编程辅导 MGEA06 Week 5 (Recorded Lecture) Iris Au 1

Chapter 11 – Income and Expenditure
This chapter aims at developing the income-expenditure model (aggregate expenditure model) – a simply model of output determination.
• Derive the consumption function
• Derive the investment function.

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• Develop the income-expenditure model.
• Examine the adjustment process under the income-expenditure model.
• Do some comparative statics under the income-expenditure model.
MGEA06 Week 5 (Recorded Lecture) Iris Au 1

Consumer Spending
Assumptions:
1) Households split their disposable income (YD = Y – T + TR) between spending and savings, i.e., YD = C + SPrivate.
 When there is a change in disposable income, households divide the change
in disposable income between change in consumption and change in (private) savings.
YD = Consumption + Sprivate
2) Households spend a constant fraction of the increase in their current
disposable income on final goods and services.
The marginal propensity to consume (MPC), the change in consumption
for a given change in disposable income, is constant
MPC = ∆ Consumption = ∆C = constant (i.e., 1 > MPC > 0)
 Given any change in disposable income is split between consumption and savings, then marginal propensity to save (MPS) + MPC = 1.
• Consumption is positively related to current disposable income.
• A simple (aggregate) consumption function:
C = C(YD) = Autonomous consumption (AC) + MPC × YD C C = AC + MPC × YD
∆Disposable income ∆YD
MGEA06 Week 5 (Recorded Lecture) Iris Au

Shifts of the Aggregate Consumption Function (i.e., Changes in AC)
Changes in Expected Future Disposable Income
• Holding all else constant, autonomous consumption (AC) increases when
expected future disposable income increases.
• The permanent income hypothesis argues that consumption ultimately
depends on the income households expected to have over the long run rather than on their current income.
 Households are forward looking and care about the future  when deciding
how much to consume today, households take their future expected income into consideration, so they treat a temporary increase income in very different way than a permanent increase in income.
 If there is a temporary increase in income, households would save most of the increase in income and just spend a small portion of the increase in income now.
 If there is a permanent increase in income, households would spend most of the increase in income now.
MGEA06 Week 5 (Recorded Lecture) Iris Au 3

Changes in Aggregate Wealth
• Holding all else constant, an increase in households’ wealth leads to an
increase in autonomous consumption.
 The life-cycle hypothesis argues households plan their consumption over
their lifetime, and they try to smooth out their consumption over their lifetime by saving some of their current income during their peak earning years and running down the wealth accumulated after retirement.
Investment Spending
• Investment is the most volatile component in GDP.
• In fact, most of the recessions originate from a fall in investment.
• Actual investment consists of 2 types of investment:
1) Planned investment (IPlanned) – the level of investments that businesses intend to undertake.
2) Unplanned investment (IUnplanned) – unexpected changes in inventories.
IActual = IPlanned + IUnplanned
MGEA06 Week 5 (Recorded Lecture) Iris Au 4

Planned Investment
• Planned investment (IPlanned) refers to the level of investment that firms intend to undertake during a given period.
Factors that affect planned investment:
1) Interest Rate
• Given the returns on investment are predetermined (Chapter 10), an increase in interest rate raises the cost of investment  planned investment falls.
• Planned investment is inversely related to the interest rate (Chapter 10).
2) Expected Future Real GDP
• The accelerator principle suggests an increase in expected future real GDP growth rate (for a given current level of production capacity) leads to an increase in planned investment because firms need to undertake more investment now in order to meet the higher demand for their products in the future due to higher future real GDP growth.
• Planned investment is positively related to the future real GDP growth.
• A typical planned investment function: IPlanned = IPlanned(i)
IPlanned = Autonomous investment (AI) – d  i, where d > 0.
MGEA06 Week 5 (Recorded Lecture) Iris Au

Inventories and Unplanned Investment Spending
• Firms hold inventories to avoid disruption in the production process and to avoid missing any unforeseen changes in sales.
• Inventory investment refers to the change in the value of total inventories during a given period; it includes quantity of goods (including materials and supplies) that firms hold in storage, work in process, and finished goods.
Inventory investment = Inventories
• Note: It is possible for inventory investment to be negative!
• Since it is very difficult to predict future sales accurately, firm may find themselves hold more or less inventories than they desired/planned.
 These unexpected changes in inventories are called unplanned inventory
investment and are equal to unplanned investment. IUnplanned = unplanned inventory investment.
Actual Investment
• Actual investment (IActual or I for short) refers to the level of investment that the economy has undertaken in a given period of time.
I = IActual = IPlanned + IUnplanned I = [AI – d  i] + IUnplanned
MGEA06 Week 5 (Recorded Lecture) Iris Au 6

