Question

The total increase in output from an initial autonomous increase of 10 with MPC = 0.8 is expressed as the infinite geometric series:

Options

• \[10\{1 - 0.8 + (0.8)^2 - \ldots\}\]

• \[10\{1 + 1.8 + (1.8)^2 + \ldots\}\]

• \[10\{1 + 0.8 + (0.8)^2 + \ldots\}\]

• \[10\{0.8 + (0.8)^2 + (0.8)^3 + \ldots\}\]

Answer 1

The round-by-round increments are \[10,\ (0.8) \times 10,\ (0.8)^2 \times 10,\ \ldots\], so the total increase in output is \[10 + (0.8) \times 10 + (0.8)^2 \times 10 + \ldots\], written as the infinite geometric series \[10\{1 + 0.8 + (0.8)^2 + \ldots\}\].