Notes on Output and Spending in Macroeconomics

Fundamental Definitions of Output and Spending

• Measuring Output (Supply):

  • The output of an economy is a measure of its supply, typically quantified through metrics like Gross Domestic Product ($GDP$).

  • $GDP$ represents the value in dollars of all goods and services produced within the economy by individuals with paying jobs in a given year.

  • Equivalently, it is the total amount in dollars that people are paid to produce goods and services within that year.

  • $GDP$ serves as a dual measure of both total output and total income (based on the payment individuals receive for production).

• Measuring Spending (Demand):

  • Aggregate Demand ($AD$) (also referred to as planned aggregate expenditure or aggregate spending) measures how much is spent on goods and services produced within the domestic economy.

  • The link between aggregate demand and output is critical for determining macroeconomic variables such as unemployment.

The Keynesian Model of Labor and Production

• The Causality of Unemployment:

  • A change in aggregate spending leads to a change in output.

  • A change in output causes a change in employment levels.

  • A change in employment leads to a change in the unemployment rate.

  • This framework was developed by John Maynard Keynes, an influential British economist whose theories gained prominence following the Great Depression.

• Producers’ Reaction to Inventory Holdings:

  • Case 1 (GDP > AD): If production exceeds demand, businesses experience inventory accumulation. In response, they decrease production, causing $GDP$ to fall.

  • Case 2 (GDP < AD): If demand exceeds production, businesses experience inventory depletion. In response, they increase production, causing $GDP$ to rise.

  • Macroeconomic Equilibrium: Occurs when $GDP = AD$, resulting in no unintended change in inventory holdings.

Components of Aggregate Demand ($AD$)

• General Equation:     −− $AD = C + I + G + (X - M)$ −−

• Consumption ($C$): Specifically identifies spending by households on final goods and services.

• Investment ($I$): Spending by businesses on new equipment, residential construction, nonresidential construction, and changes in the value of inventories.

  • Fixed Investment: Includes equipment and construction components.

• Government Spending ($G$): Spending by local, state, and federal levels on goods and services (e.g., education, defense, legal services, infrastructure).

  • Exclusions: Transfer payments (e.g., $SNAP$, Pell Grants, Social Security) are excluded because they do not involve the exchange of a good or service.

• Net Exports ($X - M$):

  • Exports ($X$): Spending by foreign entities on domestically produced goods.

  • Imports ($M$): Spending by domestic entities on goods produced in other countries.

  • Calculation Logic: Imports are subtracted from the $AD$ equation because $C$, $I$, and $G$ already include spending on foreign goods. To isolate demand for domestic output, imports must be removed.

• Global Decomposition of GDP (2013 Data):

  • United States: $C = 68.4\%$, $G = 15.1\%$, $I = 19.1\%$, Inventory Change = $0.4\%$, $X = 13.6\%$, $M = 16.6\%$.

  • Eurozone (19 countries): $C = 55.9\%$, $G = 21.1\%$, $I = 19.5\%$, Inventory Change = $0.0\%$, $X = 43.9\%$, $M = 40.5\%$.

  • China: $C = 37.3\%$, $G = 14.1\%$, $I = 47.3\%$, Inventory Change = $2.0\%$, $X = 26.2\%$, $M = 23.8\%$.

The Consumption Function and Household Behavior

• Determinants of Consumption:

  • Disposable Income ($Y_D$): Defined as total income ($Y$) plus government transfers ($TR$) minus taxes and fees ($TA$).         −− $Y_D = Y + TR - TA$ −−

  • Wealth: Total assets (houses, cars, financial holdings) minus liabilities (loans, debt). Wealth is a stock variable, whereas income is a flow variable.

  • Interest Rates: Influences both borrowers (higher rates usually decrease consumption) and savers.

  • Credit Availability: Households may be credit-constrained, limiting spending despite desire.

  • Consumer Expectations: Optimism or pessimism regarding future employment and income. For example, the University of Michigan consumer sentiment survey assesses own finances, short-term economy, and long-term economy.

