Transcript A change in autonomous planned spending is

Robert J. Gordon,
Macroeconomics, 10th edition,
2006, Addison-Wesley
Chapter 3
Spending, Income, and Interest Rates
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Spending, Income, and Interest Rates
 Business Cycles and the Theory of Income Determination
 Remember that minimizing fluctuations in real GDP is
important. Revise the volatilia and stabilia cases.
 Business cycles in USA
Figure 3-1

Note that the goals of monetary policy is to dampen business
cycle fluctuations and ensure a steady growth of real GDP.
 This is, as shown in the above figure, is far from reality.
 Ups and downs in real GDP are basically caused by changes in
shocks to aggregate demand (a significant change in desired
spending by consumers, business, government and foreigners).
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-1 Real GDP Growth in the United States, 1950–2004
Note that expansions in general lasts longer than recessions. Why?
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Improved performance of anti-cyclical fluctuations can be due
to:
1.
2.
3.
- demand shocks are smaller and less important
- monetary and fiscal policies become more effective
- a change in the conditions that make fiscal and monetary
policies more effective.
 Income determination, unemployment and the price level
 Income determination and the price level
 Shocks to AD can change either real GDP, the price level or
both.
 Changes in AS depends mainly on costs among other factors.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Suppose that the price level is fixed in the short run. All changes
in AD cause changes in real GDP by the same amount in the
same direction, since;
∆ real GDP = ∆ AD/fixed price level
(1)
 Is there any evidence to support the assumption that prices are
fixed in the short run?
1. Price labels are printed and expensive to reprint
2. Prices of mail order catalogues are set for the entire season
3. Wages and salaries usually change every year and perhaps in
more than that.
 Therefore, changes in AD are directly translated into changes in
real GDP.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 What we explain and what we take as given?
 The variables to be explained in a model are called endogenous,
while those which are taken as given are called exogenous.
 What we will consider as exogenous:
 The key instruments of monetary (money supply) and fiscal
policies (G & Tax rates), exports and other potential causes of
changes in demand shocks such as consumer and business
confidence about the future are assumed to be exogenous.
 We know that:
E ≡ C+I+G+NX
(2)
 Now let us consider the components of E
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The consumption function
 Starting with C as the only endogenous variable, C depends on
disposable income (Y-T) such that,
C = Ca + c(Y-T)
(3)
 The fixed amount Ca is autonomous consumption, which is
completely independent of disposable income.
 The change in C due to the change in (Y-T) depends on marginal
propensity to consume (c).
 c(Y-T) is the induced consumption. e.g.,
C = 500 + .75 (Y-T)
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-2 A Simple Hypothesis Regarding Consumption Behavior
Break-Even-Point
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 This function is shown in figure 3-2 below.
 Note that:


When disposable income is zero, total consumption consists
of the autonomous part only Ca.
For any extra disposable income, C changes by .75 of that
extra disposable income.
 Induced saving and the marginal propensity to save:
 Look at figure 3-2 again and note that.


The distance between the consumption function and the 450
line is the total saving.
To the right of point F saving is positive as (Y-T)>C.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 To the left of point F saving is negative as (Y-T)<C, i.e., people
either withdraw from their saving accounts or borrow in order
to consume. Note:
S=(Y-T)-C = (Y-T)- Ca-c(Y-T)
S=- Ca+ (1-c)(Y-T)
 In our example
S=-500+.25(Y-T)
 (1-C) is the marginal propensity to save
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Autonomous consumption, the interest rate and the stock
market
 There are other factors that cause a change in autonomous
consumption. These factors are:
1. Interest rates; Ca rises when interest rate falls, and falls
when interest rate rises.
2.
Household wealth (the market value of houses, stocks, bonds and bank
accounts minus liabilities); as wealth rises people will consume more even
with fixed income (lower their savings). See figure 3-3
 The economy in and out of equilibrium
 To see how income is determined note that expenditure is not
always what is desired or planned.
