Section 8: Macroeconomics in Modules: Savings, Investment, Financial Systems, and Present Value

Savings and Investment Spending

• Relationship between Savings and Investment Spending:

  • In the modern economy, individuals and firms that create physical capital often do so with "other people's money."

  • The savings-investment spending identity states that savings and investment spending are always equal for the economy as a whole.

• The Savings-Investment Spending Identity (in a Closed Economy):

  • Total spending in a closed economy (GDP): $GDP = C + I + G$

    • Where $C$ is consumer spending, $I$ is investment spending, and $G$ is government purchases of goods and services.

  • Total income in a closed economy (GDP): $GDP = C + G + S$

    • Total income can go to consumer spending ($C$), government purchases of goods and services ($G$), or be saved ($S$).

  • Derivation of S = I:

    • By setting total income equal to total spending: $C + G + S = C + G + I$

    • Subtracting $(C + G)$ from both sides yields: $S = I$

    • This means savings = investment spending in a closed economy.

• Government Budget and Savings:

  • Budget surplus: Occurs when tax revenue exceeds government spending.

  • Budget deficit: Occurs when government spending exceeds tax revenue.

  • Budget balance: The difference between tax revenue ($T$) and government spending ($G$) and government transfers ($TR$).

    • Government savings ($S<em>{Government}$): $S</em>{Government} = T - TR - G$

  • National savings ($S_{National}$): The total amount of savings generated within the economy.

    • $S<em>{National} = S</em>{Government} + S_{Private}$

  • Combining with the $S = I$ identity: $S_{National} = I$

• The Savings-Investment Spending Identity (in an Open Economy):

  • An open economy is an economy where goods and money can flow into and out of the country.

  • Net capital inflow (NCI): The total inflow of foreign funds minus the total outflow of domestic funds to other countries.

    • A positive net capital inflow means a country receives an extra flow of funds from abroad that can be used for investment spending.

    • Net capital inflow is equal to imports minus exports: $NCI = IM - X$

  • Investment spending in an open economy: $I = S_{National} + NCI$

  • Derivation:

    • Starting with GDP for an open economy: $GDP = C + I + G + X - IM$

    • Rearranging to solve for investment: $I = GDP - C - G - X + IM$

    • Group terms: $I = (GDP - C - G) + (IM - X)$

    • Since $GDP - C - G$ represents national savings ($S_{National}$), and $IM - X$ represents net capital inflow ($NCI$):

    • $I = S_{National} + NCI$

• Practice Question 1 (Capital Inflow):

  • Question: Capital inflow is the…

  • Answer: Net inflow of funds into a country, or the total inflow of foreign funds into a country minus the total outflow of domestic funds to other countries.

    • Explanation: This directly matches the definition of net capital inflow, which accounts for both foreign funds entering and domestic funds leaving.

• Practice Question 2 (Exports vs. Imports):

  • Question: Suppose a country exports $50 million worth of goods and services, while it imports$60 million. This country…

  • Answer: Has a positive capital inflow.

