The correct answer is $\boxed{\frac{1}{{1 – \frac{{\Delta C}}{{\Delta Y}}}}}$.
The investment multiplier is a measure of how much an increase in investment spending will lead to an increase in total output. It is calculated as the reciprocal of the marginal propensity to save (MPS), which is the fraction of an additional dollar of income that is saved.
The MPS is equal to $1 – MPC$, where MPC is the marginal propensity to consume. The MPC is the fraction of an additional dollar of income that is consumed.
The investment multiplier can be derived from the following equation:
$$\Delta Y = \Delta I \times \frac{1}{{1 – \frac{{\Delta C}}{{\Delta Y}}}}$$
where $\Delta Y$ is the change in total output, $\Delta I$ is the change in investment spending, and $\frac{1}{{1 – \frac{{\Delta C}}{{\Delta Y}}}}$ is the investment multiplier.
The investment multiplier is greater than 1 because a change in investment spending leads to a change in total output that is greater than the initial change in investment spending. This is because the initial change in investment spending leads to an increase in income, which leads to an increase in consumption, which leads to an increase in investment, and so on.
The investment multiplier is a powerful tool that can be used to stimulate the economy. By increasing investment spending, the government can increase total output and employment.
The other options are incorrect because they do not take into account the marginal propensity to consume.