Savings, Investment, and the Financial System

Introduction

Savings and investment are critical for increasing living standards.
Savings act as a mechanism to transfer purchasing power into the future.
Investment involves purchasing new capital, such as equipment or buildings, often financed through borrowing.
Economists study savings and investment decisions because they are central to productive capital purchases.

Saving and Investment

Overview of saving and investment in macroeconomics.

National Income Account Identity

The National Income Account Identity is used to relate macroeconomic indicators.
Equation: $Y = C + I + G + NX$
- Where:
  - $Y$ = GDP (Gross Domestic Product)
  - $C$ = Consumption
  - $I$ = Investment
  - $G$ = Government Purchases
  - $NX$ = Net Exports
An identity is always true due to variable definitions.
In an open economy: $Y = C + I + G + NX$
In a closed economy (no trade): $Y = C + I + G$

National Saving

National saving (S) is derived from the national income identity.
Equation: $S = Y - C - G = I$
National saving equals investment in a closed economy.

Types of Saving

Two types of saving:
- Private Saving
- Public Saving

Private Saving

Definition: The leftover income households have after consumption (C) and paying taxes (T).
Equation: Private Saving = $Y - C - T$

Public Saving

Definition: The leftover tax revenue the government has after paying for its spending.
Equation: Public Saving = $T - G$

Example 1

Given: Closed economy with GDP = $150,000, Investment (I) = $19,000 (capital goods) + $1,000 (inventory) + $8,000 (new homes) = $28,000, Consumption (C) = $85,000, Taxes (T) = $32,000.
Find: Public Saving
- First, calculate Government Spending (G): $G = Y - C - I = 150,000 - 85,000 - 28,000 = 37,000$
- Then, calculate Public Saving: $T - G = 32,000 - 37,000 = -5,000$
Public saving is -$5,000.

Question 1

In a small closed economy, investment is $20 billion, and private saving is $15 billion.
What are public saving and national saving?
- Given: $I = 20$ , Private Saving = $15$
- National Saving = $I = 20$
- Private Saving = $Y - C - T = 15$
- Also, $Y - C = I + G = 20 + G$
- Thus, 20 + G - T = 15 => G - T = -5
- Public Saving = $T - G = 5$
- National Saving = Private Saving + Public Saving = $15 + 5 = 20$

The Government Budget

Government budget: Defines spending allowance in a given year.
Budget balance: Determined by expenditure relative to income (tax revenue).
Budget deficit: Government spends more than it collects in tax revenue (T < G).
Budget surplus: Government spends less than it collects in tax revenue (T > G).

Peer Work Question

Given: GDP = $100 billion, Consumption = $65 billion, Budget Deficit = $3 billion, Government Spending = $2 billion in a closed economy.
Find: National Saving, Investment, Public Saving, and Taxes.
- Public Saving = $T - G = -3$ billion.
- Taxes: $T = G - 3 = 2 - 3 = -1$ billion.
- National Saving = $Y - C - G = 100 - 65 - 2 = 33$ billion.
- Investment = National Saving = $33 billion
- Since $T-G = -3$ , then $T = G-3 = 2-3 = -1$ . There seems to be a mistake in the question since taxes cannot be negative.

Indexation

Money illusion: People feel worse off when they see rising prices, focusing on nominal terms.
Nominal Interest Rate: Not corrected for inflation.
- The rate of growth in the dollar value of a deposit or debt.
Real Interest Rate: Corrected for inflation.
- The rate of growth in the purchasing power of a deposit or debt.
Fisher Equation: $R = N - \pi$
- Where:
  - $R$ = Real interest rate
  - $N$ = Nominal interest rate
  - $\pi$ = Inflation rate

Example

Deposit $1000 for one year; Nominal interest rate (N) = 9%, Inflation rate = 3.5%.
Compute the real interest rate.
- $R = N - \pi = 9 - 3.5 = 5.5$
Future value with nominal rate: 1000 + 1000 \times 0.09 = 1000(1 + 0.09) = $1090
Future value with real rate: 1000 + 1000 \times 0.055 = 1000(1 + 0.055) = $1055

Question

Nominal interest rate from 2020 to 2021 is 2.5%.
GDP deflator in 2020: 257; GDP deflator in 2021: 261.
What is the real interest rate from 2020 to 2021?
- Inflation rate: $\pi = \frac{261 - 257}{257} \times 100 \approx 1.6 %$
- Real interest rate: $R = N - \pi = 2.5 - 1.6 = 0.9 %$

The Market for Loanable Funds

Framework for understanding saving and investment dynamics.

Matching Savings and Investments

Savings = Investment for the economy overall in a closed economy.
Goal: Explain how financial markets coordinate saving and investment.
Understand how government policies and other factors affect saving, investment, and interest rates.

