Intermediate Ecnomics

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Income and Spending

Chapter #10 (DFS)

Introduction

Why output fluctuates around its potential level?
In business cycle booms and recessions, output rises and falls relative to the trend of potential output
Model in this chapter assumes a mutual interaction between output and spending: spending determines output and income, but output and income also determine spending
The Keynesian model develops the theory of AD
Assume that prices do not change at all and that firms are willing to sell any amount of output at the given level of prices  AS curve is flat
Key finding: increases in autonomous spending generate additional increases in AD

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AD and Equilibrium Output

AD is the total amount of goods demanded in the economy: (1)
Output is at its equilibrium level when the quantity of output produced is equal to the quantity demanded, or (2)
When AD is not equal to output there is unplanned inventory investment or disinvestment: (3), where IU is unplanned additions to inventory
If IU > 0, firms cut back on production until output and AD are again in equilibrium

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The Consumption Function

Consumption is the largest component of AD
Consumption increases with income  the relationship between consumption and income is described by the consumption function
If C is consumption and Y is income, the consumption function is (4), where and
The intercept of equation (4) is the level of consumption when income is zero  this is greater than zero since there is a subsistence level of consumption
The slope of equation (4) is known as the marginal propensity to consume (MPC)  the increase in consumption per unit increase in income

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The Consumption Function

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Consumption and Savings

Income is either spent or saved  a theory that explains consumption is equivalently explaining the behavior of saving
More formally, (5)  a budget constraint
Combining (4) and (5) yields the savings function:

(6)

Saving is an increasing function of the level of income because the marginal propensity to save (MPS), s = 1-c, is positive
Savings increases as income rises
Ex. If MPS is 0.1, for every extra dollar of income, savings increases by $0.10 OR consumers save 10% of an extra dollar of income

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Consumption, AD, and
Autonomous Spending

Now we incorporate the other components of AD: G, I, taxes, and foreign trade (assume autonomous)
Consumption now depends on disposable income,

(7) and (8)

AD then becomes

(9)

where A is independent of the level of income, or autonomous

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Consumption, AD, and
Autonomous Spending

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Equilibrium Income and Output

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Equilibrium occurs where Y=AD, which is illustrated by the 45° line  point E
The arrows show how the economy reaches equilibrium
At any level of output below Y0, firms’ inventories decline, and they increase production
At any level of output above Y0, firms’ inventories increase, and they decrease production

The Formula for Equilibrium Output

Can solve for the equilibrium level of output, Y0, algebraically:
The equilibrium condition is Y = AD (10)
Substituting (9) into (10) yields (11)
Solve for Y to find the equilibrium level of output:

(12)

The equilibrium level of output is higher the larger the

MPC and the higher the level of autonomous spending.

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The Formula for Equilibrium Output

Equation (12) shows the level of output as a function of the MPC and A
Frequently we are interested in knowing how a change in some component of autonomous spending would change output
Relate changes in output to changes in autonomous spending through (13)

Ex. If the MPC = 0.9, then 1/(1-c) = 10  an increase in government spending by $1 billion results in an increase in output by $10 billion
Recipients of increased government spending increase their own spending, the recipients of that spending increase their spending and so on

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Saving and Investment

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In equilibrium, planned investment equals saving in an economy with no government or trade
Vertical distance between the AD and consumption schedules equal to planned investment spending, I
The vertical distance between the consumption schedule and the 45° line measures saving at each level of income

 at Y0 the two vertical distances are equal and S = I

Saving and Investment

The equality between planned investment and saving can be seen directly from national income accounting
Income is either spent or saved:
Without G or trade,
Putting the two together:

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Saving and Investment

With government and foreign trade in the model:
Income is either spent, saved, or paid in taxes:
Complete aggregate demand is
Putting the two together:

(14)

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The Multiplier

By how much does a $1 increase in autonomous spending raise the equilibrium level of income?  The answer is not $1
Out of an additional dollar in income, $c is consumed
Output increases to meet increased expenditure; change in output = (1+c)
Expansion in output and income results in further increases