• Propensities to Consume and Save:

  • Marginal Propensity to Consume ($MPC$ ): $MPC = \frac{\Delta C}{\Delta Y_D}$.

  • Marginal Propensity to Save ($MPS$): $MPS = \frac{\Delta S}{\Delta Y_D}$.

  • Relationship: $MPC + MPS = 1$.

  • Average Propensity to Consume ($APC$): $APC = \frac{C}{Y_D}$.

  • Average Propensity to Save ($APS$): $APS = \frac{S}{Y_D}$. This is also the saving rate.

• Linear Consumption Function Model:

  • Formula: $C = c_0 + c_1 Y$.

  • $c_0$: Autonomous consumption (spending independent of income).

  • $c_1$: The $MPC$.

  • Movements vs. Shifts: Changes in disposable income cause a movement along the function. Changes in wealth, interest rates, or expectations cause a shift in the entire function.

Consumption Smoothing

• Definition: Households prefer to keep their consumption of goods and services relatively constant rather than letting it fluctuate with income shocks.

• Mechanisms:

  • Self-insurance/Co-insurance: Saving during favorable periods, borrowing during unfavorable ones, or receiving aid from family/friends.

  • Institutional Support: Taxes and benefits allow resources to move from lucky to unlucky households.

• Types of Risk:

  • Household-level risk: Specific events like a house fire, job loss, or illness.

  • Economy-wide risk: Region-wide disasters or global pandemics (e.g., COVID-19).

• Limitations:

  • Credit constraints (difficulty borrowing).

  • Weakness of will or procrastination (difficulty saving).

  • Absence of formal or informal insurance markets.

Investment Dynamics

• Volatility: Investment is significantly more volatile than both $GDP$ and consumption. While households smooth consumption, firms may delay investment during periods of pessimism and surge during periods of confidence.

• Determinants of Investment Spending:

  • Interest Rate: Higher rates increase the cost of borrowing (external finance) and the opportunity cost of using internal funds (internal finance), leading to lower investment.

  • Expected Rate of Return on Capital: Comparing capital cost with net gains. This is higher if expected revenue increases, the price of capital falls, or operating costs decrease.

Net Exports Determinants

• Incomes: Higher domestic income leads to more imports ($M$); higher foreign income leads to more exports ($X$).

• Exchange Rates:

  • Determines the price of a dollar in foreign currency (e.g., $1$ dollar = $0.85$ euros).

  • Appreciation (Rise of dollar): Foreign price of dollar increases; exports fall, imports rise.

  • Depreciation (Fall of dollar): Dollar price of units of foreign currency rises; exports rise, imports fall.

The Keynesian Cross Model

• Visualization:

  • Horizontal Axis: Real $GDP$/Income ($Y$).

  • Vertical Axis: Aggregate Demand ($AD$).

  • $45$-Degree Line: Represents all points where $AD = GDP$.

  • Macroeconomic Equilibrium: The point where the $AD$ function intersects the $45$-degree line.

• Numerical Equilibrium Example:

  • Given: $C = 20 + 0.9 Y_D$, $TA = 0.2 Y$, $I = 70$, $G = 80$, $X = 50$, $M = 0.2 Y_D$.

  • Disposable Income: $Y_D = Y - 0.2 Y = 0.8 Y$.

  • Steps:

    1. $Y = [20 + 0.9(0.8 Y)] + 70 + 80 + 50 - 0.2(0.8 Y)$

    2. $Y = 220 + 0.72 Y - 0.16 Y$

    3. $Y = 220 + 0.56 Y$

    4. $0.44 Y = 220$

    5. $Y = 500$

The Spending Multiplier Process

• The Concept: Initial spending becomes income for another person, who then spends a portion, creating more income. Consequently, an initial increase in spending increases output by more than the original amount.