 If some expenditure is unplanned, business firms will adjust
production until the unplanned component is eliminated.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-3 Consumption, Saving, and Disposable Income, 1929–2004
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Total spending that is planned is Ep, while the rest is unplanned
or undesired (E – Ep). Assume that Investment is the only
component that can contain an unplanned component, while the
rest are always equal to their planned levels.
Ep = C + Ip + G + NX
 Or
Ep = Ca +c(Y-T) + Ip + G + NX
 The word parameter is a value taken as given or known within a
particular analysis. In the consumption function Ca and c are
parameters,
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Autonomous planned spending
 Autonomous planned spending (Ap) is the spending that does not
depend on total income (Y); i.e.,
Ap = E – cY = Ca – cTa + Ip + G + NX (cY induced consumption)
 -cTa is autonomous taxes that affect C (note that so far we
consider taxes as autonomous).
 So Ap excludes induced spending only (Ca – cTa + Ip + G + NX)
 Assume that Ip = 1200, NX = -200, T=0, G=0, Ap equals
Ap = 500 – 0.75(0) + 1200 + 0 – 200 = 1500
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Now we have learned that Ep has two parts Ap and cY, i.e.,
Ep = Ap + cY
Ep = 1500 + .75 Y
 When is the economy in equilibrium
 Only when Y equals Ep, the economy will be in equilibrium, i.e.,
households, business firms, the government and the foreign
sector want to spend exactly the income generated by current
level of production.
 If the economy is out of equilibrium, (out of line with planned
expenditures) business firms will be forced to change their
production. At equilibrium production and income are equal to
their planned levels.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-4 How Equilibrium Income Is Determined
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
See figure 3-4
 At point B income equals planned expenditure, (no pressures to
change).
 What happens out of equilibrium
 The economy is out of equilibrium all points other than B. at
point J, income is 8000. planned expenditure are 7500
(Autonomous planned spending 1500 + Induced consumption
spending 6000), i.e., there will be 500 of unsold products.
 Though this is counted as investment, businesses do not desire it.
(unintended inventory investment Iu). For this reason, they will
cut production and income which moves the economy back to B.
 Note:
Y ≡ E ≡ Ep + Iu
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The economy will be at equilibrium when Iu = 0, i.e., businesses produce
exactly the amount that is demanded, or
Y = Ep
Table 3-1 Comparison of the Economy’s “Always True” and Equilibrium Situations
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Determining equilibrium real GDP.
 take cY from both sides of the above equation (Y = Ep)
Y – cY = Ep – cY
(remember Ep-cY=Ap)
(1-c)Y = Ap
 Note that mps (s) = (1-c), hence;
sY = Ap
(.25Y=1500)
 Induced saving equal autonomous planned spending. Since this
equation is obtained from equilibrium condition we can divide
both sided by s to solve for equilibrium income such that;
Y = Ap/s
or Y = 1500/.25 = 6000
 1500 of induced savings are required to balance 1500 of
autonomous planned spending.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The multiplier effect.
 Any change in Ap will cause a change in equilibrium income.
 Suppose that businesses raise their investment by 500, i.e., Ap increases from
1500 (Ap0) to 2000 (Ap1).
 Calculating the multiplier
 New equilibrium
 Subtract from old
 Equals change in income
Y1 = Ap1/s = 2000/.25 = 8000
Y0 = Ap0/s = 1500/.25 = 6000
∆Y = ∆Ap/s = 500/.25 = 2000
 The multiplier k is ∆Y over ∆Ap
Multiplier k = ∆Y/∆Ap = 1/s
∆Y/∆Ap = 1/.25 = 4
 Look at the figure and note that
k = ∆Y/∆Ap = RJ/RB = 1/s
k = 2000/500 = 4
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-5 The Change in Equilibrium Income Caused by a $500 Billion
Increase in Autonomous Planned Spending
Point B is no longer an equilibrium point
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Example of the multiplier effect in action
 If planned expenditure rises, real income must rise by 1/s as
much.
 suppose that an airway company bought 4 billion of boeing
aircrafts. This will raise Boeing workers income by 4 billion, out
of which they will soon spend .75 on goods and services, that will
raise output by 3 billion of consumer goods in the second round.
