Profit, Rent,& Interest

Sources of Economic Profit

reward for assuming uninsurable risks

(for example, unexpected changes in demand or cost conditions)

reward for innovation monopoly profits

Transfer Earnings

the amount that an input must earn in its present use to prevent it from transferring to another use.

Rent

the difference between what an input is actually paid and its transfer earnings

Example: Suppose you are willing to do a job as long as you are paid at least $8 per hour, and you are getting paid $10 per hour.

What are your transfer earnings?

8

What is your rent?

10 - 8 = 2

Example: Suppose an input is earning $10 per hour, but would be willing to do the job without pay.

What are the transfer earnings?

0

What is the rent?

10 - 0 = 10 (All of its pay is rent.)

Capital

also called physical capital. a factor of production. examples: buildings and machines.

To purchase capital, you would probably need to borrow funds. What does the market for loanable funds look like?

Demand for loanable funds

People borrow less if the price of the funds is high. (The price of the funds is the interest rate.)

So, there is an inverse relation between the interest rate and the quantity demanded of loanable funds.

So, the demand curve for loanable funds slopes downward.

Demand for loanable fundsinterest rate

loanable funds

D

Supply of loanable funds

People are willing to lend more money if the interest rate is high.

So, there is a direct relation between the interest rate and the quantity supplied of loanable funds.

So, the supply curve for loanable funds slopes upward.

Supply of loanable funds

interest rate

loanable funds

S

Combine the demand for loanable funds and the supply of loanable funds.

interest rate

loanable funds

D

S

The equilibrium quantity of loanable funds and the equilibrium interest rate.

interest rate

loanable funds

D

S

i*

Q*

real rate of interest

money rate of interest - inflation rate

If the money rate of interest is 7% and the inflation rate is 3%, what is the real rate of interest?

real rate of interest = 7% - 3% = 4%

Why are there different interest rates?

differences in costs of processing It costs more to process a $100,000 loan than a

$10,000 loan, but not ten times as much. differences in risk Will the loan be paid back on time and in full?

Some people are riskier than others. different loan durations conditions such as the inflation rate may change

during the period of the loan

Components of the Money Interest Rate

inflation premium cost premium covering processing and risk pure interest - price of earlier availability

The pure interest component:People are willing to pay to get money now

rather than wait until later because...

1. People prefer to have goods now rather than to have to wait for them.

2. People can use the money to buy something that will increase their productivity, so they can make more later.

Compounding

Suppose you put $100 in the bank with an annual interest rate of 5%.

How much will you have next year?

100 + .05(100)

= 100 + 5

= 105

or 100 (1+.05) 1

Suppose you leave the money in the bank. How much will you have 2 years from now?

105 + (.05)(105)

= 105 + 5.25

= 110.25

or 100 (1+.05) 2

How much will you have 3 years from now?

110.25 + (.05)(110.25)

= 110.25 + 5.51

= 115.76

or 100 (1+.05) 3

1 year from now: 100 (1+.05) 1 2 years from now: 100 (1+.05) 2 3 years from now: 100 (1+.05) 3

How much will you have n years from now?

100 (1+.05) n

With an interest rate of .05, n years from now, 100 dollars will become 100 (1+.05) n

Suppose you put R dollars in the bank with an annual interest rate of 5%. How much will you have n years from now?

R (1+.05) n

With an interest rate of .05, n years from now, R dollars will become R (1+.05) n

Suppose you put R dollars in the bank with an interest rate of i. How much will you have n years from now?

R (1 + i) n

We have concluded that if you put R dollars in the bank with an interest rate of i, in n years you will have

R (1 + i) n .

An alternative way of writing this information emphasizes the present and future aspects.

Let PV be the current or present value that you are putting in the bank now and FV be the future value that you take out later. Then, we have

(1 ) .nFV PV i

Present Value

Present Value (PV)

calculated by discounting, which is the opposite of compounding

also called Present Discounted Value (PDV) or Net Present Value (NPV)

Suppose you are going to receive R dollars at some time in the future.

The PV of that R dollars is the amount you need to put in the bank today, to receive the R dollars n years in the future, if the interest rate is i.

If the annual interest rate is 5% and you want to have $100 next year, how much do you

have to put in the bank now ?

PV = 100 / (1+.05) 1 = 95.24

If the annual interest rate is 5% and you want to have $100 in 2 years, how much do you

have to put in the bank now?

PV = 100 / (1+.05) 2 = 90.70

1 year: 100 / (1+.05) 1

2 years: 100 / (1+.05) 2

If the interest rate is 5% and you want to have $100 in n years, how much do you have to put in the bank now?

PV = 100 / (1+.05) n

If the interest rate is .05, to get $100 in n years, we need to put in the bank now: 100 / (1+.05) n

If the interest rate is .05, to get R dollars in n years, how much do you have to put in the bank now?

PV = R / (1+.05) n

If the interest rate is .05, to get R dollars in n years, we need to put in the bank now: R / (1+.05) n

If the interest rate is i, to get R dollars in n years, how much do you have to put in the bank now?

PV = R / (1 + i) n

We have concluded that if the interest rate is i, to get R dollars in n years,

the amount you need to put in the bank now is

Since, in this case, the R will be received in the future, let’s rewrite it as future value FV. Then, we have

.(1 )

FVPV

ni

  .(1 )

RPV

ni

Notice the similarities between our compounding and discounting formulae.

Compounding: (1 )nFV PV i

Discounting:(1 )

FVPV

ni

These formulae are actually equivalent, and one can be derived from the other simply by multiplying or dividing.

Stream of Income: How much should you put in the bank now,

with an annual interest rate of i, in order to take out FV1 one year from now,

FV2 two years from now, and FV3 three years from now?

PV =

Stream of Income: How much should you put in the bank now,

with an annual interest rate of i, in order to take out FV1 one year from now,

FV2 two years from now, and FV3 three years from now?

PV = FV1 / (1 + i)1

Stream of Income: How much should you put in the bank now,

with an annual interest rate of i, in order to take out FV1 one year from now,

FV2 two years from now, and FV3 three years from now?

PV = FV1 / (1 + i)1 + FV2 / (1 +i)2

Stream of Income: How much should you put in the bank now,

with an annual interest rate of i, in order to take out FV1 one year from now,

FV2 two years from now, and FV3 three years from now?

PV = FV1 / (1 + i)1 + FV2 / (1 +i)2 + FV3 / (1 + i)3

The present value of an amount of money received (or paid) now is that

same amount of money.

example:

The PV of $100 received now is $100.

The PV of future income increases

when the interest rate decreases. when the amount of income received

increases. when the time the income is received is

closer to the present.

Present Value of an Annuity

An annuity pays a fixed amount R every year from now on into the future.

The present value of an annuity paying R dollars every year with an interest rate of i is

PV = R / i

Compare the present value of the benefits with the present value of the costs.

How do you determine whether you should make an investment?

PV(benefits) PV(costs)

INVEST

>If

PV(benefits) PV(costs)

DON’T INVEST

<If