# Aggregate Expenditure and Equilibrium Output

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Aggregate Expenditure and Equilibrium Output

The Core of Macroeconomic Theory
Chapter is chapter 8 and 9 in the split Chapter is chapter 10 and 11 in the split Chapter 24 is chapter 12 Chapter 25 is chapter 13 Chapter 26 is 14, we skip this chapter.

Aggregate Output and Aggregate Income (Y)
Aggregate output is the total quantity of goods and services produced (or supplied) in an economy in a given period. Aggregate income is the total income received by all factors of production in a given period.

Aggregate Output and Aggregate Income (Y)
Aggregate output (income) (Y) is a combined term used to remind you of the exact equality between aggregate output and aggregate income. When we talk about output (Y), we mean real output, or the quantities of goods and services produced, not the dollars in circulation.

Explaining Spending Behavior
All income is either spent on consumption or saved in an economy in which there are no taxes. Saving / Aggregate Income - Consumption

Household Consumption and Saving
Some determinants of aggregate consumption include: Household income Household wealth Interest rates Households’ expectations about the future In The General Theory, Keynes argued that household consumption is directly related to its income.

Household Consumption and Saving
The slope of the consumption function (b) is called the marginal propensity to consume (MPC), or the fraction of a change in income that is consumed, or spent.

Household Consumption and Saving
The fraction of a change in income that is saved is called the marginal propensity to save (MPS). Once we know how much consumption will result from a given level of income, we know how much saving there will be. Therefore,

An Aggregate Consumption Function Derived from the Equation C = 100 +
An Aggregate Consumption Function Derived from the Equation C = Y At a national income of zero, consumption is \$100 billion (a). For every \$100 billion increase in income (DY), consumption rises by \$75 billion (DC).

Consumption Function (alternative formulation)
-Autonomous consumption -Marginal Propensity to Consume (MPC) If there is no government and no taxes then T=) and DI=Y -Disposable Income (DI) (Income - Net Taxes)

The Determinants of Consumption
Wealth Affects consumption expenditures The price level Affects real purchasing power of financial assets The interest rate Causes consumers to postpone consumption Expectations (of income or prices) A more optimistic outlook on the economy will raise consumers’ expenditures \$ C’’ C C’ Y

Deriving a Saving Function from a Consumption Function
Y - C = S AGGREGATE INCOME (Billions of Dollars) AGGREGATE CONSUMPTION (Billions of Dollars) AGGREGATE SAVING (Billions of Dollars) 100 -100 80 160 -80 175 -75 200 250 -50 400 600 550 50 800 700 1,000 850 150

Planned Investment (I)
Investment refers to purchases by firms of new buildings and equipment and additions to inventories, all of which add to firms’ capital stock. One component of investment—inventory change—is partly determined by how much households decide to buy, which is not under the complete control of firms. change in inventory = production – sales

Actual versus Planned Investment
Desired or planned investment refers to the additions to capital stock and inventory that are planned by firms. Actual investment is the actual amount of investment that takes place; it includes items such as unplanned changes in inventories.

The Planned Investment Function
For now, we will assume that planned investment is fixed. It does not change when income changes. When a variable, such as planned investment, is assumed not to depend on the state of the economy, it is said to be an autonomous variable.

Investment Function Investment is autonomous (independent of income)

Present Value Internal Rate of Return
The Present Value of a stream of payments Where I can be interpreted as the internal rate of return

Present Value Internal Rate of Return
The Present Value of a 100 million Lotto pay off Interest Rate Present Value 6.0% (\$60,790,582.46) 7.0% (\$56,677,976.21) 8.0% (\$53,017,996.00) 9.0% (\$49,750,573.90) 10.0% (\$46,824,600.46) 15.0% (\$35,991,155.97) 20.0% (\$29,217,478.40)

Investment and the Investment Function
Nominal interest rate At this point investment is planned investment expenditures (I) Investment is closely linked to the interest rate, since interest represents the opportunity cost of investing in capital The investment function will shift with changes in expectations for business profits D’ D Investment spending (I)

Autonomous Investment
Although investment is related to the interest rate and business expectations, investment does not depend in any significant way on disposable income As such, investment is “autonomous” However, changes in the interest rate or expectations for profits will still shift autonomous investment \$ I” I I’ Real disposable income

Determinants of Investment
Below are all the things that can cause a shift in the investment function The interest rate Expectations of future profits Technology

Planned Aggregate Expenditure (AE)
Planned aggregate expenditure is the total amount the economy plans to spend in a given period. It is equal to consumption plus planned investment.

Equilibrium Aggregate Output (Income)
Equilibrium occurs when there is no tendency for change. In the macroeconomic goods market, equilibrium occurs when planned aggregate expenditure is equal to aggregate output.

