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ECON1102 Macroeconomics 1
Chapter 3-4
Chapter 3: Interest Rates, Investment and Saving



Financial markets are where the borrowing and lending desires of economic agents are
organised
Main financial market in an economy is the bond market, stock market and FOREX market

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8% real interest rate compared to 10% of nominal rate
the real interest rate measures the return on the loan in terms of the ability to purchase
real goods and services
since the general level of prices rises by 5% over the period of the loan, $1 at the end of the
loan is worth less in terms of its ability to purchase goods and services than was $1 at the
beginning of the loan
we can think of r as the net real interest rate and 1+r as the gross real rate
using the values for the CPI we can calculate the annual rate of inflation 𝜋 as:



the approximate value for the real interest rate is given by



similar to the exact calculation of 4
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2 Investment


investment: expenditures that are concerned with the production of future goods and
services

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1 Private investment
 undertaken by businesses and households
 major categories of private investment: purchases of new machines and equipment,
investment in non-residential buildings, investment in intellectual property
 for the household sector purchases of new housing are included in investment expenditure as
dwelling construction
 combining private business investment and dwelling construction gives private gross fixed
investment
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2 Public Investment and 3
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3 Inventory Investment
 government or public sector also undertakes investment at local, state and federal levels
and also through publicly owned corporations
 inventory investment (equal to the change in the level of inventory holdings) as a share of
nominal GDP
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4 – Investment and Capital Stock
 investment expenditure is a flow variable and consequently is measured over some period
of time
 investment flows can accumulate over time and affect the level of stock of capital in an
economy
 at any point of time an economy will have some particular level of capital stock
 standard formula for the accumulation of capital is given by:
o K1 = K0 + I1 – 𝜹K0
o Where K0 is the stock of capital at the beginning of the period, I1 is gross investment
over the period, 𝛿K0 is physical depreciation on the existing capital stock
(𝛿 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑒𝑝𝑟𝑒𝑐𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒) and K1 is the stock of capital at the end of the period
 Gross investment is what is included in the expenditure approach to calculating GDP
 Can define net investment as gross investment less depreciation
o Net investment = I - 𝜹K
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5 Economic influences on investment
 the marginal product of capital is the addition to output from increasing the capital input by
one unit, with all other factors of production held fixed
 can assume that the marginal product of capital is positive, but declines with each additional
unit of capital that is added
 to obtain the value of the marginal product of capital (VMPK) we simply multiply
the marginal product of capital by the sales price of the business’s output (p)
o VMPK = MPK x p
o Provides a measure of the marginal benefit to the business from investing in new
capital

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6 – User cost of capital
 The durable nature of capital goods means the cost to a business investing in a new capital
good is not simply the purchase price of that good
 Example of buying a plane
o Interest cost of the new plane over one year will be i x Pk
o Depreciation rate of the plane is equal to 𝛿
o The amount of the plane that remains at the end of year is (1-𝛿)
o Assume at the end of the year market price for the plan will equal PK + ΔPK where
ΔPK measures any change in the price of planes over the year
 User cost = purchase price + interest payments – market price of depreciated plane
(at year end)
 UC = PK + i x PK – (1- 𝜹) [PK + 𝚫𝐏K ]
o Above formula can be used to calculate the exact dollar value of the annual user
cost of the plane
o Could compare the UC to the expected value of the marginal product of the plane
over the next year and would decide to undertake the investment in the new plane,
provided VMPK > UC
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7 – an approximation
 UC = PK [ i + 𝜹 − (𝚫𝐏K / PK )]
o Simply the nominal interest rate plus the physical depreciation rate minus the
annual rate of price change on capital goods
 We can make one final simplifying assumption to the user cost by assuming that capital
goods prices increase at the general rate of inflation
o We can replace (𝚫𝐏K / PK ) with the inflation rate 𝝅
 UC = PK [ i + 𝜹 – 𝝅]
o Or noting that the real interest rate is r=i- 𝝅
 UC = PK [r + 𝜹]
o So that UC depends on the price of the capital good, the physical depreciation rate
and the real rate of interest
 The rate of the user cost is just equal to the real interest rate and the rate of depreciation

