Chapter 10 – Savings, Investment Spending and the Financial System
• The relationship between savings and investment spending for both closed and open economies.
• Introduce the market for loanable funds.
• Factors that determine the demand for and supply of loanable funds.
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• Determination of the interest rate in the market for loanable funds.
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Matching Up Savings and Investment Spending
• Both (physical) capital and human capital play important roles in determining long-run economic growth (Chapter 9).
• In Canada, human capital is largely provided by governments through public education.
• Physical capital, with the exception of infrastructure, is mostly created by private investment spending (i.e., spending by firms and households).
• In this chapter, we discuss how (physical) investment is financed.
The Savings-Investment Spending Identity
• The savings-investment identity shows that investment MUST equal to savings for the economy as a whole, i.e.,
Investment = Savings
The Savings-Investment Spending Identity in a Closed Economy
• A closed economy is an economy that does not trade with foreigners, i.e.,
X = 0 & IM = 0
• National income identity for a closed economy is
GDP = Y = C + I + G
Total income Total spending by all sectors in the economy
Note: Since GDP (Y) measures the total level of output and total level of income at the same time, these two terms will be used interchangeably.
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• An economy can divide total income into 2 categories: spending & savings. • The level of savings by the whole economy is called national savings (SNational), which is the amount of output not devoted to current consumption:
SNational = Y – C – G
• National savings come from 2 sources:
1) Private savings, SPrivate – savings done by the households.
SPrivate = [Output (Y) – Taxes (T) + Transfers (TR)] – Consumption (C) SPrivate = Y – T + TR – C
2) Public savings, SPublic – savings done by all levels of government.
SPublic = Taxes (T) – Transfers (TR) – Government spending on final goods & services (G) = Government budget balance (GBB)
SPublic = T – TR – G = GBB
If (T – TR – G) > 0, then SPublic > 0 (i.e., a budget surplus).
If (T – TR – G) < 0, then SPublic < 0 (i.e., a budget deficit).
If (T – TR – G) = 0, then SPublic = 0 (i.e., a balanced budget).
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• Proof: SNational = SPrivate + SPublic.
• For a closed economy, the only way for a country to save is to build up capital stock (i.e. undertake investment).
Y =C + I + G
The Savings-Investment Spending Identity in an Open Economy
• An open economy is an economy that engages in international trade and
investment with foreigners (i.e., X & IM are not equal to zero).
• An open economy experiences (financial) capital inflows and outflows.
Capital outflows occur when we purchase foreign assets or when we undertake foreign investment.
Capital inflows occur when foreigners purchase domestic assets or when foreigners undertake investment in our country.
Net foreign investment (NFI) = Purchases of foreign assets from foreigners – Sales of domestic assets to foreigners
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• Net foreign investment must equal to net exports, i.e., NFI = X – IM = NX
The international flows of funds (NFI) = The international flows of goods & services.
Suppose a country runs a trade surplus (NX > 0), this implies export
revenues earned > import payments made.
• An open economy can allocate its savings in two ways:
1) Accumulate physical capital – undertake domestic investment (I). 2) Acquire foreign assets – undertake foreign investment (NFI).
SNational = I + NFI
• Proof: Y = C + I + G + NX
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The Domestic Market for Loanable Funds
Assumptions:
• There is only one type of loan and only one interest rate in the economy.
• The loanable funds market is a hypothetical market that brings the savers
(those who want to lend) and the borrowers (those who have profitable
investment opportunities) together.
• The (nominal) interest rate is determined in the market for loanable funds.
The (Domestic) Demand for Loanable Funds
• The demand for funds comes from investment because those who have
investment opportunities (mainly households and firms) need to borrow funds
to finance their investment.
• Assumptions:
The returns on investment projects are given or known.
Only investment projects with positive net present value (NPV) will be
undertaken.
The interest rate represents the opportunity cost of investment.
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More on the Net Present Value
NPV of an investment = Present value of the return on this investment – Present value of the cost of this investment.