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The Multiplier

If we write out the successive rounds of increased spending, starting with the initial increase in autonomous demand, we have:

(15)

This is a geometric series, where c < 1, that simplifies to:

(16)

Multiplier = amount by which equilibrium output changes when autonomous aggregate demand increases by 1 unit
The general definition of the multiplier is

(17)

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The Multiplier

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Effect of an increase in autonomous spending on the equilibrium level of output:
The initial equilibrium is at point E, with income at Y0
If autonomous spending increases, the AD curve shifts up by , and income increases to Y’
The new equilibrium is at E’ with income at

The Government Sector

The government affects the level of equilibrium output in two ways:

Government expenditures (component of AD)

Taxes and transfers

Fiscal policy is the policy of the government with regards to G, TR, and TA
Assume G and TR are constant, and that there is a proportional income tax (t)
The consumption function becomes: (19)

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The Government Sector

Combining (19) with AD:

(20)

Using the equilibrium condition, Y=AD, and equation (19), the equilibrium level of output is:

(21)

The presence of the government sector flattens the AD curve and reduces the multiplier to

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Income Taxes as an Automatic Stabilizer

Automatic stabilizer is any mechanism in the economy that automatically (without case-by-case government intervention) reduces the amount by which output changes in response to a change in autonomous demand
One explanation of the business cycle is that it is caused by shifts in autonomous demand, especially investment
Swings in investment demand have a smaller effect on output when automatic stabilizers are in place (ex. Proportional income tax)
Unemployment benefits are another example of an automatic stabilizer  enables unemployed to continue consuming even though they do not have a job

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Effects of a Change in Fiscal Policy

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Suppose government expenditures increase
Results in a change in autonomous spending and shifts the AD schedule upward by the amount of that change
At the initial level of output, Y0, the demand for goods > output, and firms increase production until reach new equilibrium (E’)
How much does income expand? The change in equilibrium income is:

(22)

Effects of a Change in Fiscal Policy

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(22)

A $1 increase in G will lead to an increase in income in excess of a dollar
If c = 0.80 and t = 0.25, the multiplier is 2.5

A $1 increase in G results in an increase in equilibrium income of $2.50
G, Y shown in Figure 10-3

Effects of a Change in Fiscal Policy

Suppose government increases TR instead
Autonomous spending would increase by only cTR, so output would increase by G cTR
The multiplier for transfer payments is smaller than that for G by a factor of c
Part of any increase in TR is saved (since considered income)
If the government increases marginal tax rates, two things happen:
The direct effect is that AD is reduced since disposable income decreases, and thus consumption falls
The multiplier is smaller, and the shock will have a smaller effect on AD

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The Budget

Government budget deficits have been the norm in the U.S. since the 1960s
Is there a reason for concern over a budget deficit?
The fear is that the government’s borrowing makes it difficult for private firms to borrow and invest  slows economic growth

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The Budget

The budget surplus is the excess of the government’s revenues, TA, over its initial expenditures consisting of purchases of goods and services and TR: (24)
A negative budget surplus is a budget deficit

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The Budget

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If TA = tY, the budget surplus is defined as: (24a)
Figure 10-6 plots the BS as a function of the level of income for given G, TR, and t
At low levels of income, the budget is in deficit since spends more than it receives in income
At high levels of income, the budget is in surplus since the government receives more in income than it spends

The Budget

Figure 10-6 shows that the budget deficit depends on the government’s policy choices (G, t, and TR) and also anything else that shifts the level of income
Ex. Suppose that there is an increase in I demand that increases the level of output

 budget deficit will fall as tax revenues increase

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Effects of Government Purchases
and Tax Changes on the BS

How do changes in fiscal policy affect the budget? OR Must an increase in G reduce the BS?
An increase in G reduces the surplus, but also increases income, and thus tax revenues

Possibility that increased tax collections > increase in G

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Effects of Government Purchases
and Tax Changes on the BS

The change in income due to increased G is equal to

, a fraction of which is collected in taxes

Tax revenues increases by

The change in BS is

(25)

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