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8 – investment demand curve
 An increase in the real interest rate will
increase the user cost of capital and hence
make it less likely that the value of the
marginal product of a new investment will
exceed its user cost
 A rise in the real interest rate will make
investment less attractive

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The higher the real interest rate makes investment less attractive and
causes a move along the I curve
 the increase in the budget deficit will shift the NS curve to the left, but does not produce any
change in the investment curve
 the fall in the national saving curve results in an increase in the real interest rate and
caushing a shift along the l(r) curve and hence a lower level of investment

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11 – investment slumps
 the fall in business confidence causes the investment schedule to shift inwards
 graph demonstrates a decline in the real interest rate and a fall in both investment and
national saving

chapter four – income expenditure model of GDP
Keynesian Model
 prices of goods are fixed (common to say sticky) in the short run
o firms do not change prices in response to a change in demand for their product
o instead they fix their price and then meet the demand by varying level of production
 in the short run firms will:
o accommodate a cut in demand by reducing output and employment, not by
reducing prices
o accommodate a rise in demand by increasing output and employment, not by
increasing prices
 deeper assumptions: firms have some ability to set prices (not perfectly competitive world)
and firms face some cost to changing prices – these are called menu costs
 in the long run: sustained or persistent changes in demand will eventually lead firms to
change their prices and cause production to return to normal capacity
frictionless view of the world
 fluctuations in demand will be accommodated by flexible prices and wages without changes
in output and employment
 there will never be excess production because firms will cut prices to sell it
 there will never be persistent unemployment because workers will cut their wages to keep
and get jobs

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2 – Two Sector Model: households and businesses


In the two-sector model PAE is comprised of household consumption and
planned business investment PAE = C + IP, no government and foreign sector

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1 – Planned investment
 In the case of planned investment we make the simplifying assumption that I P is an
autonomous or exogenous variable determined by factors other than the level fo real
GDP
 In terms of the income-expenditure model this amounts to assuming that planned
investment equals some given value (number) and does not depend upon the level of Y
 Notation for exogenous/autonomous variable: IP = I0
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2 – Household consumption
 It is considerably less volatile than business investment
 Sometimes used to classify consumption expenditure into three basic types; non durable
consumption (goods that are for immediate consumption), durable consumption (flows over a
relatively long period of time) and consumption of services (movies, education)
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3 – a model of consumption
 Keynesian consumption function assumes aggregate household
consumption depends upon current household disposable income
 C = C0 + c(Y-T) linear relationship
o C is real consumption expenditure
o C0 is exogenous (autonomous) consumption
o Disposable income = (Y-T)
o Y is real national income or GDP and T equals total taxes
(TA) less transfer payments (TR) less interest payments on public debt (INT)
o Assume retained earnings (RE = 0)
o C(Y-T) captures the effect of disposable income on consumption (sometimes
called induced consumption)
o There are two parameters in the model,
C0 is a constant term that indicates what aggregate consumption will be if
aggregate disposable income is zero
Conventional to assume C0 > 0 which suggests there are factors other than
disposable income that influence consumption
Other parameter is c, which is known as the marginal propensity to consume
 Marginal propensity to consumer
o Is the change in consumption when disposable income changes by a dollar

∆𝑪 = 𝒄∆(𝒀 − 𝑻) (assume ∆𝑪0 = 0)
𝑴𝑷𝑪 =

∆𝑪

∆(𝒀–𝑻

=𝒄

o

c is the marginal propensity to consume (MPC) out of disposable income
key assumption of Keynesian consumption function is that MPC is 0average propensity to consume is simply the ratio of consumption to disposable
income (proportion of income that is used for consumption)
𝐶
}–
𝑇

o

=

t
}–
𝑇

+𝑐

APC > MPC but approaches MPC as Y-T increases

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4 – Equilibrium in Two-sector model
 Can solve the above model for equilibrium Y using
thefollowing technique