    • Explanation: If imports ($60 million) are greater than exports ($50 million), then IM - X = $60 million - $50 million = $10 million. Since $NCI = IM - X$, the net capital inflow is positive ($10 million). A country that spends more on imports than it earns from exports must borrow the difference from foreigners, leading to capital inflow.</p></li></ul></li></ul></li></ul><h3 id="a818c3f7-dc44-40b4-8f7a-b4e2d51d3825" data-toc-id="a818c3f7-dc44-40b4-8f7a-b4e2d51d3825" collapsed="false" seolevelmigrated="true">The Market for Loanable Funds</h3><img src="https://knowt-user-attachments.s3.amazonaws.com/016ee282-58f2-4c42-8904-8c99a1c935c3.png" data-width="100$r^$), only projects that are profitable at$r^$or higher are funded.</p></li><li><p>Similarly, only lenders willing to lend at$r^*$or less have their offers accepted.</p></li></ul></li><li><p><strong>Shifts of the Demand for Loanable Funds:</strong></p><ul><li><p>Factors that can shift the demand curve:</p><ul><li><p><strong>Changes in perceived business opportunities:</strong> If businesses become more optimistic about future economic growth or new profitable technologies emerge, they will demand more funds at any given interest rate, shifting the demand curve to the right and leading to a rise in the equilibrium interest rate.</p></li><li><p><strong>Changes in government borrowing:</strong> An increase in government borrowing (e.g., due to a budget deficit) increases the aggregate demand for loanable funds, shifting the demand curve to the right and causing interest rates to rise.</p><ul><li><p><span style="color: red;"><strong>Crowding out</strong></span><strong>:</strong> Occurs when a government budget deficit drives up the interest rate and leads to reduced private investment spending. This is generally a concern only in a robust economy. In a depressed economy, increased government spending can raise income, which may also raise private savings, mitigating crowding out.</p></li></ul></li></ul></li></ul></li></ul><img src="https://knowt-user-attachments.s3.amazonaws.com/9eb52148-dab3-42ea-8517-36212a8dee7d.png" data-width="100$Real Interest Rate = Nominal Interest Rate - Inflation Rate$</p></li><li><p>$r{real} = r{nominal} - ext{inflation}$</p></li></ul></li><li><p>Loan contracts specify a <strong>nominal interest rate</strong> because actual future inflation is unknown to lenders and borrowers.</p></li></ul></li><li><p><strong>Practice Question 1 (Real Interest Rate Calculation):</strong></p><ul><li><p>Question: If the yearly nominal interest rate on a savings account is$5\%$and the rate of inflation over the same period is$2\%$, what is the real interest rate?</p></li><li><p>Answer:$3\%$</p><ul><li><p><em>Explanation:</em> Using the formula:$r_{real} = 5\% - 2\% = 3\%$.</p></li></ul></li></ul></li><li><p><strong>The Fisher Effect:</strong></p><ul><li><p><span style="color: yellow;">According to the Fisher effect, an increase in <strong>expected future inflation</strong> drives up the <strong>nominal interest rate</strong>, leaving the <strong>expected real interest rate unchanged</strong>.</span></p></li><li><p>This implies that the nominal interest rate adjusts one-for-one with changes in expected inflation to maintain a constant expected real interest rate.</p></li><li><p>$Nominal Interest Rate = Real Interest Rate + Expected Inflation Rate$</p><ul><li><p>Where the inflation premium is the difference between the nominal and real interest rates, equal to the anticipated inflation.</p></li></ul></li><li><p></p><img src="https://knowt-user-attachments.s3.amazonaws.com/c1878885-c8c3-4b64-b9f7-09f095393090.png" data-width="100$3\%$to$6\%$.</p><ul><li><p>a) How will the real interest rate be affected by this change? <em>Answer: The expected real interest rate will remain unchanged, assuming the Fisher effect holds.</em></p></li><li><p>b) How will the nominal interest rate be affected by this change? <em>Answer: The nominal interest rate will rise by 3 percentage points (from$r{real} + 3\%$to$r{real} + 6\%$), reflecting the increased expected inflation.</em></p></li><li><p>c) What will happen to the equilibrium quantity of loanable funds? <em>Answer: The equilibrium quantity of loanable funds will not be affected. The Fisher effect only explains the adjustment of the nominal interest rate in response to expected inflation; it doesn't shift the underlying supply and demand for loanable funds in real terms.</em></p></li></ul></li></ul></li></ul><h3 id="a337f17b-d7a4-4e6f-8aec-cd8d7d6de212" data-toc-id="a337f17b-d7a4-4e6f-8aec-cd8d7d6de212" collapsed="false" seolevelmigrated="true">The Financial System</h3><ul><li><p><strong>Purpose of the Financial System:</strong></p><ul><li><p>Most economies have a financial system to manage household wealth and facilitate loans.</p></li><li><p><strong>Wealth:</strong> The total value of a household's accumulated savings.</p></li><li><p><strong>Financial asset:</strong> A paper claim entitling the buyer to future income from the seller.</p></li><li><p><strong>Physical asset:</strong> A tangible object that can be used to generate future income.</p></li><li><p><strong>Liability:</strong> A requirement to pay income in the future.</p></li></ul></li><li><p><strong>Importance of a Sound Financial System:</strong></p><ul><li><p>It is critical for achieving long-run economic growth because it:</p><ul><li><p>Encourages greater savings and investment spending.</p></li><li><p>Ensures that savings and investment spending are undertaken efficiently.</p></li></ul></li></ul></li><li><p><strong>Three Tasks of a Financial System:</strong></p><ul><li><p><strong>1. Reducing Transaction Costs:</strong></p><ul><li><p><strong>Transaction costs:</strong> The expenses involved in negotiating and executing a deal. The financial system minimizes these for borrowers and lenders.</p></li></ul></li><li><p><strong>2. Reducing Risk:</strong></p><ul><li><p><strong>Financial risk:</strong> Uncertainty about future outcomes that involve financial losses or gains.</p></li><li><p><strong>Diversification:</strong> The practice of investing in several assets with unrelated, or independent, risks to reduce overall financial risk.</p></li></ul></li><li><p><strong>3. Providing Liquidity:</strong></p><ul><li><p><strong>Liquidity:</strong><span style="color: yellow;"> A measure of how quickly an asset can be converted into cash with relatively little loss of value.</span></p></li></ul></li></ul></li><li><p><strong>Practice Question 1 (Liquidity):</strong></p><ul><li><p>Question: Which of the following assets is most liquid?</p></li><li><p>Answer: A checking account balance of$1,000.

      • Explanation: Cash in a checking account is immediately available at its full value, making it highly liquid compared to real estate, art, or jewelry which require time and potentially incur costs to convert to cash.

  • Practice Question 2 (Benefits of Financial Markets):

    • Question: Financial markets provide a means for:

    • Answer: Answers (a), (b), and (c) are all correct.

