Chapter 11: Income and Expenditure

THE MULTIPLIER: AN INFORMAL INTRODUCTION (1 of 5)

  • A rise or fall in aggregate expenditure leads to changes in income, which further leads to changes in aggregate expenditure.

  • Four simplifying assumptions are made:

    1. Producers are willing to supply additional output at a fixed price, meaning changes in aggregate expenditure translate to changes in aggregate output (NOT price).

    2. The interest rate is taken as given.

    3. There is no government spending and no taxes in this analysis.

    4. Exports and imports are zero.

THE MULTIPLIER: AN INFORMAL INTRODUCTION (2 of 5)

  • Example Scenario: Suppose home builders sp

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  • end an extra $10 billion on home construction.

    • Aggregate output will increase by $10 billion immediately.

    • This increase in aggregate output will lead to increased profits and wages flowing to households, further increasing consumer spending.

    • Increased consumer spending induces firms to increase output again, creating multiple rounds of expenditure increases.

THE MULTIPLIER: AN INFORMAL INTRODUCTION (3 of 5)

  • Marginal propensity to consume (MPC): defined as the increase in consumer spending when disposable income increases by $1.

    • Formula: MPC = \frac{\Delta c}{\Delta disposable\ income}

    • Example: If consumer spending rises by $6 when disposable income rises by $10, then MPC = \frac{6}{10} = 0.6.

  • Marginal propensity to save (MPS): the fraction of additional disposable income that is saved, defined as:

    • MPS = 1 - MPC

THE MULTIPLIER: AN INFORMAL INTRODUCTION (4 of 5)

  • The initial $100 billion increase in investment spending causes real GDP to increase by $100 billion.

  • Subsequent increases in GDP can be calculated as:

    • Second-round increase: MPC \times 10\ billion

    • Third-round increase: MPC \times MPC \times 10\ billion

  • After infinitely many rounds, the total effect on real GDP can be computed from the infinite series:

    • Total\ increase\ in\ GDP = (1 + MPC + MPC^2 + MPC^3 + … ) \times 10\ billion

    • Utilizing the formula for a geometric series:

    • If x is between 0 and 1: \frac{1}{1-x} thus:
      Total\ increase\ in\ GDP = \frac{1}{1-MPC} \times 10\ billion

THE MULTIPLIER: AN INFORMAL INTRODUCTION (5 of 5)

  • It's crucial to distinguish between the initial change and the additional change in aggregate expenditure through the process of change unfolding.

  • The term autonomous change in aggregate expenditure refers to the initial change in aggregate expenditure at a given level of real GDP.

  • The multiplier can be mathematically expressed as:

    • Multiplier = \frac{\Delta Y}{\Delta AE_0}

    • Here, \Delta Y = change in real GDP; \Delta AE_0 = autonomous change in aggregate expenditure.

LEARN BY DOING: DISCUSSION QUESTION 1

  • Scenario: Given an MPS of 0.2 and an increase in investment spending of $200 this year, trace out the total increase in real GDP, showing the increase in consumer spending for the second, third, and fourth rounds of spending.

  • The analysis assumes no government sector, no taxes, and no transfers with fixed price levels.

  • Solution: Total increases = $200 + $160 + $128 + $102.4 … totaling $1,000.

LEARN BY DOING: PRACTICE QUESTION 1

  • Question: Holding everything else constant in an economy, the larger the MPS, the _____.

  • Options:
    a) smaller the value of the multiplier
    b) larger the value of the multiplier

  • Correct Answer: a) smaller the value of the multiplier.

CONSUMER SPENDING

  • Consumer spending typically constitutes almost 60% of total spending on final goods and services.

  • The primary determinant of consumer spending is current disposable income.

CURRENT DISPOSABLE INCOME AND CONSUMER SPENDING (1 of 4)

  • Current disposable income: income after taxes and government transfers.

  • Example: Average income in 2021 = $68,650; Average spending = $61,875.

CURRENT DISPOSABLE INCOME AND CONSUMER SPENDING (2 of 4)

  • Individual consumption function: an equation illustrating how a household's consumer spending varies with its disposable income:

    • c = ac + MPC \times yd

    • Where:

      • c = household's consumer spending

      • y_d = household disposable income

      • MPC = marginal propensity to consume

      • a_c = autonomous consumer spending.

CURRENT DISPOSABLE INCOME AND CONSUMER SPENDING (3 of 4)

  • Recall: MPC = \frac{\Delta c}{\Delta y_d}

  • Rearranging gives:

    • MPC \times \Delta y_d = \Delta c

  • This means for every $1 increase in disposable income, consumer spending rises by MPC x $1.

THE CONSUMPTION FUNCTION

  • The variable ac denotes individual household autonomous consumer spending: the value of c when yd equals zero—indicating a consumption level without any income.

  • The MPC represents the slope of the function (rise over run).

LEARN BY DOING: PRACTICE QUESTION 2

  • Scenario: When Sue’s disposable income is $10,000, she spends $8,000; at $20,000, she spends $14,000.

  • Questions:

    • Determine Sue’s autonomous consumer spending and MPS.

  • Correct answers: Autonomous consumer spending is $2,000; MPS is equal to 0.6.

A CONSUMPTION FUNCTION FITTED TO DATA

  • Autonomous spending approximated at $28,712; with MPC = 0.46.

  • Fitted consumption function: C = 28,712 + 0.46y_d

CURRENT DISPOSABLE INCOME AND CONSUMER SPENDING (4 of 4)

  • Aggregate consumption function: appears similarly structured as the individual consumption function, showing the relationship for the entire economy between aggregate disposable income and aggregate consumer spending.