Equilibrium Aggregate Output (Income)
aggregate output / Y planned aggregate expenditure / AE / C + I equilibrium: Y = AE, or Y = C + I Disequilibria: Y > C + I aggregate output > planned aggregate expenditure inventory investment is greater than planned actual investment is greater than planned investment C + I > Y planned aggregate expenditure > aggregate output inventory investment is smaller than planned actual investment is less than planned investment

Equilibrium Aggregate Output (Income)

Equilibrium Aggregate Output (Income)
Deriving the Planned Aggregate Expenditure Schedule and Finding Equilibrium (All Figures in Billions of Dollars) The Figures in Column 2 are Based on the Equation C = Y. (1) (2) (3) (4) (5) (6) AGGREGATE OUTPUT (INCOME) (Y) AGGREGATE CONSUMPTION (C) PLANNED INVESTMENT (I) PLANNED AGGREGATE EXPENDITURE (AE) C + I UNPLANNED INVENTORY CHANGE Y - (C + I) EQUILIBRIUM? (Y = AE?) 100 175 25 200 - 100 No 250 275 - 75 400 425 - 25 500 475 Yes 600 550 575 + 25 800 700 725 + 75 1,000 850 875 + 125

Equilibrium Aggregate Output (Income)
(1) (2) There is only one value of Y for which this statement is true. We can find it by rearranging terms: (3) By substituting (2) and (3) into (1) we get:

The Saving/Investment Approach to Equilibrium
If planned investment is exactly equal to saving, then planned aggregate expenditure is exactly equal to aggregate output, and there is equilibrium.

The S = I Approach to Equilibrium
Aggregate output will be equal to planned aggregate expenditure only when saving equals planned investment (S = I).

The Multiplier The multiplier is the ratio of the change in the equilibrium level of output to a change in some autonomous variable. An autonomous variable is a variable that is assumed not to depend on the state of the economy—that is, it does not change when the economy changes. In this chapter, for example, we consider planned investment to be autonomous.

The Multiplier The multiplier of autonomous investment describes the impact of an initial increase in planned investment on production, income, consumption spending, and equilibrium income. The size of the multiplier depends on the slope of the planned aggregate expenditure line.

The Multiplier Equation
The marginal propensity to save may be expressed as: Because DS must be equal to DI for equilibrium to be restored, we can substitute DI for DS and solve: therefore, , or

The Multiplier After an increase in planned investment, equilibrium output is four times the amount of the increase in planned investment.

The Size of the Multiplier in the Real World
The size of the multiplier in the U.S. economy is about For example, a sustained increase in autonomous spending of \$10 billion into the U.S. economy can be expected to raise real GDP over time by \$14 billion.

The Paradox of Thrift When households become concerned about the future and decide to save more, the corresponding decrease in consumption leads to a drop in spending and income. Households end up consuming less, but they have not saved any more.

Government Expenditures and Autonomous Net Taxes
We will assume that government expenditures (G) and net taxes (T) are autonomous This assumption will keep our models from becoming overly complex It will also allow us to easily analyze fiscal policy as both G and T change It would be possible to consider taxes that vary with GDP (income taxes) \$ G T Real income

Autonomous Net Exports (X - M)
If both exports (X) and imports (M) are autonomous, then net exports are autonomous \$ X’’-M’’ X-M X’-M’ Real disposable income

Determinants of X-M The following will cause a shift in the net export function. The Exchange Rate If the Dollar appreciates, then exports fall and imports rise, both causing net exports to fall, or shift down. Foreign GDP (Income) As foreign income rises, they import more goods from around the world including the US. So our exports will rise as we satisfy their demand for our goods.

Variable Imports \$ Imports may very well be related to income
This makes net exports decrease with income \$ X-M Real disposable income

Aggregate Expenditure and Income

Planned Expenditures What about the behavior (the “plans”) of our economic actors? Consumption (C) is “planned” on the basis of disposable income Investment (I) is “planned” based on the interest rate and business expectations (although it is autonomous with respect to GDP, or income) G and (X-M) are simply autonomous According to Keynes, aggregate planned expenditures (demand) determine output and income, even in the long run

The Income-Expenditure Model
A relationship between aggregate income and planned aggregate expenditures that determines, for a given price level, where income (and GDP) equals planned expenditures The aggregate expenditure function is a relationship showing the amount of planned spending for each level of income Equilibrium occurs in the model where planned aggregate expenditures equal income (GDP) Unintended changes in inventories play a key role

Planned Aggregate Expenditure (trillions of dollars)

Deriving Equilibrium Income and Output
\$ 45o C+I+G+(X-M) Equilibrium Real GDP Real GDP

The Simple Spending Multipliers
\$ C+I’+G+(X-M) 45o C+I+G+(X-M) I Simple spending multiplier = GDP/I = 1/(1-MPC) = 1/MPS GDP Real GDP