Market for Loanable Funds

Loanable Funds: Income people save and lend out rather than consume and the amount investors borrow for projects.
Flow of resources available to fund private investment.
Assumption: Only one financial market.
- Savers deposit their savings.
- Borrowers take out loans.
- One interest rate serves as both return to saving and cost of borrowing.

Supply of Loanable Funds

Saving is the source of the supply of loanable funds.
Households with extra income lend it out and earn interest.
Upward-sloping supply curve: As interest rates increase, the quantity of loanable funds supplied increases.

Demand for Loanable Funds

Investment is the source of the demand for loanable funds.
Firms borrow funds for new equipment, factories, etc.
Households borrow funds to purchase new houses.
Downward-sloping demand curve: As interest rates increase, the quantity of loanable funds demanded decreases.

Equilibrium in the Market for Loanable Funds

Equilibrium: Supply = Demand
Saving = Investment.
Equilibrium interest rate and quantity of loanable funds.

Demand and Supply

Demand for Loanable Funds: Governed by the Law of Demand.
- Price = real interest rate.
- As the real interest rate increases, the quantity of loanable funds demanded decreases.
Supply for Loanable Funds: Governed by the Law of Supply.
- Price = real interest rate.
- As the real interest rate increases, the quantity of loanable funds supplied increases.

How Government Policy Affects Equilibrium

Government policies influence saving and investment behavior.

Changes in Saving and Investment Behavior

Policies shift supply or demand curves.
- Determine the direction of the shift.
- Analyze how the equilibrium changes.

Policy Choices: 1) Saving Incentives

Designed to encourage people to save more.
- Reduce taxes on interest income.
Decreasing risk/financial safety nets
- Federal Deposit Insurance Corporation (FDIC): Guarantees savings even if the bank fails.
  - 1980-2008: covered $100,000
  - 2008-today: covers $250,000
Tax benefits on saving encourage more savings, shifting the supply curve to the right.

Analysis of Saving Incentives

Change in tax policy encourages more saving, increasing the supply of loanable funds.
Supply increases, leading to a fall in the interest rate and stimulating investment, thus increasing the quantity of loanable funds.

Goal of Saving Incentives

Increase national savings.
Effects of introducing a savings incentive:
- The supply curve of Loanable Funds shifts to the right.
- Higher equilibrium quantity of loanable funds.
- Lower equilibrium real interest rate.

Policy Choices: 2) Investment Incentives

Attempt to increase the amount people are willing to borrow at every interest rate.
Investment Tax Credits
- A reduction in taxable income for investing in specific manners.
- Ex) Federal Investment Tax Credit (ITC) to a 30% tax credit on the total cost of installing solar panels and other clean energy property.
Investment becomes more appealing, encouraging more borrowing.

Analysis of Investment Incentives

Demand shifts to the right as borrowing becomes more attractive.
Higher interest rate and increased quantity of loanable funds.

Goal of Investment Incentives

Increase investment, which boosts living standards.
Effects of introducing an investment incentive:
- Demand curve for Loanable Funds shifts to the right.
- Higher equilibrium quantity of loanable funds.
- Higher equilibrium real interest rate.

Policy Choices: Save or Invest?

Both saving and investment incentives can increase living standards.
Saving incentives decrease the interest rate, while investment incentives increase it.

Policy Choices: 3) Gov’ Budget Deficit and Surplus

The government can actively influence savings and investment through policies.
Influence the market for loanable funds directly via savings behavior.
National savings = private savings + public savings.
Budget surplus or deficit alters the amount of national savings in the loanable funds market.
Ex) The U.S. Federal government often runs a budget deficit, decreasing the supply of loanable funds.

Budget Deficit

Government finances deficits by borrowing in the bond market.
Accumulation of past borrowing = government debt.
Crowding Out Effect
- Government borrowing to cover deficits crowds out private investment by raising interest rates.
- Reduces the economy's growth rate and future living standards.

Analysis of Budget Deficit

Budget deficit lowers saving, shifting the supply curve to the left.
Higher interest rates and decreased loanable funds.

Effects of Budget Deficit

When the government runs a budget deficit:
- Supply curve for Loanable Funds shifts to the left.
- Lower equilibrium quantity of loanable funds.
- Higher equilibrium real interest rate.

Group Work Problem

Analyze the effects of a government budget surplus using the loanable funds model.
- The surplus increases the supply of loanable funds, shifting the supply curve to the right.
- This results in a lower equilibrium interest rate and increased investment.

Question 2

A shift of the supply curve from S1 to S2 represents an increase in the supply of loanable funds.