Suppose that you borrow $1000 to be paid back in a lump
sum at 5 percent annual interest in 5 years. When the loan
comes due you will have to pay back

$1000 (1 + r)^{n} = $1000 (1.05)^{5} = $1276.28.

Suppose, however, that during this five year interval the price level doubles. The amount of goods you will have to give up to pay back this loan will be only half as much as the required dollar payment would indicate because a dollar will be worth only half as much in real terms.

In real terms, therefore, you will have to pay back only $638.14, valued in goods at the time the money was borrowed. From your point of view, this is great. You will have borrowed $1000 worth of real goods for five years and paid back less than $640 of real goods. The interest rate you will have actually paid (as opposed to the 5 percent you contracted for) can be found by substituting the real amount borrowed and the real amount repaid into the formula

A_{0} = A_{1} ⁄ (1 + r)^{n}

to yield $1000 = $638.14 ⁄ (1 + r)^{5} from
which r = [(638.14/1000)^{1/5}] - 1 = -.085 or
minus 8.5 percent.

Although you contracted to pay the individual you borrowed
from an interest rate of 5 percent, that person actually ended up
paying you interest at the rate of 8.5 percent per year to borrow
from her. The unexpected inflation will have redistributed real
wealth from your creditor to you. You are contracting to pay
$1276.28 in five years and will actually pay $638.14 in real terms.
Or to put it differently, the $1276.28 which you pay back will buy
only half as many goods as was expected when the loan was made. The
present value of that difference, discounted at the market
interest rate of 5 percent, is $638.14 ⁄ (1 + r)^{5}
= $500. This figure should not be surprising because a doubling of
the price level is wiping out half of the value of the loan measured
in current dollars.

Of course, were you to lend $1000 for five years to somebody
under circumstances where the price level unexpectedly doubles
during the term of the loan, the person you lend to will gain $500,
in current dollars, at your expense. **Unexpected inflation always
redistributes wealth from people who have contracted to receive fixed
nominal amounts in the future to the people who have contracted to pay
those fixed nominal amounts.
**

**
Unanticipated deflation has the opposite effect**. The person
who has borrowed a fixed nominal amount has to pay back with
dollars that are worth more in terms of real goods than he/she
had contracted for, and the person who is the creditor is paid
an amount that is greater in real terms than anticipated so that
**wealth is redistributed from debtors to creditors.
**

**
When there an unanticipated movement of the price level, the real
interest rate actually realized on loans will be different from
the interest rate at which the loan contract was made**. This realized
real interest rate can be calculated quite easily in the case
of one-year loans. Suppose that you borrow $100 for one year at
an agreed upon interest rate of 6 percent and that, contrary to
what both you and the lender expect when you make the loan, the
inflation rate turns out to be 3 percent rather than zero percent.
You pay the lender $106 at the end of the year, but that $106 is
worth only about $103 because $100 will buy $3 less goods at the
end of the year. The interest rate actually realized is thus only
about $3/$100 or 3 percent. **The realized real interest rate is
thus approximately equal to the contracted interest rate minus the
actual rate of inflation.
**

**
Unanticipated inflation has very important wealth redistribution
effects in an economy.** People who take out mortgages in
order to buy houses at fixed interest rates end up paying back
less in real terms than they had contracted for---**wealth is
redistributed from banks and other financial institutions (or,
more correctly, the people that own them) to homeowners with
mortgages**. Individuals who retire on pensions that are fixed in
nominal amount will find the values of those pensions in terms of
the goods they buy eroded as years pass---in this case the **redistribution**
is **from pensioners to the owners of insurance companies and other
financial institutions that have contracted to pay them fixed dollar
amounts.**

Unanticipated inflation has **additional distribution effects
that work through the tax system**. Many countries have progressive
income tax systems under which high income people pay higher
percentage rates of tax on additions to their income than low
income people. Since **income tax rates are based on nominal rather than
real income**, the inflation of nominal incomes will put people in
higher tax brackets, increasing the amount of taxes paid to the
government in greater proportion than the increase in the price
level. Real tax payments and the availability of resources to the
government will therefore increase. Unless the tax system is
modified to take it into account, fully anticipated inflation
has these same effects.

Also, business firms are normally allowed to deduct allowances for
the depreciation of their capital from their revenues in order to
calculate the profits on which they must pay taxes to the government.
**Depreciation allowances are usually calculated as a percentage of
historic cost**. When inflation occurs and all nominal prices and wages
rise together, these depreciation allowances based on the prices
prevailing when the capital was purchased do not rise. The real value
of firm's cost deductions therefore declines, leading to a rise in
real taxes paid. Since the real costs of replacing depreciated capital
are not lowered by inflation and real taxes increase, firm's real profits
fall. Different industries will be affected differently depending upon
the particular rules the tax law requires them to follow in calculating
their depreciation allowances.

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Question 1

Question 2

Question 3

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