hkale economics

CH9-Factor Market(2)

By Mr. LAU san-fat 1

HKALE Economics

Chapter 9: Factor Market(2)-Capital, Interest and Investment

Exchange & Production, Alchian & Allen, Chapter 6Advanced Level Microeconomics, LAM pun-lee, Chapter 13A-Level Microeconomics, CHAN & KWOK, Chapter 8HKALE Microeconomics, LEUNG man-por, Chapter 13



Capital and Capital Assets

Capital: Traditional Classification a result of different physical

characteristics man-made resources

Capital: Modern Viewpoint is durable good is any asset that is capable of generating

a stream of future services or income



Capital and Capital Assets

Irving Fisher’s concept of capital assets: Capital assets are goods with future

income potential ALL factors are capital as they are

capable of generating future services or income.



Reasons for Interest

1. For earlier availability People usually have a positive

marginal time preference or human impatient, i.e. we prefer present to future goods.

Interest is the premium paid by borrower to obtain goods earlier

Interest is the premium received by the lender in return for deferring consumption.



Reasons for Interest

2. Productivity of capital Future goods are worth less than the same

present goods because present goods can sometimes be converted to even more valuable future goods via investment.

Interest is the yield or gain from the productivity of capital

If the interest expected by an investor exceeds the interest charged by the lender, an exchange of present and future goods between them is possible and mutually beneficial.



Assumptions Behind

No inflation or no money Interest exists with or without money

because people prefer earlier availability of goods

No risk or uncertainty Interest is for deferring our present

consumption



Assumptions BehindNo transaction costs So the interest paid by the borrower

is the same as that received by the lender, i.e. only one market rate at a time.

Goods are transferable The market capital values & income or

interest of non-transferable goods cannot be determined.



The Market Rate of Interest

The market rate of interest is determined in the loanable fund market.

Demand for loanable fund: Demand for consumption loans: People w

ill demand for loanable fund for earlier consumption if his positive marginal rate of time preference is higher than the market rate of interest.




Demand for loanable fund: Demand for investment loans: People will

demand for loanable fund for investment if he regards his marginal productivity of capital/investment is higher than the market interest rate.




Supply of loanable fund: People will supply loanable fund by deferr

ing his consumption if his marginal rate of time preference is lower than the market rate of interest.

The demand and supply curves of loanable funds will change if the marginal rate of time preference and the marginal productivity of capital change.



The Market Rate of Interest%

D S

r

L Loanable fundsDetermining market interest rate in the loanable fund market




Competition among borrowers or investors and lenders or savers moves the market interest rate toward an equilibrium. If the market demand for loanable fund i

ncreases and at the original market interest rate, shortage exists. Borrowers or investors are thus willing to pay more, resulting in a higher equilibrium market rate of interest; vice versa.




Competition among borrowers or investors and lenders or savers moves the market interest rate toward an equilibrium. If the market supply of loanable fund incr

eases and at the original market interest rate, surplus exists. Lenders or savers are thus willing to pay more, resulting in a lower equilibrium market rate of interest; vice versa.




Exercise 1: Interest can be both a value and a cost. Why?

Interest reflects the value people place on the earlier availability of goods and the cost of obtaining goods earlier. At the margin, they are the same.



Compounding

The process of compounding is to find the future amount of income when it is invested at the market rate of interest.

P(1+r)t = I

Where P = present amount invested r = the market rate of interest I = the future amount t = the number of years



Discounting

The process of discounting or capitalization is to turn the future stream of services or income into its equivalent present value at present market rate of interest.Investment is profitable if the discounted present value is equal to or larger than the capital price/value.



Discounting 1

Discounting the present value of a single future amount

PV = I/(1+r)t

Where PV = present value r = the market rate of interest I = the future amount t = the number of years



Discounting 2

Discounting the present value of a finite stream of future income

PV = I0+I1/(1+r)1+I2/(1+r)2+…+It/(1+r)t

I0, I1, I2 …It = payments received now, after 1 year, 2 years, … and t years respectively



Discounting 2

Discounting the present value of a finite stream of future income

PV = I0+I1/(1+r)1+I2/(1+r)2+…+It/(1+r)t

If I0, I1, I2 …It are the same, the (same) payment for each year is called an annuity.



Discounting 3

Discounting the present value of an infinite stream of future income.If the future payment every year and forever is the same, it is called perpetuity or infinite annuity.

