econ dept jccss(tm)1 2 the theory of interest --- return to ‘capital’? traditional approach of...

ECON DEPT JCCSS(TM) 1


The Theory of Interest --- Return to The Theory of Interest --- Return to ‘Capital’?‘Capital’?

Traditional approach of capital----- capital Traditional approach of capital----- capital is man-made resources that could be is man-made resources that could be used in the production of other goods.used in the production of other goods.

Capital has the characteristics of:--Capital has the characteristics of:--Its production requires the use of scarce Its production requires the use of scarce

resources;resources;Its creation involves an opportunity cost Its creation involves an opportunity cost

or a sacrifice of present consumption or a sacrifice of present consumption forfor futurefuture consumption;consumption;


Capital is durable. It provides a stream Capital is durable. It provides a stream of services.of services.

InvestmentInvestment is the part of present income is the part of present income not for present consumption but for the not for present consumption but for the creation of future income.creation of future income.

Note: investment is a flow concept & Note: investment is a flow concept & capital is a stock conceptcapital is a stock concept

Capital & Capital & InvestmentInvestment


Rental Price of CapitalRental Price of Capital

At the market optimal, rental price of capital At the market optimal, rental price of capital (i.e. the price paid for the use of capital for (i.e. the price paid for the use of capital for a specific period of time) a specific period of time) is equal to the is equal to the MRP of the capital generated during the MRP of the capital generated during the period.period.

The purchase price of capitalThe purchase price of capital is the price is the price paid to acquire ownership of the capital paid to acquire ownership of the capital stock (i.e. the price paid to acquire the stock (i.e. the price paid to acquire the right to receive right to receive a stream of incomesa stream of incomes from from the services of the capital in the the services of the capital in the futurefuture.).)


Marginal Productivity of Capital &Marginal Productivity of Capital & Classical Theory of Interest: Classical Theory of Interest:

Marginal productivity of capitalMarginal productivity of capital is the increase is the increase in output of the last unit of capital added to a in output of the last unit of capital added to a fixed quantity of other factor inputs. fixed quantity of other factor inputs. (MP of K =Δ TP /ΔK )(MP of K =Δ TP /ΔK )

Classical theory of Interest: Classical theory of Interest: Interest is the Interest is the return to capital due to productivity return to capital due to productivity determined by determined by Demand and SupplyDemand and Supply of Capital.of Capital.


Demand for Capital by a Single Demand for Capital by a Single Firm (Perfectly Competitive) :Firm (Perfectly Competitive) :

To buy a capital good, the firm pays a current cash To buy a capital good, the firm pays a current cash

sum, sum, PPkk (which is the cost of acquiring the capita(which is the cost of acquiring the capita

l good), in anticipation of a stream of future retul good), in anticipation of a stream of future retu

rns (incomes):rns (incomes):

II00 , I , I11 , I , I22 …I …Itt where t is the life of the capital g where t is the life of the capital good. (Note : Iood. (Note : I ii = MRP = MRPkk ) )


Marginal Efficiency of Capital Marginal Efficiency of Capital (MEC):(MEC):

It is the It is the rate of discountrate of discount that equates the that equates the price of a new price of a new capital stockcapital stock with the with the Present Value (PPresent Value (Pvv)) of the stream of the stream

of future cash returnsof future cash returns from the additional capital stoc from the additional capital stock.k.

I.e. Assuming a new capital, K, has no scrap value,I.e. Assuming a new capital, K, has no scrap value,

The price of K:The price of K:

PPkk = I= I00 + I + I11/(1+e) + I/(1+e) + I22/(1+e)/(1+e)2 2 + I + I33/(1+e)/(1+e)3 3 + …. + I + …. + Inn/(1+e)/(1+e)n n

Where: e = Marginal Efficiency of Capital (MEC).Where: e = Marginal Efficiency of Capital (MEC).E.g. If Pk = 10 000, I0 = 0, & I1 = 11 000 then.10 000 = 0 + 11 000/(1+e), e = 10%.


Marginal Efficiency of Capital Marginal Efficiency of Capital (MEC)(MEC)

It is a schedule or curve shows the inverse It is a schedule or curve shows the inverse relationship between the amount ofrelationship between the amount of capital capital stock stock and theand the rates of return of the capital rates of return of the capital stock stock at the margin.at the margin.