    • C = AC + MPC \times YD

LEARN BY DOING: PRACTICE QUESTION 3

  • Given conditions of aggregate consumer spending at $5,000 when disposable income is zero and a $70 increase in spending with $300 to $400 disposable income increase, determine the equation for the aggregate consumption function.

  • Correct answer: C = 5,000 + 0.7YD.

SHIFTS OF THE AGGREGATE CONSUMPTION FUNCTION

  • Shifts occur due to changes in expected future disposable income and changes in aggregate wealth.

    • Changes in expected future income affect consumer spending based on perceived long-term earnings reflecting on the permanent income hypothesis.

    • Changes in aggregate wealth, driven by market fluctuations such as the stock market rise, can shift the consumption function upward.

INVESTMENT SPENDING (1 of 2)

  • Investment spending, though smaller than consumer spending, drives cycles of economic booms and recessions.

INVESTMENT SPENDING (2 of 2)

  • Planned investment spending: reflects the investment that firms intend to undertake over a given period, determined by:

    1. Interest rate

    2. Expected future real GDP

    3. Current production capacity.

THE INTEREST RATE AND INVESTMENT SPENDING

  • Firms will proceed with an investment project if expected returns justify project costs. Increased interest rates reduce project feasibility. Conversely, falling rates promote project funding.

  • Retained earnings play a role in opportunity costs relating to their investment decisions.

EXPECTED FUTURE REAL GDP, PRODUCTION CAPACITY, AND INVESTMENT SPENDING

  • Firms will reduce investment if current capacity is high and expected sales increases are low.

  • The accelerator principle states that a higher GDP growth leads to increased investment spending, while lower growth levels correlate with lower investment spending.

INVENTORIES AND UNPLANNED INVESTMENT SPENDING

  • Inventories: goods stocks held for future sales.

  • Inventory investment: the total value change of inventories over a time period.

  • Unplanned inventory investment: occurs from unexpected changes in actual sales compared to expectations.

  • Actual investment spending formula: I = I{Unplanned} + I{Planned}.

THE INCOME–EXPENDITURE MODEL (1 of 2)

  • Investigation into how spending changes lead to GDP changes through inventory adjustments yielding multipliers.

THE INCOME–EXPENDITURE MODEL (2 of 2)

  • Underlying assumptions influencing the multiplier process include:

    • Changes in overall spending directly relate to aggregate output changes.

    • Interest rate remains unchanged.

    • Absence of taxes or government transfers.

    • No exports or imports involved.

PLANNED AGGREGATE EXPENDITURE AND REAL GDP (1 of 2)

  • With no taxes/ transfers, GDP = C + I holds; thus YD = GDP, maintaining function of both consumption and investment within aggregate functions.

PLANNED AGGREGATE EXPENDITURE AND REAL GDP (2 of 2)

  • Example: With C = 300 + 0.6 \times YD generate a table of equilibrium linking real GDP with planned aggregate expenditures.

INCOME–EXPENDITURE EQUILIBRIUM (1 of 5)

  • Economy stabilizes at the point where no unplanned inventory investments exist.

  • Table illustrates equilibrium dynamics of aggregate expenditure against GDP.

INCOME–EXPENDITURE EQUILIBRIUM (2 of 5)

  • Planned aggregate expenditure differs from real GDP contingent upon unplanned inventory levels.

  • Situational outcomes illustrated by overproducing or underproducing relative to sales estimates.

LEARN BY DOING: PRACTICE QUESTION 4

  • Question asked under condition of planned aggregate expenditure of $500 with a real GDP of $600.

  • Correct answer: unplanned increases in inventories are occurring.

INCOME–EXPENDITURE EQUILIBRIUM (3 of 5)

  • The relationship shows inventory changes based on the adequacy of aggregate output to meet expenditures, with projections for output adjustments devoid of price changes.

INCOME–EXPENDITURE EQUILIBRIUM (4 of 5)

  • Defined income–expenditure equilibrium, Y^*, where the real GDP equals planned aggregate expenditure.

INCOME–EXPENDITURE EQUILIBRIUM (5 of 5)

  • Income-expenditure equilibrium illustrated in graphical form, demonstrating equilibrium points on the Keynesian cross.

LEARN BY DOING: DISCUSSION QUESTION 2

  • Inquiry into conditions when output exceeds expenditures to evaluate consumption and inventory levels in relation to equilibrium.

THE MULTIPLIER PROCESS AND INVENTORY ADJUSTMENT (1 of 3)

  • The relationship between shifts in planned aggregate expenditure dimensions and outcomes.

THE MULTIPLIER PROCESS AND INVENTORY ADJUSTMENT (2 of 3)

  • Establishing mathematical relationships among increments in planned aggregate expenditure and GDP changes, reflecting MPS interactions.

THE MULTIPLIER PROCESS AND INVENTORY ADJUSTMENT (3 of 3)

  • Disparities between planned expenditures and aggregate output highlighted by changes in inventory statuses serve as economic predictors.

THE PARADOX OF THRIFT

  • Individual actions can collectively yield undesired outcomes, seen in economic downturns when investment spending decreases, causing an expansive fall in income–expenditure equilibrium GDP, leading individuals worse off than if spending had not been reduced.

WHAT ABOUT EXPORTS AND IMPORTS? (1 of 2)

  • Discussion of incorporating international trade into the model, defining exports as akin to autonomous expenditure increases.

WHAT ABOUT EXPORTS AND IMPORTS? (2 of 2)

  • Trade interrelations yield joint economic cycles, indicating simultaneous recessions and recoveries across nations.