PV = I/r



Compounding and Discounting

Exercise 2: Suppose the market interest rate is 8%. Find the present value of $1 million, to be received after 5 years.Exercise 3: Suppose you can borrow $1 000 at zero interest rate for 3 years. If the market rate of interest is 10%, what is the present value of the benefits from zero-interest borrowing?Exercise 4: Suppose the market interest rate is 6%. Consider an asset which provides the following income stream: $1 000 received after 1 year, $1 500 received after 2 years, and $2 000 received after 3 years. Are you willing to pay $4 000 to buy the asset?



Compounding and Discounting

Exercise 5: A bond promised to pay $10 interest a year. The face value is $100 and the maturity is 3 years. If the market rate of interest is 8%, what is the present value of the bond?Exercise 6: Suppose a taxi licence allows the holder to receive a fixed income of $100 000 every year. Given a market interest rate of 5%, determine the market value of a taxi licence. What will be the effect on the licence value if the interest rate decreases?



Factor Affecting Present Value

As PV = I/(1+r)t

Thus, the PV of a future stream of income falls when: The smaller is the future amount, I The higher is the market rate of

interest, r The farther in the future is the future

amount, t



Factor Affecting Present Value

As PV = I/(1+r)t

Thus, The longer the life duration of an

asset (i.e. larger value of t), the more susceptible is the present value to changes in the market rate of interest; vice versa.

The changes in the market rate of interest will have a greater effect on the PV of long-lived assets relative to short-lived assets.



Marginal Efficiency of Capital

The marginal efficiency of capital (MEC) is the rate of discount that equates the price of a new capital good with the present value of the stream of future cash returns from the additional capital.

In short, MEC is the internal rate of return of an extra unit of capital.




P= I0+I1/(1+e)1+I2/(1+e)2+…+It/(1+e)t

I0, I1, I2 …It = stream of future cash returns of an extra unit of capital, with a given existing stock of capital.

P = purchase price of the capital good e = MEC t = life of the capital good




If the MEC (e) is greater than the market rate of interest (r), it implies that the present value (PV) of the capital good is greater than its purchase price (P) and the firm should invest; vice versa.

If e > r, then I0+I1/(1+e)1+I2/(1+e)2+…+It/(1+e)t >

I0+I1/(1+r)1+I2/(1+r)2+…+It/(1+r)t

P < PV Profitable to invest




The MEC schedule is decreasing because the marginal product of capital is decreasing. The MEC shows the negative relationship between the internal rate of return and the stock of capital.

Internal rate of return (%)

MEC

0 Stock of capital



Marginal Efficiency of Investment

It takes time to increase the stock of capital via investment when there is a fall in the market rate of interest. A single firm will increase its capital stock in responding to a reduction in the market interest rate. However, if all firms try to increase the capital stock, this will push up the purchase price of capital goods.




As the purchase price of capital goods rises, the MEC will fall and the MEC schedule will shift downward, resulting in a less-than-expected increase in the stock of capital.

The marginal efficiency of investment (MEI) shows the effect of rising purchase price of new capital as investment actually takes place upon the expected rates of returns on investment.




Internal rate of return (%)

MEI MEC1 MEC2

r1

r2

0 Q1 Q3 Q2 Stock of capital

Remarks:-Market rate falls (from r1 to r2)-Stock of capital increases from Q1 to Q3 initially-rise in capital price leads to a leftward-shifting of MEC curve (from MEC1 to MEC2)-the actual increase in the stock of capital (from Q1 to Q3) is less than expected, which is shown by a steeper-sloped MEI curve.



Remarks on Interest Rate

If inflation is expected to occur, lenders and borrowers can compensate for it by adjusting the nominal rate of interest so as to maintain the value of real rate of interest.

Nominal rate of interest =real rate of interest + anticipated inflation rate




If risk and uncertainty exist, riskier loans demand higher rate of interest and promise higher yields to the lenders; vice versa.

To borrowers, they are willing to pay a higher rate of interest for long-term loans as they are certain of having use of the amount for longer period; vice versa.




If transaction costs exist in collecting information and negotiating the transactions of loans, the rate of interest being received and paid would not be the same.With the provision of professional services in facilitating borrowing and lending, financial intermediaries earn the difference in borrowing and lending rates.




An underpriced asset (with its price smaller than its PV) would give a higher rate of return than other assets, so people drive up its price as they compete for that asset. An overpriced asset however will yield less than the market rate of interest, so no one would want to hold it at that price and its price would fall.




