Question

The sum of the infinite geometric series \[10\{1 + 0.8 + (0.8)^2 + \ldots\}\] is:

Options

• 18

• 25

• 50

• 80

Answer 1

Using the formula for an infinite geometric series with first term 10 and common ratio 0.8, the sum is \[\frac{10}{1-0.8}=\frac{10}{0.2}=50\]. Hence the total increase in equilibrium output (and income) is 50, greater than the initial autonomous increase of 10.