First, a simple version of the answer: Your one real apple becomes eight nominal pseudoapples (at 700%), which is four real apples after 100% inflation. One goes bad, so you are left with three apples, i.e., a rate of return of 200%.

Now, the more complete version: Your numeraire is one apple (1a) that costs $1. You will get $8 in nominal terms, next year (a . (1 + rnominal, before tax) = a . (1 + 700%) = 8 . a). This will purchase apples that cost $2 each ((1 + π) = (1 + 100%) = $2), that is, four apples (a . (1 + rnominal, before tax)/(1 + π) =

1a . (1 + 700%)/(1 + 100%) = 4a).However, one of the apples (d = 25%) is bad, so you will get only three apples (a1

= a0 . (1 + rnominal, before tax)/(1 + π) . (1 −

d) = 1 . a0 . (1 + 700%)/(1 + 100%) . 75% =

3 . a0). Therefore, the real rate of return is (a1

− a0)/a0, or

The “1a” of course cancels, because the formula applies to any number of apples or other goods.

Transcribed Image Text:

(la. 1+700% 1+100% 75%) la Treal, after tax, post default= la [la 1+nominal, before tax 1+ (1-d)]-la Treal, after tax, post default: la 300% 1 200% - =