Equilibrium in the Goods Market and the Loanable Funds Market

Equilibrium in the Goods Market

The lecture discusses how the supply and demand for goods and services reach equilibrium.
The circular flow diagram from chapter three is referenced, where the supply of goods (y) equals the demand.
In a closed economy, demand is the sum of consumption (C), investment (I), and government spending (G).
$Y = C + I + G$
Y is determined by technology, capital stock (K), and labor (L).
C, I, and G depend on the choices of households, firms, and the government.

Price and Equilibrium

In microeconomics, price balances quantity demanded and quantity supplied.
The general price level isn't the equilibrating factor because neither supply nor demand depends on it, as people focus on real values.
Real prices are unaffected by changes in the general price level.
The real interest rate is the price that ensures equilibrium in the goods market.

Demand for Goods and Services

The demand for goods and services originates from consumption, investment, and government spending.
Consumption depends on disposable income (Y - T), where T represents net taxes (taxes minus transfer payments).
Investment depends on the real interest rate (r).
Government spending (G) and taxes (T) are considered exogenous.

Supply and Demand Integration

The level of output (Y) is determined by capital (K), labor (L), and the production function: $Y = F(K, L)$ .
Combining this with consumption and investment functions and substituting into the national income identity results in:
$Y = C(Y - T) + I(r) + G$
Government spending and taxes are policy-determined, and total output is fixed by the production function and factors of production.
The equation becomes: $\bar{Y} = C(\bar{Y} - \bar{T}) + I(r) + \bar{G}$
This equation shows that total output supplied ($\bar{Y}$) equals the total demand, which consists of consumption, investment, and government spending.

The Role of the Real Interest Rate

In the equation, the real interest rate is the endogenous variable.
It adjusts to bring demand and supply into equilibrium.
A high real interest rate discourages investment, reducing overall demand.
If the real interest rate is too high, quantity demanded falls short of production.
A low real interest rate encourages investment, potentially leading to quantity demanded exceeding quantity supplied.

Financial Markets and Equilibrium

Financial markets determine the real interest rate.
The real interest rate is the cost of borrowing and return to lending.
Rearranging the GDP equation: $Y = C + I + G$
Subtracting consumption and government spending from both sides: $Y - C - G = I$
Y - C - G represents national saving.
In a closed economy, national saving equals investment.
National saving is split into private saving (Y - T - C) and public saving (T - G).
Private saving is disposable income minus consumption.
Public saving is taxes minus government spending.
National saving is the sum of private and public saving.
The goods market equilibrium condition, when rewritten in terms of saving and investment, represents equilibrium in financial markets.
Investment is the demand for loanable funds, while saving (by individuals, households, and the government) provides the supply.
If the real interest rate is too high, investment is low relative to saving, and the real interest rate falls.
The opposite occurs if the real interest rate is too low.

Exercise: Calculating Savings and Investment

Given: GDP = R19,000,000, Consumption = R13,000,000, Government Spending = R2,500,000, Budget Deficit = R1,200,000.
Find: Public Saving, Taxes, Private Saving, National Saving, and Investment.
Public Saving: T - G
Since there's a budget deficit of R1,200,000, public saving = -R1,200,000.
Taxes: Public Saving = T - G => -1,200,000 = T - 2,500,000 => T = R1,300,000.
Private Saving: Y - T - C = 19,000,000 - 1,300,000 - 13,000,000 = R4,700,000.
National Saving: Y - C - G = 19,000,000 - 13,000,000 - 2,500,000 = R3,500,000.
Investment: In a closed economy, National Saving = Investment = R3,500,000.
This type of calculation is common in tests and exams.

Loanable Funds Market

A simple demand and supply model of the financial system.
Simplifying assumptions:
- One asset: loanable funds.
- Demand for loanable funds: investment.
- Supply of loanable funds: national saving (private + public).
- Price of loanable funds: real interest rate.
Purpose: to explain how financial markets coordinate saving and investment.
This model helps channel finance to businesses.
It also analyzes government policies that influence saving and investment.
The demand and supply of loanable funds determine the real interest rate.
The economy has only one financial market: the market for loanable funds.
All savers deposit their saving, and all borrowers get their loans in this market.
Loanable funds refer to all income saved and lent out rather than used for consumption.
There is only one interest rate, which is both the return to saving and the cost of borrowing.

Demand for Loanable Funds

Comes from households and firms that want to borrow for investments.
Includes home loans and firms borrowing to buy equipment or build factories.
Investment is the source of demand.

Supply of Loanable Funds

Comes from people who have extra income they want to save and lend out.
Can occur directly (households buy bonds) or indirectly (households deposit in banks).
Saving is the source of supply.
The government can contribute to saving via a budget surplus.

Investment Curve (Demand for Loanable Funds)

Slopes downward.
High real interest rate (e.g., 20%) leads to low quantity of loanable funds demanded.
Low real interest rate (e.g., 3%) leads to high quantity of loanable funds demanded.
Inverse relationship between real interest rate and investment.
Movements occur when the real interest rate changes.
Shifts occur when exogenous variables change.

Movements vs. Shifts

A decrease in the real interest rate decreases the cost of borrowing, increasing quantity demanded (downward movement).
Changes in the real interest rate cause movements along the curve.

Shifts in Demand for Loanable Funds

The demand curve shifts to the right if:
- Firms expect higher rates of return on investment.
- Profitable new products are developed.
- Technological innovations occur.
- Business taxes are lowered (investment tax credit).