It is subject to the rule of diminishing marginal It is subject to the rule of diminishing marginal returns….returns…...as after an additional stock of as after an additional stock of KK is is addedadded to the existing capital stock, we to the existing capital stock, we continue to continue to addadd one more unit of one more unit of KK, the stream , the stream of future cash return of future cash return will declinewill decline......


Marginal Efficiency of

Marginal Efficiency of

Capital Curve

Capital Curvee1

e2

Capital StockCapital Stock

M. E. M. E. C.C.

0


By the Above Formula:By the Above Formula:

for the last unit offor the last unit of KK,,

I.e. Assume the I.e. Assume the KK has no scrap value, has no scrap value,

PPkk = I = I00 + I + I11/(1+e) + I/(1+e) + I22/(1+e)/(1+e)22 + I + I33/(1+e)/(1+e)3 3 + … + I + … + Inn/(1+e)/(1+e)nn

For the value of For the value of PPkk remains unchanged, as I remains unchanged, as I ii decre decre

ases, the value of ‘e’ also decreases.ases, the value of ‘e’ also decreases.That is theThat is the increaseincrease in quantity ofin quantity of KK willwill decreasedecrease

MECMEC,, subject to the rule of diminishing returns.subject to the rule of diminishing returns.


Present Value

The Present Value (Pv) of the stream of income can be discounted by the market rate interest.

PPvv = I = I00 + I + I11/(1+r) + I/(1+r) + I22/(1+r)/(1+r)2 2 + I + I33/(1+r)/(1+r)33 + …. + I + …. + Inn/(1+r)/(1+r)nn

Note the equation:Note the equation: PPvv = I = I00 + I + I11/(1+r) + I/(1+r) + I22/(1+r)/(1+r)22 + I + I33/(1+r)/(1+r)33 + … + I + … + Inn/(1+r)/(1+r)n n ,, P Pvv is o is o

btained by btained by discountingdiscounting the future income strethe future income streamam


PPvv = I = I00 + I + I11/(1+r) + I/(1+r) + I22/(1+r)/(1+r)22 + I + I33/(1+r)/(1+r)33 + …. + I + …. + Inn/(1+r)/(1+r)nn

Where r = current market rate of interestWhere r = current market rate of interest If PIf Pkk = P = Pvv , then: e must equal to r , then: e must equal to r

If PIf Pkk > P > Pvv , then: e < r, the producer should reduce the cap , then: e < r, the producer should reduce the cap

ital (K) stock and back to the equilibrium;ital (K) stock and back to the equilibrium;

If PIf Pkk < P < Pvv , then: e > r, the producer should increase the ca , then: e > r, the producer should increase the ca

pital (K) stock in order to gain more.pital (K) stock in order to gain more.

We can conclude that the Demand for Capital (K) is the MEWe can conclude that the Demand for Capital (K) is the MEC (or ‘e’) curve at which MEC is equating current market C (or ‘e’) curve at which MEC is equating current market interest rate, r, at equilibrium. interest rate, r, at equilibrium.

The optimal amount of K is reached at every point of e = r.The optimal amount of K is reached at every point of e = r.


Marginal Efficiency of Capital

Marginal Efficiency of Capital

Curve = DD for Capital

Curve = DD for Capital

r1 =e1

r2 =e2

Capital StockCapital Stock

M. E. C. M. E. C. or or market market interest interest rate, r rate, r (%)(%)

0


Marginal Efficiency of Investment Marginal Efficiency of Investment (MEI)(MEI)

shows the inverse relationship between the shows the inverse relationship between the capital capital investedinvested currentlycurrently and the and the changing market changing market interest ratesinterest rates of an individual firm in a of an individual firm in a competitive market.competitive market.

Note that:Note that: Investment is a flow conceptInvestment is a flow concept

Demand for capital of the whole industry is ---Demand for capital of the whole industry is ---Horizontal summation of Marginal Efficiency Horizontal summation of Marginal Efficiency of Investment (MEI) schedules.of Investment (MEI) schedules.


However, You Should Note --However, You Should Note --

The Difference BetweenThe Difference Between

Marginal Efficiency of Capital (MEC) Marginal Efficiency of Capital (MEC)

and Marginal Efficiency of and Marginal Efficiency of

Investment (MEI) Schedule:Investment (MEI) Schedule:


Think About It….Think About It….