The Income-Expenditure Model
• The income-expenditure model is a simple model of output determination, which examines the chain reaction of an initial change in autonomous expenditure (AE0) on output so that we can explain the business cycles.
 Autonomous expenditure is the desired level of spending by all sectors in
the economy (households, firms, government, and the rest of the world)
that is not affected by the level of real GDP.
• The income-expenditure model argues that the ultimate change in output (Y)
for a given change in autonomous expenditure (AE0) is: Y = M × AE0, where M = the multiplier.
Assumptions of the Income-Expenditure Model (In the Meantime)
• Producers are willing supply additional output at a fixed price  change in aggregate expenditure leads to change in aggregate output (real GDP).
 G = G, T = T (lump-sum taxes), and TR = TR (lump-sum transfers). 00
• Exports and imports are given.
 X = X0 (autonomous exports) and IM = IM0 (autonomous imports).
• Interest rate is held fixed. ̅
• Government spending, taxes and transfers are given.
MGEA06 Week 5 (Recorded Lecture) Iris Au 7

Planned Aggregate Expenditure and Real GDP
• Planned aggregate expenditure (or planned expenditure) refers to the desired/planned level of spending by all sectors in the economy.
AEPlanned = C + IPlanned + G + X – IM
AEPlanned = (AC + MPC × YD) + (AI – d × i) + G + X0 – IM0  Since YD = Y – T + TR = Y – T0 + TR0
AEPlanned = [AC + MPC × (Y – T0 + TR0)] + (AI – d × i) + G + X0 – IM0
AEPlanned = AE0 + MPC × Y
Real GDP, Y
MGEA06 Week 5 (Recorded Lecture) Iris Au

Income-Expenditure Equilibrium
Planned aggregate expenditure:
National income: (Actual expenditure)
AEPlanned = C + IPlanned + G + X – IM AEPlanned = AE0 + MPC × Y
Y = C + IActual + G + X – IM
Y = C + (IPlanned + IUnplanned) + G + X – IM Y = AEPlanned + IUnplanned
• Equilibrium in income-expenditure model is defined as the level of output such that actual expenditure is equal to planned expenditure.
For actual expenditure and planned expenditure to be the same, we need
IActual = Iplanned (i.e., IUnplanned = 0).
GDP = Y = AEPlanned
AEPlanned = Y
The Keynesian Cross Diagram
45 MGEA06 Week 5 (Recorded Lecture)

The Multiplier Process and Inventory Adjustment
The Multiplier
• Earlier we stated that the income-expenditure model argues that:
Y = M × AE0, where M = the multiplier.
• The multiplier (M) measures the change in equilibrium output/income that
results from a unit change in autonomous expenditure, i.e., M = ∆Y* . ∆AE0
• We can derive the multiplier from the income-expenditure model. Equilibrium: Y = AEPlanned
Y = AE0 + MPC × Y
• Note: In here, a unit change in AE0 will lead to more than a unit change in Y. It is because when person 1 spends more, person 2 finds his/her income rises (recall, one’s spending = another’s income), this allows person 2 to spend more on goods and services and increase the income of person 3. The multiplier process just summarizes the overall effect of the initial change in spending by person 1 on total output. (see textbook for details)
MGEA06 Week 5 (Recorded Lecture) Iris Au 10

Example: Finding Equilibrium Level of Output & the Adjustment Process Suppose a closed economy can be described as follows:
Consumption: Investment: Government spending: (Lump-sum) Taxes: (Lump-sum) Transfers:
C = 58 + 0.8YD
IPlanned = 96 – 100i, & i̅ = 0.06 (i = 6%) G = 20
T = T0 = 15
TR = TR0 = 5
• Step 1: Express the consumption function as a function of Y.
• Step 2: Derive the planned expenditure, AEPlanned, function.
• Step 3: Solve for the equilibrium level of output.
MGEA06 Week 5 (Recorded Lecture) Iris Au 11

AEPlanned = Y
AEPlanned = 160 + 0.8Y
• Suppose the initial level of output, Y0, is 740, what will happen?
 If Y = 740, AEPlannded =
Implications:
• If the initial Y < Y*, IUnplanned < 0  production   Y  to Y*. • If the initial Y > Y*, IUnplanned > 0  production   Y  to Y*.
The initial level of Y DOES NOT matter, the economy will always adjust itself
and converge to Y*.
MGEA06 Week 5 (Recorded Lecture) Iris Au 12

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