A rise in income by 3 billion will raise spending by 2.25,….., and
so on.
 Total change in income = 4 x 1/.25 = 16 billion
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Sources of shifts in planned spending
 What might cause actual real GDP to decline below the desired
level?. A drop in planned investment is a major cause of actual
real world recession and depressions.
 All other components of autonomous planned spending, can
change, (Ca, cTa, Ip, G, and NX).
 Government spending and taxation
 The government can adjust its expenditures and taxes to offset
fluctuations in real GDP caused by movements in autonomous
consumption, in planned investment and net exports. We know
that;
Ap = E – cY = Ca – cTa + Ip + G + NX
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 A change in autonomous planned spending is;
∆Ap = ∆Ca – c ∆Ta + ∆Ip + ∆G + ∆NX
 A $1 change in Ca changes Ap by $1 in the same direction
 A $1 change in Ta changes Ap by $1 in the opposite direction
 A $1 change in Ip changes Ap by $1 in the same direction
 A $1 change in G changes Ap by $1 in the same direction
 A $1 change in NX changes Ap by $1 in the same direction
 Once a change in Ap is calculated, the multiplier determines the
resulting change in income.
∆Y = ∆Ap/s
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Fiscal expansion
 Suppose that the desired level of income is 8000. If the

1.
2.
3.
autonomous spending Ap = 1500, real income is 6000, as shown
at point B, but this is unsatisfactory as actual real GDP is 2000
lower than desired.
How fiscal policy correct for this situation through control over
G? From 3.14, an increase in real income by 2000 is achieved by
any action to raise Ap by 500. There are two possibilities:
raise G by 500
reduce autonomous tax revenue by 667
A 500 rise in G will have the same impact as any other 500
increase in Ap. k for ∆G is the same
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The government budget deficit and its financing
 Any change in G or tax revenue has a consequence for the


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budget. We know that
T-G ≡ I + NX – S (recall the magic equation)
and
∆T-∆G ≡ ∆I + ∆NX – ∆S 3.17
Assume that ∆Ca = ∆I = ∆NX = 0, and ∆T = 0, such that the only
elements of 3.17 that are changing ∆S and ∆G.
∆G is the value of fiscal stimulus. Now
∆T - ∆G = ∆I + ∆NX – s(∆Y - ∆T)
0 - ∆G = 0 + 0 – .25(∆Y - 0)
0 - 500 = 0 + 0 – .25(2000 - 0) = -500
(There is a deficit of 500)
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The extra saving of 500 are to be used to buy government bonds
that the government must sell to finance its 500 deficit, in order
to raise real GDP BY 2000.
 The tax multiplier
 As an alternative to using G by 500, the government can reduce
taxes by 667 to have the same impact. Thus;
∆Y = ∆Ap/s = -cTa/s ∆Y=-(.75)(-667)/.25 = 500/.25 = 2000
 The multiplier for a change in taxes is the income change divided
by ∆Ta:
∆Y/∆Ta = ∆Ap/s∆Ta = -c∆Ta/s∆Ta = -c/s
∆Y/∆Ta = -.75/.25 = -3.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Financing the tax cut
 To see how the budget deficit due to a tax cut is financed we use
the same equation:
 ∆T - ∆G = ∆I + ∆NX – s(∆Y - ∆T)
 -667 - 0 = 0 + 0 – .25(2000 – (-667))
 - 667 = -.25(20667) = -667
(There is a deficit of 667)
 The tax cut of 667 raised disposable income by 2667 or 667 extra
savings is available for households to buy 667 government bonds.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The balanced budget multiplier
 The government can stimulate the economy even if it needs to
maintain a balanced budget. To see this add the G and T
multipliers
 Balanced budget multiplier 1/s + -c/s = 1-c/s = 1
 this states that the balanced multiplier is one no matter what the
value of c is.