If current market rate of interest If current market rate of interest decreasesdecreases, a firm can i, a firm can increase its capital stock by purchasing ncrease its capital stock by purchasing more more KK goods goods at the going market price of capital.at the going market price of capital.

However, for a decline in the current market interest rate, allall firmsfirms increaseincrease their purchase of capital in the capital market, the value of Pk (i.e. (i.e. priceprice of the capital) of the capital)

increases.increases.

As Pk (i.e. (i.e. priceprice of the capital) of the capital) increases, the MEC decreases since they have inversely related. ( Pk ↑ e↓ and vice versa).


There Will Be a Downward Shifting of MEC Schedule

That is the MEC curve has been moved to have anan

other new lower MEC curveother new lower MEC curve.

We join all the equilibrium points of all MECi and

the market interest rates of this particular firm a

nd thus forms a STEEPERSTEEPER downward sloping

marginal efficiency of investment (MEI) schedu

le.


Shift in DD for Capital(MECs) and Shift in DD for Capital(MECs) and Marginal Efficiency of InvestmentMarginal Efficiency of Investment

M E C1

R%

Capital Stock

M E C2

0

ME I


Interest is the price of earlier availability; Interest is the price of earlier availability; Interest is the same as premium paid for Interest is the same as premium paid for

stream of service;stream of service;The income for the growth of a good;The income for the growth of a good;Interest is the yield from the net productivity Interest is the yield from the net productivity

of investment: the increase in income of investment: the increase in income created by investment today to transform created by investment today to transform some resources into a more highly valued some resources into a more highly valued form (e.G. Infra-structure) for later use;form (e.G. Infra-structure) for later use;

Fisherian Concept of Capital & Interest:Fisherian Concept of Capital & Interest:Irving Fisher (1867-1947) Asserted His RemarkaIrving Fisher (1867-1947) Asserted His Remarkable Theory of Interest That…ble Theory of Interest That…


Interest is the foreseeable growth in Interest is the foreseeable growth in wealth that is consumable without wealth that is consumable without reducing the initial amount.reducing the initial amount.

Interest is the expected income from one’s Interest is the expected income from one’s wealth. wealth. I = W * rI = W * r

Where I =income, w=wealth and Where I =income, w=wealth and R = rate of interest.R = rate of interest.

I.E.I.E. All expected future income All expected future income yielded is regarded as interest.yielded is regarded as interest.

Fisherian Concept of Capital & Interest:Fisherian Concept of Capital & Interest:


#There is no risk #There is no risk that what expected will happen is that what expected will happen is interest interest but but notnot a risk premium; a risk premium;

#There is #There is nono transaction cost:-- Contract of lending and transaction cost:-- Contract of lending and borrowing can be drawn on enforced costlessly borrowing can be drawn on enforced costlessly only only one rate of interest;one rate of interest;

#There is #There is notnot necessarily the money to be existed. Even necessarily the money to be existed. Even though money exists, it is only a unit of account. though money exists, it is only a unit of account. no no inflation or deflation is assumed.inflation or deflation is assumed.

#There is no non-transferable goods as #There is no non-transferable goods as all goods are marketall goods are marketable and have market prices.able and have market prices.

#The market is perfectly competitive.#The market is perfectly competitive.

Assumptions of Fisherian Theory of InAssumptions of Fisherian Theory of Interest: terest:


There Are DD for and SS of loanable There Are DD for and SS of loanable Funds Because Difference In:Funds Because Difference In:

Time preference or some economists term it Time preference or some economists term it as ‘temporal preference’---as ‘temporal preference’---

It shows theIt shows the marginal preferencemarginal preference of present of present over future consumption is positive.over future consumption is positive.

People People prefer prefer earlierearlier availability availability of goodsof goods and and different people have different degrees ofdifferent people have different degrees of time preference...time preference...


E.G. Two Persons, Mr A and Ms B:E.G. Two Persons, Mr A and Ms B:

Mr A has strong preference on present goods and Mr A has strong preference on present goods and willing to give up $130 next year to obtain $100 willing to give up $130 next year to obtain $100 now. now. And Ms B has weak preference for present And Ms B has weak preference for present goods and willing to give up $100 now for $110 goods and willing to give up $100 now for $110 next year:----next year:----

If r = 20% p.a. Mr A will borrow from Ms B.If r = 20% p.a. Mr A will borrow from Ms B. The Then, Mr A has to pay Ms B only $120 next year fon, Mr A has to pay Ms B only $120 next year for $100 now. r $100 now.