• The present value of an investment project is:
PV = ∑𝑛 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡, where n = year to maturity
𝑡=1 (1+𝑖)𝑡
Example: Suppose a bond1 with a face value of $1000, a coupon rate of 8%, and a maturity of 4 years. The cash flow of this 4-year bond:
In 1 year In 2 years In 3 years In 4 years Cash flow $80 $80 $80 $1080
• The present value of the bond (which is also the price of the bond):
PV = bond price =
Interest rate, i
6% (i = 0.06) 8% (i = 0.08) 10% (i = 0.1)
$80 + (1+𝑖)1
$80 + $80 + ($1000+$80) (1+𝑖)2 (1+𝑖)3 (1+𝑖)4
PV of the bond = bond price
• Observation: Holding all else constant, the PV of the bond (or the bond price) when interest rate .
• Indeed, similar logic can be applied to any investment projects.
1 A bond is a piece of paper with a face value (the value stated on the bond), a maturity date (when you will receive the face value
if you are a bond holder) and a coupon rate (the stated rate of interest on the face of the bond).
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Example: Suppose you have an opportunity to invest in a project that costs $100 now. This project will give you a return of $120 in 3 years and after that there is nothing left.
Now In 1 year In 2 years In 3 years Cash flow – $100 $0 $0 $120
• Whether this project is an attractive one depends on the interest rate (i). NPV Decision
• Observation: Holding all else constant, a rise in interest rate makes investment less attractive.
When interest rate , PV of the future payoffs of an investment project . Number of projects that have positive NPV level of investment . This implies there is an inverse relationship between interest rate and
investment (i.e., the demand for loanable funds slopes downward).
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Shifts of the Domestic Demand for Loanable Funds
• Any factors that affect investment other than interest rate will shift the
demand curve for loanable funds.
1) Changes in perceived business opportunities/Changes in the perceived
future payoffs of investment
Suppose there is technological innovation such that future TFP :
2) Changes in government policies that affect investment
Suppose the government provides a tax credit on investment:
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The (Domestic) Supply of Loanable Funds
• The supply of funds comes from national savings.
• There is a positive relationship between interest rate and supply of funds (i.e.,
the supply of loanable funds slopes upward) because:
Savers/lenders face a trade-off between current consumption and future
consumption holding all else constant, if savers save more, they have to
give up more current consumption for higher future consumption.
When interest rate , today’s consumption becomes more expensive while
the returns on savings people are willing to save more SNational .
Shifts of the Domestic Supply of Loanable Funds
• Any factors that affect national savings other than interest rate will shift the
supply curve of loanable funds.
1) Changes in private savings behaviour such as changes in households’
wealth, changes in preference between current and future consumption Suppose households find that the value of their houses :
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2) Changes in government budget balance
Recall, SPublic = the government budget balance (GBB).
Suppose there is an increase in the government budget deficit:
The Equilibrium Interest Rate
Equilibrium in the loanable funds market:
Demand for loanable funds = Supply of loanable funds.
The Market for Loanable Funds Interest rate, i SF
Quantity of loanable funds (QF)
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Shifts of Both Domestic Demand and Domestic Supply of Loanable Funds
Expected Inflation and Interest Rates
• Before we start, it is important to point out that the true cost of borrowing is the real interest rate because
Inflation erodes the purchasing power of money over time.
The real interest rate is a better measure of the real return to savings and
the real cost of borrowing because the effect of inflation has been taken into
account and has been corrected for it.
• Given that it is the real interest rate that matters, the vertical axis of the
loanable funds market measures the nominal interest rate for a given expected future inflation rate, πe.
Along the demand for funds and the supply of funds curves, expected
inflation rate (πe) is held fixed. Changes in πe will shift both curves.
• Nominal interest rate is put on the vertical axis of the diagram because Both lenders and borrowers do not know what the future inflation will be, they make use of the expected inflation rate and agree on a nominal interest
rate when signing the loan contracts.
If the expected inflation is held fixed, any shifts in demand and supply of
loanable funds curves will cause the nominal interest rate to change. The
change in nominal interest rate is driven by the change in real interest rate.
Expectation form of Fisher equation: i = r + e
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• Changes in expected inflation rate will shift both demand and supply curves in the loanable funds market because:
When πe , for any given quantity of funds demanded, borrowers are
willing to pay a higher nominal interest rate that is equal to the change in
πe because real cost of borrowing does not change.
When πe , in order for the lenders to supply the same quantity of funds,
they will demand a higher nominal interest rate that is equal to the change in πe so that the real return on lending does not change.
Suppose the market believes the expected inflation rate, πe, will increase by x percentage points:
Interest rate
S0(e = e,0) F
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D0(e = e,0) F QF
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