Theory of Interest

A brief overview of modern interest theories

Knut Wicksell (1851-1926)Knut Wicksell (1851-1926)

Born in Stockholm, Sweden, 1851 Son of a successful businessman and

real estate broker Orphan at the age of 15 Mathematics and Physics 1887: Economics 1898: Interest and Prices 1916: Swedish government advisor on

financial and banking issues main intellectual rival was the American

economist Irving Fisher

Interest and Prices

natural rate of interest vs. money rate of interest

real profit (r)

MPK

money market (i)

Cumulative Process model

MPK > i I > S M rises

Demand > Supply prices rise The demand for loans will continue accumulating, and the banking system's deposit

creation continues indefinitely - with savings never really catching up. Money supply will expand endogenously without limit and prices will also rise without end.

What can end this process?

Reserve Requirement Constraint

Irving Fisher (1867-1947)Irving Fisher (1867-1947)

Born in New York, 1867Born in New York, 1867 Yale UniversityYale University

• 1888: B.A.1888: B.A.• 1891: Ph.D.1891: Ph.D.

Mathematics & EconomicsMathematics & Economics 1930: 1930: The Theory of InterestThe Theory of Interest

The Theory of Interest:The Theory of Interest:As determined by the As determined by the

impatience to spend income impatience to spend income and and

opportunity to invest it.opportunity to invest it.

IncomeIncome CapitalCapital InterestInterest

Income Income

3 stages:3 stages:• Psychic income or enjoyment incomePsychic income or enjoyment income• Real incomeReal income• Money income or cost of livingMoney income or cost of living

real incomereal income

The Thames below WestminsterThe Thames below Westminsterabout 1871about 1871

Oil on canvas 47 x 72.5 cm. Oil on canvas 47 x 72.5 cm.

Money IncomeMoney Income

CapitalCapital

““The value of any property, or rights to wealth, is its value The value of any property, or rights to wealth, is its value as a as a source of income source of income and is found by discounting that expected and is found by discounting that expected income” (Fisher, 1930, p.14).income” (Fisher, 1930, p.14).

the value of capital is the present value of the flow the value of capital is the present value of the flow of (net) income that the asset generatesof (net) income that the asset generates

any asset that produces a flow of income over timeany asset that produces a flow of income over time

Capital goods Income

Income valueCapital value

Rate of InterestRate of Interest

capital value X capital value X rate of interestrate of interest = interest = interest

(a) the time preference people have for consuming today versus consumption at a later time, and

(b)the expectation that income saved and invested today will yield greater income tomorrow – capital produced today will generate greater future production than was required to construct the capital

IMPATIENCE

OPPORTUNITY

Difference between Classical Difference between Classical economists and Irving Fishereconomists and Irving Fisher

According classical economists there are four According classical economists there are four sources of income:sources of income:

• RentRent• WagesWages• ProfitsProfits• InterestInterest

Fisher treated interest not as a separate entity of Fisher treated interest not as a separate entity of income, but as sub-entity within each of the 3 income, but as sub-entity within each of the 3 sources of incomesources of income

Other non-economic factors that Other non-economic factors that influence rate of interest:influence rate of interest:

Foresight - intelligenceForesight - intelligence Self-control – willingnessSelf-control – willingness HabitHabit Life ExpectancyLife Expectancy The love of one's childrenThe love of one's children FashionFashion

Fisher, Irving. The Nature of Capital and Income. New York: The Macmillan Company, 1906.

Octavo, 1st edition in original green cloth. $1600.Source: http://www.manhattanrarebooks.com/fisher.htm

John Maynard Keynes (1883-1946)

Born in Cambridge, 1883Born in Cambridge, 1883King's College, CambridgeKing's College, Cambridge

Mathematics in 1905Mathematics in 1905Alfred Marshall and Arthur PigouAlfred Marshall and Arthur Pigou

1936: 1936: General TheoryGeneral Theory1942: was made a lord1942: was made a lord1944: Bretton Woods Conference1944: Bretton Woods ConferenceApril 21, 1946 passed awayApril 21, 1946 passed away

General TheoryGeneral Theory““Liquidity-preference”Liquidity-preference”

iIlliquid assets Liquid assets

Financial wealth

Wealth is allocated between liquid and illiquid assetsWealth is allocated between liquid and illiquid assets

“ “Thus the rate of interest at any time, being the Thus the rate of interest at any time, being the reward for parting with liquidity, is a measure of the reward for parting with liquidity, is a measure of the unwillingness of those who possess money to part unwillingness of those who possess money to part with their liquid control over it. The rate of interest is with their liquid control over it. The rate of interest is not the “price” which brings into equilibrium the not the “price” which brings into equilibrium the demand for resources to invest with the readiness to demand for resources to invest with the readiness to abstain from present consumption. It is the “price” abstain from present consumption. It is the “price” which equilibrates the desire to hold wealth in the which equilibrates the desire to hold wealth in the form of cash with the available quantity of cash; — form of cash with the available quantity of cash; — which implies that if the rate of interest were lower, which implies that if the rate of interest were lower, i.e. i.e. if the reward for parting with cash were if the reward for parting with cash were diminished, the aggregate amount of cash which the diminished, the aggregate amount of cash which the public would wish to hold would exceed the available public would wish to hold would exceed the available supply, and that if the rate of interest were raised, supply, and that if the rate of interest were raised, there would be a surplus of cash which no one would there would be a surplus of cash which no one would be willing to hold.” (Keynes, 1936).be willing to hold.” (Keynes, 1936).

Money Demand TheoryMoney Demand Theory

People hold money for three reasons:People hold money for three reasons:

► Transaction MotiveTransaction Motive► Precaution MotivePrecaution Motive► Speculation MotiveSpeculation Motive UncertaintyUncertainty

Expectation

On expectationOn expectation

► If E(If E(ΔΔii) > 0 ) > 0 M Mdd > 0 > 0

► If E(If E(ΔΔii) < 0 ) < 0 M Mdd < 0 < 0

Md (E(E(ΔΔii))))

Interest Rate is a function of money demand and Interest Rate is a function of money demand and money supply; it is a monetary factormoney supply; it is a monetary factor

ii* * = = ii (M (Mdd, M, Mss))

Sir John Hicks (1904 - 1989) Sir John Hicks (1904 - 1989)

Sir John HicksSir John Hicks

Born in 1904 at Warwick, EnglandBorn in 1904 at Warwick, England MathematicsMathematics Clifton College (1917-22) Clifton College (1917-22) Balliol College, Oxford (1922-26)Balliol College, Oxford (1922-26) 1937: IS-LM model1937: IS-LM model

IS-LM modelIS-LM model

Based on John M. Keynes’s Based on John M. Keynes’s General TheoryGeneral TheoryAll equilibria in both commodity and money All equilibria in both commodity and money

marketsmarkets

IS curve: IS curve: Y = fY = f((ii) ) equality of S and I equality of S and I LM curve: LM curve: ii = = ff((YY) ) equality of Ms and Md equality of Ms and Md

In 1982 Hicks rejected this model because although In 1982 Hicks rejected this model because although it is a very useful apparatus to understanding it is a very useful apparatus to understanding Keynes’ Keynes’ General Theory General Theory but it lacks one very but it lacks one very essential thing that Keynes already knew:essential thing that Keynes already knew:

Uncertainty