BOTH PARTIES WILL BE HAPPY THEN!BOTH PARTIES WILL BE HAPPY THEN!


After the Transaction of Lending After the Transaction of Lending and Borrowing:and Borrowing:

in view of diminishing marginal rate of time preferein view of diminishing marginal rate of time preference, nce, Mr. A’s preference for present consumptionMr. A’s preference for present consumption↓and Ms B’s preference for present consumption ↓and Ms B’s preference for present consumption ↑↑

The change of interest rate depends on the The change of interest rate depends on the relative strength of therelative strength of the DDDD and and SSSS force of force of loanable funds.loanable funds.

And, undAnd, under the working of market mechanism, er the working of market mechanism, equilequilibrium rate of interest is then reached.ibrium rate of interest is then reached.


There Are DD for and SS of loanable There Are DD for and SS of loanable Funds Because Difference Also In:Funds Because Difference Also In:

Investment opportunities:Investment opportunities: r↑ r↑ I ↓ and vice versa, I ↓ and vice versa, where r = rate of interest and I = investment. Lenwhere r = rate of interest and I = investment. Lending is an investment activity…ding is an investment activity…

E.g. lend $100 now for $110 next year E.g. lend $100 now for $110 next year investmen investment of the $100 with the rate of return of investment t of the $100 with the rate of return of investment = 10%. = 10%.

If lending of $100 now can get $120 next year, such If lending of $100 now can get $120 next year, such persons are willing to lend (invest).persons are willing to lend (invest).


Principles Developed FromPrinciples Developed From the Fisherian Theory of Ithe Fisherian Theory of Interest: nterest: All Resources Yield the Same Percentage oAll Resources Yield the Same Percentage of Its Capital Value!!f Its Capital Value!!

It is because:It is because: If P If Pk k = P = Pvv e = r e = r

If PIf Pk k > P > Pvv e < r e < r P Pkk ↓ ↓ e↑ e↑

If PIf Pk k < P < Pvv e > r e > r P Pkk ↑ ↑ e↓ e↓

To improve future income, it is necessary to To improve future income, it is necessary to maximize present value of wealth.maximize present value of wealth.


Fisher’s Separation Theorem:Fisher’s Separation Theorem:

Under competitive conditionUnder competitive condition, the decision on , the decision on production to earn income production to earn income is made is made separately fromseparately from the consumption decision the consumption decision as postulated by the as postulated by the maximization of maximization of present value of wealth.present value of wealth.


How the relationship among How the relationship among wealth wealth maximizationmaximization, , income maximizationincome maximization and and utility maximizationutility maximization, assuming , assuming people are maximizers?people are maximizers?

Some Remarks About Interest:Some Remarks About Interest:


(1) Wealth maximization versus inco(1) Wealth maximization versus income maximization:me maximization:

The postulate of maximizing income, whether it is The postulate of maximizing income, whether it is total income over time total income over time oror income in a particular income in a particular period of time, is in general period of time, is in general NOTNOT the same as the the same as the postulate of maximizing wealth; postulate of maximizing wealth; BECAUSEBECAUSE::

Income may fluctuate over time, hence it becomes Income may fluctuate over time, hence it becomes meaningless to pick a particular income for meaningless to pick a particular income for maximization maximization without considering the income without considering the income stream.stream.


(1) Wealth maximization versus income (1) Wealth maximization versus income maximization:maximization:

The profession with the highest total The profession with the highest total sum of income may sum of income may NOTNOT be the one be the one with the highest present value.with the highest present value.

Refer to your textbook ... illustration of Refer to your textbook ... illustration of Fisher’s Separation Theorem on P. about Fisher’s Separation Theorem on P. about the different income streams of three the different income streams of three different occupations!!different occupations!!


Perpetuity (Perpetuity ( 永續年金永續年金 ))

However, However, ifif income is expressed in terms income is expressed in terms of an infinitely long annuity (or of an infinitely long annuity (or perpetuity): perpetuity):

W = I / r, W = I / r, then maximizing either W or I then maximizing either W or I will be the same.will be the same.In a situation where there is In a situation where there is absenceabsence of of market rate of interest,market rate of interest, wealth wealth cannotcannot be derived.be derived.