      • Explanation: Financial markets reduce risk (through diversification), reduce transaction costs (by connecting many buyers and sellers), and enhance liquidity (by providing mechanisms to quickly convert assets to cash).

  • Types of Financial Assets:

    • Loan: A lending agreement made directly between an individual lender and an individual borrower.

      • Good: Customizable to specific needs.

      • Bad: High transaction costs to create and monitor.

    • Bond: Borrowing in the form of an IOU that pays interest.

      • A default occurs when a borrower fails to make payments as specified by the loan or bond contract.

    • Loan-backed security: An asset created by pooling individual loans (like mortgages) and selling shares in that pool.

    • Stock: A share in the ownership of a company, held by a shareholder.

  • Financial Intermediaries:

    • Institutions that transform funds gathered from many individuals into financial assets.

    • Mutual funds: Financial intermediaries that build a diversified stock portfolio and resell shares of this portfolio to individual investors. They solve the problem of small investors being unable to effectively diversify.

      • Example: Fidelity 500 Index Fund holds diverse company stocks like Apple, Microsoft, Exxon Mobil, Johnson & Johnson, etc.

    • Pension funds: Types of mutual funds that hold assets to provide retirement income to their members.

    • Life insurance companies: Sell policies that guarantee a payment to a policyholder’s beneficiaries when the policyholder dies.

    • Banks: Financial intermediaries that provide liquid assets (bank deposits) to lenders and use those funds to finance the illiquid investment spending needs of borrowers who prefer not to use stock or bond markets.

      • A bank deposit is a financial asset owned by the depositor and a liability of the bank.

  • Macroeconomic Instability from Asset Markets:

    • Asset market fluctuations (e.g., the "Great American Housing Bubble" prior to 2008) can be a source of macroeconomic instability. Policymakers often worry when abnormal asset value increases cause an economic slowdown.

  Present Value and the Time Value of Money

  • The Time Value of Money Principle:

    • A fundamental concept stating that a dollar today is worth more than having a dollar a year from now. This is due to the potential to earn interest or returns on money held today.

  • Present Value (PV):

    • The amount of money needed today to receive a given amount of money at a future date, given the prevailing interest rate ($r$).

    • Basic formula: If you need $1$ dollar in $N$ years, its present value is: PV = rac{$1}{(1 + r)^N}

    • Example 1 (one year): If you need $1,000 in one year and the interest rate on savings is$ r$, the amount you need to put in the bank now ($X$) is:</p><ul><li><p>$X imes (1 + r) = $1,000$</p></li><li><p>Rearranging:$X = rac{$1,000}{(1 + r)}$</p></li></ul></li><li><p><strong>Example 2 (two years):</strong> To determine the present value of$1$dollar realized two years in the future:</p><ul><li><p>If you lend$X$today at an interest rate$r$, you get$X(1 + r)$in one year.</p></li><li><p>Re-lending that sum for another year yields:$X imes (1 + r) imes (1 + r) = X imes (1 + r)^2$</p></li><li><p>So, if$X imes (1 + r)^2 = $1$, then$X = rac{$1}{(1 + r)^2}$</p></li><li><p>If$r = 0.10$, then$X = rac{$1}{(1.10)^2} = rac{$1}{1.21} hickapprox $0.83$</p></li></ul></li></ul></li><li><p><strong>Present Value and Investment Decisions:</strong></p><ul><li><p>An investment is worth making only if it generates a future return whose present value is greater than the monetary cost of making the investment today.</p></li><li><p><strong>Example:</strong> A firm has two projects, each yielding$1,000 in one year:

      • Project 1 requires borrowing $900 today.</p></li><li><p>Project 2 requires borrowing$950 today.

      • If interest rate $r = 10\%$, the present value of $1,000 one year from now is$ rac{$1,000}{(1 + 0.10)} = rac{$1,000}{1.10} hickapprox $909.09$</p></li><li><p>Only Project 1 (cost$900) is worth doing because its initial cost is less than the present value of its future return (900 < $909.09).

      • More projects become worthwhile as the interest rate falls (because the present value of future returns increases).

  • Net Present Value (NPV):

    • The net present value of a project is the present value of current and future benefits minus the present value of current and future costs.

    • NPV Rule: Do all projects that have a positive net present value.

      • By following this rule, a manager maximizes shareholder wealth.

    • Characteristics of Good Projects (leading to high NPV):

      1. High expected future net cash flows.

      2. Low initial outlays.

      3. Low rates of discount (i.e., low interest rates).

  • Economics in Action: Mega Millions Jackpot Example:

    • A Mega Millions jackpot of 656 million was offered either as an annuity over $26$ years or a lump sum of $474 million.</p></li><li><p>The difference arises from the time value of money: The$474 million lump sum represented the present value of the $656 million annuity, calculated by investing the total amount in U.S. government bonds at prevailing interest rates over$26$$ years. This demonstrates how future payments are discounted to their value today.