 How can monetary policy affect planned spending
 For the time being we will take the interest rate as given, while
converting autonomous consumption from an exogenous into an
endogenous variable, but interest rate is still an exogenous
variable.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Functions of interest rate
 Interest rates help the economy allocate saving among alternative uses. For
consumers it is the reward from abstaining from consumption, the higher the
interest rate the greater the incentive to save. Also people will borrow less and
purchase fewer goods.
 Interest rates are central to the role of monetary policy, the government can
affect the cost of funds to private borrowers by affecting interest rates
 Types of interest rates.
 Deposits short term interest rates; for deposits of 3 months or less; while long
term interest rates; for a year or more.
 Borrowed funds rates: short term rates on funds borrowed by the
government (treasury bill rate), by business (commercial paper), and by
banks (federal funds rate). There are long term rates on funds borrowed by
the government (Treasury bond rate), by businesses (corporate bond rate)
and by households (the mortgage rate).
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The relation of autonomous planned spending to the interest rate
 Ip depends on interest rates, since business firms attempt to profit by
borrowing in order to buy investment goods. business can stay in the business
only if earnings are enough to pay the interest on borrowed funds.
 Example of an airline’s investment decision
 If earnings on Boeing jet airliner is 10 m, while its cost is 50 m (interest, fuel,
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food...etc).
Earnings are 20% rate of return (10/50). If interest rate is 10%, return is
sufficient to pay the interest expense.
Look at figure 3-6 which shows the rate of return on 1-5 planes
The first plane earn more because it is operated on the most profitable routs,
compared to the second…etc.
Up to the third plane can be bought.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-6 The Payoff to Investment for an Airline and the Economy
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 Interest rate and the rate of return line.
 Figure 3-6 shows the relationship between interest rates and real
private autonomous planned spending. Determination of the
level of Ip + Ca is a two step process. First we plot the rate of
return line. Second we find the level of Ip+Ca at the point where
the rate of return crosses the interest rate level.
 Business and consumer optimism
 Can purchases change when interest rate is held constant?
Certainly an increase in business and consumer optimism about
expected payoff of additional purchases can shift the entire rate
of return line to the RHS. See figure 3-7.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-7 Effect on Autonomous Planned Spending of an Increase in
Business and Consumer Confidence
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The demand for autonomous planned spending
 We know that autonomous spending is composed of 5
components. There is a negative relationship between interest
rates and Ip+Ca, the other 3 do not depend on interest (GcTa+NX). See figure 3-8.
 Shifts in the Ap demand schedule
 A change in G, T and NX shift the Ap demand schedule. A shift
in business expectations, and improvement in consumer
confidence will also shift the Ap demand schedule.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-8 Relation of the Various Components of Autonomous Planned
Spending to the Interest Rate
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 The IS curve
 Ap depends on interest rate. Real GDP and real income depend
on Ap, therefore, real GDP and real income depend on interest
rate. The IS curve shows the different combinations of interest
rate and real income that are compatible with equilibrium.
 How to derive the IS curve.
 the LHS OF figure 3-9 shows the demand for Ap at different
levels of interest rates. Assume that there are no G, T, and NX,
so that Ap consists of Ip + Ca, both is negatively related to
interest rate. Given a multiplier of 4, at different points of Ap,
real income is determined.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Figure 3-9 Relation of the IS Curve to the Demand for Autonomous
Spending
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
 What the IS curve shows
 The IS shows different combinations of interest rate (r) and
income (y), at which the market is in equilibrium when y = Ap.
At any point out of the IS the economy is out of equilibrium.
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University
Macroeconomic Theory
Prof. M. El-Sakka
CBA. Kuwait University