A postulate of income maximization A postulate of income maximization would be entertained then.would be entertained then.


(2) Wealth maximization versus utility (2) Wealth maximization versus utility maximization:maximization:There are activities that entail non-pecuniary There are activities that entail non-pecuniary

benefits and costs, benefits and costs, such as marriage, such as marriage, friendship and child rearingfriendship and child rearing etcetc without without transferable market, which can only be transferable market, which can only be justified in terms of justified in terms of utility.utility.

In such situation, the postulate of wealth In such situation, the postulate of wealth maximization may not be useful.maximization may not be useful.

However, compared with the wealth criterion, However, compared with the wealth criterion, the utility criterion lacks the utility criterion lacks operational operational simplicitysimplicity in obtaining useful implications. in obtaining useful implications.


There is There is no no such thing as such thing as ‘profit maximization.’‘profit maximization.’

Since profit is an unexpected increase in wealth Since profit is an unexpected increase in wealth or income.or income.

Profit is the windfall gainProfit is the windfall gain that is not accounted that is not accounted

for previously by the receipt of interest from for previously by the receipt of interest from

the investment of savings.the investment of savings.

It is meaningless to study about ‘profit It is meaningless to study about ‘profit

maximization’.maximization’.

(2) Profit maximization???(2) Profit maximization???


Think…..Think….. & Recall Derived Recall Derived Demand....Demand....

Income is derived from capital goods, Income is derived from capital goods,

but the value of income is NOT but the value of income is NOT

derived from the value of the capital derived from the value of the capital

goods. goods.

Hence, the capital value Hence, the capital value is derivedis derived from from

the value of its the value of its future incomefuture income. .

Therefore capital isTherefore capital is NOT NOT the same as the same as

capital valuecapital value..


A Famous Dictum From Fisher:A Famous Dictum From Fisher:

““Interest is the whole of income, Interest is the whole of income, NOTNOT part part of income.”of income.”

The factor incomes of land and labour The factor incomes of land and labour (rent and wage) reflect their productivity (rent and wage) reflect their productivity over timeover time, so they are INTERESTS., so they are INTERESTS.

The The incomeincome of an individual is the of an individual is the maximum amount he or she can maximum amount he or she can consume per period of time while consume per period of time while leaving its wealth leaving its wealth unchangedunchanged..


Irving fisher pointed out that the distinctionIrving fisher pointed out that the distinctions betweens between wage, rent and interestwage, rent and interest areare mismisleading.leading.

The factor inputs are such a source of prodThe factor inputs are such a source of productive service capable of generating uctive service capable of generating a stra stream of future income.eam of future income.

Income or value is Income or value is NOT NOT just derived from lajust derived from labour service, but also from bour service, but also from any physical eany physical entityntity as capital and land. as capital and land.

Fisherian Concept of Interest:Fisherian Concept of Interest:


Questions for Assignment H.W.(1)

Q1. (A) define capital goods. Give examples.Q1. (A) define capital goods. Give examples.

(B) what is the market value (or current (B) what is the market value (or current

price) of a capital good?price) of a capital good?

Q2.What is 'wealth' in economic sense?Q2.What is 'wealth' in economic sense?

Q3 .What is the relationship between investment Q3 .What is the relationship between investment

and saving? and saving? Give Give examples of investment.examples of investment.


Answers for Assignment H.W.(1) Q.1

(a)Capital goods are durables that can produce a (a)Capital goods are durables that can produce a stream of goods and services in the future. stream of goods and services in the future. Examples include labour, good health, good Examples include labour, good health, good appearance, knowledge, land, property, appearance, knowledge, land, property, machines …etc. machines …etc.

(b) The market value of a capital good is the (b) The market value of a capital good is the summation of the value of current services and summation of the value of current services and the present values of the the present values of the future expected future expected servicesservices generated generated byby this capital. this capital.


Answers for Assignment H.W.(1) Q2

Wealth refers to the market value of all Wealth refers to the market value of all goods and services. Physical wealth is the goods and services. Physical wealth is the current stock of economic goods. …….current stock of economic goods. …….

The present value or the value of the wealth The present value or the value of the wealth is the stream of income or value of future is the stream of income or value of future services services discounted discounted with a known market with a known market interest rate .interest rate .


