ECONOMICS 3600
THIRD SPREADSHEET EXERCISE
ANSWERS
What are the values of the discount operators, D12 , D25, and D45 for  = 0 __12.0__, __25.0__,
__45.0___? For  = .02 _10.57___, __19.52___, __29.49___? For  = 0.05 __8.86__, ___14.09___,
__17.77___? For  = .10 _6.81___, __9.08___, __9.86___? For  = .20 ___4.44___, __4.95___,
__5.00___?
For values of greater than .02, why is D24 less than 2·D12?
Because the denominator is non-linear and rising by the power of t. (This statement is actually true
for =.02 too.) So the denominators of t = 13 to 24 are all smaller, much smaller in most cases, than
the denominators of t = 1 to 12. Adding two of the latter will thus give a (much) larger number than
adding one of the latter to one of the former.
Why is the value in Column F, Row45 so small?
Because you are niw dividing one by 1.2 to the power of 45 which is 3657. Note how these go up so
quickly: 1.1 to the power of 45 is only 72.
Why do the values all decline in each row as you move from left to right?
Because the values of the denominators, which are larger numbers as you move from left to right, are
all being taken to the same power. So the denominators get larger as you move from left to right; the
numerator is constant at one.
Why do the values all decline in each column as you move down?
Because the power – which is t from column A – to which you are taking the constant values, increases as you
move down, so the denominators get larger as you move down.
If you are twenty years old today, how much influence on your decision today will your income
“when you’re sixty-four” have?
Depends on your discount rate. If it is near zero, your income “when you’re sixty-four” will have
the same impact on your decision today as does your income today. If your discount rate is, say 5%
= .05, your income “when you’re sixty-four” will have 17% of the impact on your decision today as
does your income today. And if your discount rate is, say 20% = .20, your income “when you’re
sixty-four” will have less than three one-hundreths of one percent of the impact on your decision
today as does your income today.