, Where A is the amount of output for each unit of capital (A is exogenous & constant). Investment: sY Depreciation: δK Equation of motion for total capital: ΔK = s Y − δ K Divide through by K and use Y = A K, get:

ΔY = ΔK = s A −δ

Y K

If s A >δ, then income will grow forever, and investment is the “engine of growth.” Here, the permanent growth rate depends on s. In Solow model, it does not.

A TWO-SECTOR MODEL

u = fraction of labor in research (u is exogenous)

•  Manufacturing production function:

Y = F [K, (1-u) E L]

•  Research production function:

Δ E = g (u) E

•  Capital accumulation:

Δ K = s Y − δ K

•  In the steady state, manufacturing output per worker and the standard of living grow at rate:

ΔE/E = g (u). Key variables are: s: affects the level of income, but not its growth rate (same as in Solow model) u: affects level and growth rate of income

TIME HORIZONS

• Long run: Prices are flexible, respond to changes in supply or demand
• Short run: many prices are “sticky” at some predetermined level

The economy behaves much differently when prices are sticky. The aggregate demand curve shows the relationship between the price level and the quantity of output demanded. For an intro to the AD/AS model, we use a simple theory of aggregate demand based on the Quantity Theory of Money.

THE QUANTITY EQUATION AS AGGREGATE DEMAND

Quantity equation: M V = P Y The money demand function it implies: (M/P) d = k Y, Where V = 1/k = velocity. For given values of M and V, these equations imply an inverse relationship between P and Y.

THE DOWNWARD-SLOPING AD CURVE

An increase in the price level causes a fall in real money balances (M/P), causing a decrease in the demand for goods & services.

SHIFTING THE AD CURVE

An increase in the money supply shifts the AD curve to the right.

AGGREGATE SUPPLY IN THE LONG RUN

In the long run, output is determined by factor supplies and technology:

Y · F K · L

Y is the full-employment or natural level of output,

LONG-RUN EFFECTS OF AN INCREASE IN MONEY

An increase in M shifts the AD curve to the right.

FROM THE SHORT RUN TO THE LONG RUN

Over time, prices gradually become “unstuck.” When they do, will they rise or fall?

In the short-run equilibrium, if

then over time, the price level will

Y > Y Rise Y < Y Fall Y = Y Remain constant

Predicted effects of the oil price shock:

Inflation ↑, Output ↓, Unemployment ↑ and then a gradual recovery.

THE KEYNESIAN CROSS

It is the simple closed economy model in which income is determined by expenditure. This model is presented by J.M. Keynes.

Notations:

I = planned investment E = C + I + G = planned expenditure Y = real GDP = actual expenditure

Actual expenditure is the amount that households, firms and the government spend on goods and services; it equals the economy’s gross domestic product (GDP).

Planned expenditure is the amount households, firms and the government would like to spend on goods and services.

ELEMENTS OF THE KEYNESIAN CROSS

Consumption function: C =C (Y −T) Govt policy variables

G · G T · T

For now investment is exogenous

I

I

Planned expenditure

E · C Y · T · I · G

Equilibrium condition: Actual expenditure = Planned expenditure

Y = E

AN INCREASE IN GOVERNMENT PURCHASES

Equilibrium condition Y = C + I + G In changes form ΔY = ΔC + ΔI + ΔG Since I is exogenous= Δ C + ΔG Because ΔC = MPC × ΔY= M P C × ΔY + ΔG Collect terms with ΔY on the left side of the equals sign: (1 − M P C) × Δ Y = Δ G Finally, solve for ΔY:

1 MPC

Y · G · THE GOVERNMENT PURCHASES MULTIPLIER

The increase in income resulting from Rs.1 increase in G is known as government purchases multiplier. In this model, the G multiplier equals:

1 MPC

Y

G

 WHY THE MULTIPLIER IS GREATER THAN 1?

Initially, the increase in G causes an equal increase in Y: ΔY = ΔG. But ↑Y ⇒ ↑C ⇒ further ↑Y ⇒ further ↑C ⇒ further ↑Y