Therefore, at equilibrium, by competition, the capital price must be equal to the present value of its stream of future income, and its expected rate of return must be equal to the only market rate of interest. However, in reality, there may have more than one market rates of interest so as to reflect the existence of transaction costs or differences in risk, expected inflation rates, duration of loans, and the terms and costs of administration.



Wealth and Income

Wealth, in physical sense is the stock of economic goods at a particular time while in value sense, it is the market value of the current stock of economic goods.

Income (or interest) is the flow of potential consumption or the foreseeable growth in wealth which can be made without trenching on wealth.



Wealth and Income

In physical sense, wealth (W) creates income (I), or capital (K) produces interest (r).

W x r = I



Wealth and income

If the future income stream is an infinite annuity, the present value of one’s wealth is the future income discounted.Therefore, in value sense, it is the (discounted future) income (I) that determines (the market value of) wealth (W), or interest (r) produces capital (K).

W = I/r



Saving or Investment

Saving is the non-consumption of income.Investment is the use of unconsumed income to create more future income. It is the balancing of consumption over time, present consumption being sacrificed for (expected more) future consumption.

Exercise 7: Explain whether converting fresh oysters into dried oysters is investment.




If there is zero cost of storing or any other transaction cost, investors will keep their investment project for a period that will maximize its present value. Alternatively, investors will keep their investment projects until the rate of increase in the market value (or internal rate of return) of the item is equal to the market rate of interest.




However, if significant transaction costs such as cost of storing exist, investment period would be shortened. The change in the market value, however, as age increases must surpass both the market rate of interest and the storage (or transaction) cost.



Investment and Profit

Profit is then an unexpected increase in wealth or income when the actual rate of return is higher than the expected rate of return or market rate of interest.

In the absence of perfect foresight or with the presence of transaction costs, profits can be realized.



Fisher’s Separation Theorem

Fisher’s Separation Theorem states that under competitive conditions, the decision on production to earn income is made separately from the decision of consumption. Since consumption can be independent of production, a person will select a stream of future income that yields the highest present value, in order to obtain the greatest opportunities for consumption over time.



Choice Among Professionals

Assumptions: The objective is to maximize one’s wealth,

i.e. maximizing the present value of a stream of future income.

One could lend or borrow at the same interest rate to adjust the ‘shape’ or pattern of the income stream of different professionals.



Choice Among Professionals

Exercise 8: Explain which of the three professionals would be chosen if (1) the market rate of interest is zero; (2) the market rate of interest is quite high; and (3) the market rate of interest is sufficiently low.



Wealth Vs. Income Maximization

Because: Wealth is a stock concept while income is a

flow Incomes in different periods of time may have

different value

Therefore, the postulate of maximizing income, whether it is total income over time or income in a particular period of time, is in general not the same as the postulate of maximizing wealth.



Wealth Vs. Income Maximization

As income may fluctuate over time, it is meaningless to pick a particular income for maximization without considering the income stream. If income stream is an infinitely long annuity or perpetuity, then maximizing wealth or income will be the same.However, the postulate of income maximization would be preferable if there is no market rate of interest and wealth cannot be derived.



Wealth Vs. Utility Maximization

The postulate of utility maximization would be preferable to wealth maximization for those activities entail non-monetary or non-pecuniary gains and costs.

When using the postulate of utility maximization, we have to identify the options which will give us non-monetary gains and costs. However, these are not easy tasks and we are prone to falling into the trap of tautology while using this postulate. Compared with the wealth criterion, however, the utility criterion lacks operational simplicity in obtaining implications refutable by fact.



Concluding Remarks

Capital is not the same as capital value, which is derived from the value of the capital’s future income.



Concluding Remarks

Capital value is the value of future income discounted: K = I0+I1/(1+r)1+I2/(1+r)2+…+It/(1+r)t

While wealth in value sense is the market value of the current stock of economic goods, which includes the present good enjoyed by the owner: W = I0+I1/(1+r)1+I2/(1+r)2+…+It/(1+r)t

Thus, capital value (K) is not exactly equal to the wealth (W) in value sense: K = W – I0



Concluding Remarks

According to Irving Fisher, all factors of production are capital as they are all capable of generating a stream of future services or income. Therefore, Interest is not part of income, but the whole of income.

Moreover, income or value is not just derived from labor service, but also from capital and land.

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