Q3 .Q3 .What is the relationship between What is the relationship between investment and saving? Give examples of investment and saving? Give examples of investment.investment.

Saving is defined as the non-consumption of standard Saving is defined as the non-consumption of standard income. People reduce their present consumption in income. People reduce their present consumption in the pursuit of future consumption. However, the pursuit of future consumption. However, investment is to transform the saving (not yet investment is to transform the saving (not yet consumed income )into productive capital for more consumed income )into productive capital for more future income.future income.

Hence, saving & investment work together.Hence, saving & investment work together.E.g. the conversion of milk into cheese, preserving E.g. the conversion of milk into cheese, preserving

salted eggs, raising of poultry, using steel instead of salted eggs, raising of poultry, using steel instead of wood, using pipelines instead of trucks. ….etc. wood, using pipelines instead of trucks. ….etc.


Questions for Assignment H.W.Questions for Assignment H.W.(2)(2)

44.What is interest? Give two reasons f.What is interest? Give two reasons for its occurrence.or its occurrence.

55.Explain why interest is a price? Fro.Explain why interest is a price? From the consumer's and investor's poinm the consumer's and investor's point of view, of what is 'interest' a 'price' t of view, of what is 'interest' a 'price' ??


Answer 4. What is interest? Give two Answer 4. What is interest? Give two reasons for its occurrence.reasons for its occurrence.

Interest is the price of earlier availabilityInterest is the price of earlier availability; I.e. the ; I.e. the premium paid by the borrower to obtain wealth premium paid by the borrower to obtain wealth earlier. It is because humans have a positive earlier. It is because humans have a positive rate of time preference (people are impatient to rate of time preference (people are impatient to wait). wait). They are willing to pay more in the They are willing to pay more in the future in order to get the goods now.future in order to get the goods now.

Interest is the same as premium paid for stream Interest is the same as premium paid for stream of service ; as there’re opportunity for of service ; as there’re opportunity for investment.investment.


Answer 4. What is interest? Give two reasons for Answer 4. What is interest? Give two reasons for its occurrence.its occurrence. Ans Cont’d…. Ans Cont’d….

The earlier availability of value is more valuable. The earlier availability of value is more valuable. To induce other to lend us, we must give To induce other to lend us, we must give interest to compensate for their loss of the interest to compensate for their loss of the value from present consumptionvalue from present consumption

In short:In short:Interest is the price of earlier availability; Interest is the price of earlier availability; Interest is the same as premium paid for Interest is the same as premium paid for

stream of service;stream of service;the income for the growth of a good too!!the income for the growth of a good too!!


Ans 5. Explain why interest is a price? From the coAns 5. Explain why interest is a price? From the consumer's and investor's point of view, what is 'intnsumer's and investor's point of view, what is 'interest' a 'price' of?erest' a 'price' of?

Interest is price because it is a sacrifice as one Interest is price because it is a sacrifice as one must make to exchange for something later.must make to exchange for something later.

From the consumer’s point of view, interest is the From the consumer’s point of view, interest is the price of the earlier consumption of goods.price of the earlier consumption of goods.

On the other hand, from the investor’s point of view, On the other hand, from the investor’s point of view, interest is the price or the cost of investment.interest is the price or the cost of investment.

It is true only for real interest rate It is true only for real interest rate (note that: (note that: nominal interest r = real interest r plus inflation nominal interest r = real interest r plus inflation rate)rate) and transaction cost is zero. and transaction cost is zero.


More Question: Q6 for discussion:More Question: Q6 for discussion:

(a) Is interest a stock or a flow?(a) Is interest a stock or a flow?

(b) Does interest exist without money?(b) Does interest exist without money?

(c) Does interest exist without market?(c) Does interest exist without market?(Answers to be followed)(Answers to be followed)

(a) Interest is a stream of receipts (income or services) (a) Interest is a stream of receipts (income or services) available at different periods of time. It is a flow.available at different periods of time. It is a flow.

(b) As receipts can be made in terms of money or other (b) As receipts can be made in terms of money or other commodities, interest exists with or without money.commodities, interest exists with or without money.


(c) Does interest exist without (c) Does interest exist without market?market?

If interest refers to the return of capital(in If interest refers to the return of capital(in broad sense), it exists with or without market. broad sense), it exists with or without market.