The Spending Multiplier and the Circular Flow (MPC = .8)

Keynes and the Great Depression
John Maynard Keynes argued that prices and wages are not sufficiently flexible to ensure the full employment of resources Furthermore, Keynes argued that when resources (especially labor) are not fully employed (due to a lack of private investment expenditures), the government could provide offsetting expenditures as a means of stabilizing the economy Thus, Keynesian economics places emphasis on planned expenditures and all its components

Appendix B--The Algebra of the Income and Expenditure Model

Appendix B--Introducing Variable Imports

Appendix Slides after this point will most likely not be covered in class. However they may contain useful definitions, or further elaborate on important concepts, particularly materials covered in the text book. They may contain examples I’ve used in the past, or slides I just don’t want to delete as I may use them in the future.

Household Consumption and Saving
The relationship between consumption and income is called the consumption function. For an individual household, the consumption function shows the level of consumption at each level of household income.

Income, Consumption, and Saving (Y, C, and S)
A household can do two, and only two, things with its income: It can buy goods and services—that is, it can consume—or it can save. Saving (S) is the part of its income that a household does not consume in a given period. Distinguished from savings, which is the current stock of accumulated saving.

An Aggregate Consumption Function Derived from the Equation C = 100 +
An Aggregate Consumption Function Derived from the Equation C = Y AGGREGATE INCOME, Y (BILLIONS OF DOLLARS) AGGREGATE CONSUMPTION, C (BILLIONS OF DOLLARS) 100 80 160 175 200 250 400 550 800 700 1,000 850

Aggregate Demand and Changes in the Price Level
An increase in the price level has a negative impact on real GDP for three reasons As the price level increases the real value of fixed financial assets is diminished. This reduces consumption demand and GDP. An increase in the price level puts upward pressure on interest rates and downward pressure on investment As the price level increases, foreign goods become more attractive Of course all of these effects are reversed for a decrease in the price level

The Aggregate Demand Curve
Y P AE (P) 45o AE’’ (P’’) AE’ (P’) P’ P’’ AD

Shifts in the Aggregate Demand Curve

Appendix A--Variable Net Exports
X-M Real GDP C+I+G P C+I+G+(X-M) Real GDP

The Circular Flow of Income and Expenditure
aggregate income = GDP transfer payments taxes Disposable income Financial markets consumption (C) S Investment (I) Gov’t (G) X-M C+I+G+X-M

Review Terms and Concepts
actual investment aggregate income aggregate output aggregate output (income) (Y) autonomous variable change in inventory consumption function desired, or planned, investment (I) equilibrium identity investment marginal propensity to consume (MPC) marginal propensity to save (MPS) multiplier paradox of thrift planned aggregate expenditure (AE) saving (S)

Consumption and Aggregate Expenditure

Classical Economists A group of 18th- and 19th-century economists who believed that recessions and depressions were short-run phenomena that corrected themselves through natural market forces; thus the economy was self-adjusting

Consumption Consumption is the portion of disposable income that is spent and not saved Consumption spending bears a close relationship to disposable income Consumption makes up the largest share of aggregate planned expenditures Approximately 2/3 of GDP

The Consumption and Savings Functions
\$ C C DI MPC = C/DI \$ real disposable income S MPS = S/DI real disposable income

The Marginal Propensity to Consume and Save
The marginal propensity to consume (MPC) is the fraction of a change in income that is spent on added consumption The marginal propensity to save (MPS) is the fraction of a change in income that is devoted to added savings 0 < MPC < 1 MPS = 1 - MPC

Planned Versus Actual Investment
Planned investment is the amount of investment firms plan to undertake during a year Actual investment is the amount of investment actually undertaken during a year Actual investment equals planned investment plus unplanned changes in inventories

The Income Half of the Circular Flow
Since profits (the difference between expenditures on output and production-related costs) are paid to firms’ owners, GDP equals income: GDP = Aggregate Income Since disposable income is aggregate income minus taxes (less transfer payments), GDP must equal disposable income (DI) plus net taxes (T): GDP = Aggregate income = DI + T

The Expenditure Half of the Circular Flow
Disposable income is either spent on consumption (C) or put into savings (S): DI = C + S From an earlier chapter, aggregate expenditure has four components Consumption (C), Investment (I), Government Purchases (G) , Net Exports (X - M) As a result, C + I + G + ( X - M ) = GDP

Leakages Equal Injections
The two equalities for GDP written together give, GDP = Y=DI + T = C + I + G + ( X - M ) Since S = DI - C S + T + M = I + G + X (leakages = injections)

Leakages and Injections
A leakage is any diversion of income from the domestic spending stream An injection is any payment of income other than by firms, or any spending other than by domestic households