• Formulas:

  • $\text{Multiplier} = \frac{\text{Total } \Delta GDP}{\text{Initial } \Delta \text{Spending}} = \frac{1}{1 - MPC}$.

  • Example with $MPC = 0.8$ and $\text{Initial Spending} = 100$:

    1. Initial increase: $100$.

    2. Round two: $100 \times 0.8 = 80$.

    3. Round three: $80 \times 0.8 = 64$.

    4. Total change: $100(1 + 0.8 + 0.8^2 + 0.8^3 + \dots) = 100 \times \frac{1}{1 - 0.8} = 100 \times 5 = 500$.

• Factors Reducing the Multiplier Size:

  • Taxes: Proportional taxes reduce the amount of income that becomes disposable income.

  • Imports: Spending on foreign goods removes money from the domestic circular flow.

  • Saving: Withdrawing money from the spending stream.

  • Open Economy Multiplier Formula:         −− $\text{Multiplier} = \frac{1}{1 - (1 - t)MPC + MPI}$ −−         (where $t$ is tax rate and $MPI$ is marginal propensity to import).

The Aggregate Demand/Aggregate Supply ($AS/AD$) Model

• Axes: Real $GDP$ ($X$-axis) and Price Level ($Y$-axis).

• Aggregate Demand ($AD$) Curve:

  • Downward sloping due to three effects:

    1. Wealth Effect: Higher prices erode the value of non-inflation-linked assets, reducing consumption ($C$).

    2. Interest Rate Effect: Higher prices increase demand for money/credit, driving up interest rates and reducing investment ($I$) and consumption ($C$).

    3. Foreign Price Effect: Higher domestic prices relative to foreign prices reduce exports and increase imports.

  • Shifts: Fiscal policy ($G$, $TR$, $TA$), Monetary policy (money supply), saving preferences, wealth changes (unrelated to output prices), and business expectations.

• Long-Run Aggregate Supply ($LRAS$):

  • A vertical line at Potential $GDP$ (full-employment $GDP$).

  • Assumes long-run flexibility in all prices and wages (no stickiness).

  • Depends on technology, resources, laws, and institutions.

• Short-Run Aggregate Supply ($SRAS$):

  • An upward-sloping line.

  • Why? Sticky wages/input costs mean higher output prices temporarily increase profit margins.

  • Shape: Flatter at low $GDP$ (slack resources) and steeper as $GDP$ approaches potential.

  • Transpassing Potential: $SRAS$ can go beyond $LRAS$ temporarily (e.g., overtime, pushing machines), but this is costly and unsustainable.

• Shifts in Supply:

  • Quantity of inputs or productivity shifts both $LRAS$ and $SRAS$.

  • Increased input costs (e.g., energy prices) shift $SRAS$ left but do not change Potential $GDP$ ($LRAS$).

Macroeconomic Equilibrium and Shocks

• Demand-Pull Inflation: An increase in $AD$ shifts the curve right, resulting in higher prices and higher $GDP$.

• Cost-Push Inflation (Stagflation): $SRAS$ shifts left due to input cost increases, resulting in higher prices but lower $GDP$.

• Output Gap: The difference between current $GDP$ and Potential $GDP$.

Theoretical Perspectives

• Keynesian Perspective:

  • Focuses on aggregate demand as the primary driver of business cycles.

  • Emphasizes wage and price stickiness.

  • Inflation may be a necessary trade-off for lower unemployment.

  • Most applicable in the short run or deep recessions.

• Neoclassical Perspective:

  • Focuses on aggregate supply as the key determinant of output/employment.

  • Sees inflation as a cost with no unemployment benefit.

  • Most applicable in the long run.

• AS Curve Zones:

  • Keynesian Zone: Far left of $SRAS$; shifts in $AD$ affect output but not price level.

  • Neoclassical Zone: Far right of $SRAS$ (near vertical); shifts in $AD$ affect prices but not output.

  • Intermediate Zone: Middle of $SRAS$; shifts in $AD$ affect both output and price level.