Loanable Funds Supply Curve

Can be vertical (supply doesn't depend on the real interest rate) or upward sloping (supply depends on the real interest rate).
If the supply curve does not depend on the real interest rate, it is vertical.
If it does depend on the real interest rate, it is upward sloping.
A vertical supply curve means national saving doesn't depend on the real interest rate.
An increase in the real interest rate causes an upward movement along the curve.

Supply Curve That Depends on the Real Interest Rate

An upward-sloping supply curve indicates that an increase in the real interest rate makes saving more attractive, increasing the quantity of loanable funds supplied.
Changes in the real interest rate cause movements along the curve.

Shifts in Supply of Loanable Funds

The supply curve shifts to the right if:
- Disposable income increases.
- Household's real wealth decreases (holding everything else constant, lowers saving).
- Lower household's expected future income increases current saving.
- The government runs a budget surplus.

Equilibrium in the Loanable Funds Market

Equilibrium occurs where demand and supply intersect.
Real interest rate adjusts until the amount firms want to invest equals the amount households want to save.
If the real interest rate is too low, demand exceeds supply, and the real interest rate increases.
If the real interest rate is too high, supply exceeds demand, and the real interest rate falls.
At equilibrium, the real interest rate balances the desire to save and invest.

Delta Notation

Expresses changes concisely in economics.
Delta ($\Delta$) means "change in."
$\Delta x$ means the change in the variable x.
If $\Delta l = 1$, it means the amount of labor used has increased by one unit.
Marginal Product of Labor (MPL) can be expressed using delta: $MPL = \frac{\Delta Y}{\Delta L}$ .
This shows how output changes per unit change in labor.
$\Delta C = MPC \times (\Delta Y - \Delta T), where MPC is the marginal propensity to consume.
$\Delta C = MPC \times \Delta Y - MPC \times \Delta T$ shows separate effects of changes in income and taxes.

Exercise: Calculating Change in Saving

Assume MPC = 0.8 and MPL = 20.
Calculate the change in national saving ($\Delta S$) for each scenario.
$\Delta S = \Delta Y - \Delta C - \Delta G = \Delta Y - MPC(\Delta Y - \Delta T) - \Delta G$
$\Delta S = \Delta Y - 0.8(\Delta Y - \Delta T) - \Delta G = 0.2\Delta Y + 0.8\Delta T - \Delta G$

Scenarios

Change in Government Spending ($\Delta G$) = 100: $\Delta S = 0.2(0) + 0.8(0) - 100 = -100$.
- An increase in government spending by 100 without changes in income or taxes leads to a decrease in national savings by 100.
Change in Taxes ($\Delta T$) = 100: $\Delta S = 0.2(0) + 0.8(100) - 0 = 80$.
- An increase in taxes by 100 without any changes in income or government spending leads to an increase in national saving of 80.
Change in Income ($\Delta Y$) = 100: $\Delta S = 0.2(100) + 0.8(0) - 0 = 20$.
- An increase in income of 100 units. Without changes in your government spending or taxes, with a marginal propensity to consume of 0,8 says to me, I've got 0,2 left to save. MPC plus MPS is equal to one.
Change in Labor ($\Delta L$) = 10: Since $\Delta Y = MPL \times \Delta L = 20 \times 10 = 200$, then $\Delta S = 0.2(200) + 0.8(0) - 0 = 40$.
- Given our marginal propensity to consume is telling me how much of the increased income is consumed, 60 units in this case, and how much is gonna be saved, ie 40 units.

Mastering the Model

Know which variables are endogenous and exogenous.
For each curve, know its definition, intuition for its slope, and factors that cause it to shift.
Use the model to analyze the effects of changes.

Example: Reagan Deficits

The American government implemented expansionary fiscal policy by increasing government spending and cutting taxes.
This increased the government budget deficit, leading to a fall in national saving.
National Saving = Private Saving (Y - T - C) + Public Saving (T - G).

Graphical Analysis

Axes: real interest rate (y-axis) and saving/investment (x-axis).
National saving curve is vertical (assuming independence from the real interest rate).
Downward-sloping demand for loanable funds (investment curve).
Equilibrium at intersection.
Tax cuts and increased government spending shift the national saving curve to the left.
This increases the real interest rate and decreases the quantity of investment.

Crowding Out

The reduction in investment due to increased government spending is known as crowding out.
The crowding out is represented by the movement along the demand curve.
Increased government spending crowds out investment completely.
This assumes a closed economy.
In an open economy, firms can borrow from the rest of the world.
Budget deficits in an open economy lead to indebtedness and reduce the amount of income for other spending.

Data Consistency

The model says that investment should have fallen by as much as saving.
But it didn't because it's an open economy.
Firms could finance investment by borrowing from the rest of the world.

Effects of Increased Government Spending

Increases demand for goods and services/aggregate demand.
Total output is fixed. Increase in G must be met by a fall in another category of demand.
Disposable income is unchanged so consumption is unchanged.
Increase in government spending must be met by a fall in investment.
To make investment fall by increasing the real interest rates.
Government spending crowds out private investment

Effect of Decreased Taxes

The immediate impact of a fall in taxes is to increase my disposable income and thus to increase consumption.

New Calculation

Government cuts taxes by \R300,000$$. Find the new budget deficit and answers to a, if consumers were to save the entire tax cut or if consumers were to save a third and spend the other two thirds of the tax cut.

Supply that does not depend on the interest rate.

What happens to the real interest rate and investment?
The total amount of taxes affects our disposable income. But even if we hold total taxes constant, a change in the structure or composition of taxes can have an effect.