Ye to indicate the equilibrium level of output
Two sector model implies that the equilibrium level of real GDP depends upon the sum of
the levels of autonomous consumption expenditure and planned investment

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5 – graphical representation
 Two sector income expenditure model can be
represented in a diagram – Y = PAE
 While the 45=degree line represents all possible points
of equilibrium, it is not by itself sufficient to indicate
what will be the level of equilibrium GDP
 On the vertical axis we measure PAE and its
components consumption and planned investment
 The consumption function has an autonomous
component C0 (vertical intercept) and a component
that depends on Y
 It has an upward slope equal to the MPC which is less
than one
 The PAE line is simply obtained by vertically
summing the values for consumption and planned
invested for each level of Y
 To determine equilibrium GDP, we add the PAE line to
the 45-degree diagram, equilibrium GDP obtains at the
level of Y for which the PAE line cuts the 45-degree line

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6 – dis-equilibrium
 The figure below demonstrates how the economy
behaves if for some reason the level of production is
not at Ye
 We illustrate the situation in which for a given PAE
curve, level of aggregate output is either YL < Ye or
YH > Ye
 Since the desired level of expenditure exceeds the
level of output, the business sector will experience
an unplanned decline in their level of inventories
(excess demand for services)
 The business sector will respond to the excess
demand and inventory decline by increasing their level of production
e
 Will result in an increase in output – above YL and will move the level of GDP towards Y
 For any output level below Ye businesses will experience unplanned inventory decumulation
and will have an incentive to increase production until Y = Ye
 When production was at YH its apparent that PAE H < YH so business sector will experience
anunplanned increase in their level of inventories and this will provide a signal for
businesses to cut back on their level of production
 Output will fall below YH and move closer to Ye
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7 – changes in equilibrium GDP
 A reduction in planned investment from I 0 to I1 will
shift the PAE curve downwards, the reduction in
PAE will produce a fall in the equilibrium level of
real GDP
to Ye
1
 The change in Y is larger than the change in IP
 Multiplier: in the income expenditure model is a
measure of the change in equilibrium GDP in
response to a given exogenous change in
planned expenditure
o An additional dollar of exogenous PAE
generates more than a dollars worth of
GDP
∆𝒀

o

k = ∆𝑰𝒑

o

in order to calculate the numerical value of a multiplier we can use our above
solution for equilibrium GDO

o

the multiplier for an exogenous change in planned investment is

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8 – mechanics of the multiplier process
 increase in income will be spent on increased
consumption and keeps circling through the economy
 the increase in GDP associated with the multiplier
process is given by:
 ∆𝒀 = 𝟏 × 𝟏𝟎𝟎 𝒘𝒉𝒆𝒏 𝟎 < 𝒄 < 𝟏
𝟏–𝒄

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9 – saving and planned investment in two-sector model
 in the two-sector model the equilibrium level of GDP
– Y = PAE
 PAE = C + IP Y-C=IP
o The left hand side of the second equation is
just equal to aggregate saving in the twosector model
 instead of using Y = PAE as the condition for
equilibrium, we can use an equivalent equilibrium
condition os saving equal to planned investments S =
IP
 S = Y – C and C = C0 + cY we obtain S = -C0 + (1-c)Y
o (1-c) is just the marginal propensity to save


also obtain the same result for equilibrium GDP

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10 – paradox of thrift
 the paradox of thrift is a example of a fallacy of
composition, which is a fallacy of assuming what is
true for an individual component of some whole, is
also true for the whole
 a given increase in autonomous saving is
equivalent to an equal decrease in autonomous
consumption spending
 the attempt by all households to increase their
autonomous saving results in a fall in real GDP
which declines by just enough to lower induced
saving so that it exacly offsets the autonomous
increase
 thus while an individual household can raise its
total level of saving, in the income-expenditure
model this is not possible for all households in
aggreagte

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Title: ECON1102 Macroeconomics 1 NOTES chapter 3-4
Description: ECON1102 Macroeconomics 1 NOTES chapter 3-4 I studied these notes and attained straight A’s

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