What describes the relationship between the level of induced investment and the rate of change of national income?

The correct answer, the accelerator, describes the relationship between the level of induced investment and the rate of change of national income by demonstrating how changes in national income can lead to proportional changes in investment. As national income increases, businesses typically find themselves with higher levels of demand for their products. This, in turn, prompts them to invest more in capital goods to expand production and meet the demand, leading to increased levels of induced investment.

The accelerator principle posits that the rate of investment is not constant but varies with changes in income. When national income rises, the increase in demand can lead to a more significant increase in investments, as firms adjust their capital stock to align with growing sales. Conversely, if national income falls, the accelerator suggests that investment would decrease, reflecting businesses' revised expectations about future demand.

This principle is closely linked to the concept of the multiplier effect, but it specifically focuses on the relationship between income changes and induced investments rather than the initial change in spending alone. The other options do not adequately capture this specific relationship; for example, a deflationary gap refers more to a situation where actual output is less than potential output, while investment gradient does not have established use in macroeconomic theory.