If interest refers to the cost of borrowing or the If interest refers to the cost of borrowing or the extra value of an entity owned today over the extra value of an entity owned today over the entity owned in future (in the narrow sense), it entity owned in future (in the narrow sense), it does not exist if there is no borrowing or does not exist if there is no borrowing or lending. So without market, interest does not lending. So without market, interest does not exist.exist.


Further Question 1 for Further Question 1 for discussion:discussion:

Suppose there are two brands of air-conditioner. Their life Suppose there are two brands of air-conditioner. Their life

spans (5 years) and functions are the same but their prices, spans (5 years) and functions are the same but their prices,

energy consumption and maintenance costs are different. energy consumption and maintenance costs are different.

Given the information in the table below, which brand of Given the information in the table below, which brand of

air-conditioner will you buy if the interest rate is 10%?air-conditioner will you buy if the interest rate is 10%?

Energy consumption and main. costEnergy consumption and main. cost

Brand Brand Price Price ( (To be paid at the end of each year)To be paid at the end of each year)

A $4000 A $4000 $ 1555$ 1555

BB $4200 $4200 $ 1500$ 1500


Further Q1---Key Thinking:Further Q1---Key Thinking:

If two durable goods perform the same If two durable goods perform the same function, a buyer (maybe a consumer or function, a buyer (maybe a consumer or producer) would choose the one involving the producer) would choose the one involving the minimum cost.minimum cost.

As future costs involved, for comparison, present As future costs involved, for comparison, present value of the costs should be found out.value of the costs should be found out.


Further Q1---Key :Further Q1---Key :

Present value of the total cost paid of Brand APresent value of the total cost paid of Brand A

=4000+(1555/0.1)[1- 1/(1.1)=4000+(1555/0.1)[1- 1/(1.1)55]]==9894.679894.67Present value of the total cost paid of Brand BPresent value of the total cost paid of Brand B

=4200+(1500/0.1)[1- 1/(1.1)=4200+(1500/0.1)[1- 1/(1.1)55]]==9886.189886.18

To minimize cost, Brand B air-conditioner would be To minimize cost, Brand B air-conditioner would be chosen.chosen.


Further Question 2 for discussion:Further Question 2 for discussion:

Suppose you have a mortgage loan with a Suppose you have a mortgage loan with a bank. You borrow $2 000 000 at an interbank. You borrow $2 000 000 at an interest rate of 8.25% (the prime rate) for 20 est rate of 8.25% (the prime rate) for 20 years. years.

What is your monthly installment?What is your monthly installment?



Hire purchase is the payment by installment. The Hire purchase is the payment by installment. The present value of installments is equal to the present value of installments is equal to the purchase price (or the amount borrowed).purchase price (or the amount borrowed).

Let I be the monthly installment:Let I be the monthly installment:(I/0.6875%)[1-1/(1+0.6875%)(I/0.6875%)[1-1/(1+0.6875%)240240] = 2 000 000] = 2 000 000

117.36 I = 2000 000117.36 I = 2000 000I = 17041.58I = 17041.58


Note: When market interest rate is Note: When market interest rate is up, thenup, then

the present value of the installments drops. the present value of the installments drops.

To repay the loan, either the amount of To repay the loan, either the amount of

installment or the number of installments installment or the number of installments

has to be increased. has to be increased.



Suppose you have purchased a bottle of wine at Suppose you have purchased a bottle of wine at the price of $100. After adding in some herbal the price of $100. After adding in some herbal medicine, its value is expected to grow by $15 medicine, its value is expected to grow by $15 each year. If the market rate of interest is 10%, each year. If the market rate of interest is 10%, when will you sell your bottle of wine?when will you sell your bottle of wine?

Refer to the data above:Refer to the data above:What happen to the optimal year of sale, ifWhat happen to the optimal year of sale, if(a) the interest rate rises?(a) the interest rate rises?(b) the storage of the wine involves cost? (b) the storage of the wine involves cost?


Further Q3---Principle & Key Further Q3---Principle & Key ::

Crops, livestock, fish, wine etc. are assets with a Crops, livestock, fish, wine etc. are assets with a growing future value. Note that these assets can growing future value. Note that these assets can be sold once only. To maximize wealth, they are be sold once only. To maximize wealth, they are sold at the year giving the LARGEST gain. sold at the year giving the LARGEST gain. However, it is the PRESENT VALUE, NOT the However, it is the PRESENT VALUE, NOT the future market value to be maximized. future market value to be maximized. So the So the optimal year of sale is the year that the market optimal year of sale is the year that the market price yields the price yields the largest largest present value.present value.



Year Year Market Future valueMarket Future value Discounted valueDiscounted value

00 $100$100 $100.00$100.00

11 $115$115 $104.50$104.50

22 $130$130 $107.44$107.44

33 $145$145 $108.94$108.94

44 $160$160 $109.28$109.28

55 $175$175 $108.66$108.66

66 $190$190 $107.25$107.25


Further Q3---Principle & Key :Further Q3---Principle & Key :

If (a) the interest rate risesIf (a) the interest rate risesthe optimal year of sale will be shorter the optimal year of sale will be shorter

than 4 years,than 4 years,

(b) the storage of the wine involves cost(b) the storage of the wine involves costthe optimal year of sale will be shorter the optimal year of sale will be shorter

than 4 years also.than 4 years also.



Suppose you are the monopolist of an Suppose you are the monopolist of an

exhaustible resource and you want to exhaustible resource and you want to

use up the resource in five years. What use up the resource in five years. What

will be the amount of resource sold in will be the amount of resource sold in

each year if you face a stable demand?each year if you face a stable demand?


Further Q 4 ---Key Thinking :Further Q 4 ---Key Thinking :

Market value of a resource at different Market value of a resource at different years cannot be compared unless they are years cannot be compared unless they are discounted into present values. discounted into present values.

To maximize wealth, resources would be To maximize wealth, resources would be allocated and sold in different years such allocated and sold in different years such that the discounted values of the prices in that the discounted values of the prices in different years are the same.different years are the same.

REASON??REASON??


Further Q 4 ---Key Thinking :Further Q 4 ---Key Thinking :

It is because from the stable demand, the It is because from the stable demand, the future market price can be correctly future market price can be correctly expected and then the Present Value can be expected and then the Present Value can be calculated.calculated.

To max wealth, some resources would be re-To max wealth, some resources would be re-allocated from the year with a price of allocated from the year with a price of LOWER present value to the year with a LOWER present value to the year with a price of HIGHER present value, hence the price of HIGHER present value, hence the present value at different years are equated.present value at different years are equated.



At an interest rate of 5%, what is the At an interest rate of 5%, what is the maximum price of the following asset?maximum price of the following asset?

Suppose a bond yields a fixed annual Suppose a bond yields a fixed annual return of $1000 for 5 years and it will return of $1000 for 5 years and it will redeemed at $10 000 at end of the fifth redeemed at $10 000 at end of the fifth year. What is the price of the bond?year. What is the price of the bond?


Further Q 5---Key :Further Q 5---Key :

The capital value (maximum The capital value (maximum price) of the bond is:price) of the bond is:

($1000/0.05)[1-1/(1.05)($1000/0.05)[1-1/(1.05)44] + $11000/(1.05)] + $11000/(1.05)55

= $3545.95 + $8618.79= $3545.95 + $8618.79

= $12,164.74= $12,164.74



At an interest rate of 5%, what is the At an interest rate of 5%, what is the maximum price of the following asset?maximum price of the following asset?

Suppose a taxi license entitles its owner to Suppose a taxi license entitles its owner to operate a taxi forever. The cost of operating operate a taxi forever. The cost of operating a taxi is $200,000 a year, gross income is a taxi is $200,000 a year, gross income is $350,000 a year and the tax rate is 15% of $350,000 a year and the tax rate is 15% of the net income. the net income.

Estimate the maximum price of the license.Estimate the maximum price of the license.


Further Q 6---Key :Further Q 6---Key :

The annual net return of a taxi owner is:The annual net return of a taxi owner is:350000 - 200000 - 0.15(350000-200000) = 127500350000 - 200000 - 0.15(350000-200000) = 127500

As the net future returns last forever As the net future returns last forever annually, the maximum capital value of annually, the maximum capital value of the taxi license is :the taxi license is :

= $127 500 / 0.05 = $2,550,000= $127 500 / 0.05 = $2,550,000

(note: the calculation of perpetuity)(note: the calculation of perpetuity)

econ dept jccss(tm)1 2 the theory of interest --- return to ‘capital’? traditional approach of...

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