If investment is dependent on income in addition to interest rate (assuming C and G have usual forms) then the Keynesian multiplier will

A. Not Exist

B. Equal to as compared to the case where investment is not dependent on Y

C. Smaller as compared to the case where investment is not dependent on Y

D. Larger as compared to the case where investment is not dependent on Y

To determine the impact of investment dependence on income and interest rate on the Keynesian multiplier, we need to understand the concept of the Keynesian multiplier and its factors.

The Keynesian multiplier measures the total change in economic output (Gross Domestic Product - GDP) resulting from an initial change in autonomous spending, such as investment. It represents the magnifying effect of changes in spending on overall economic activity.

In the given scenario, when investment is dependent on income in addition to the interest rate, it means that the level of investment spending in the economy is influenced by both factors. Generally, investment spending is considered to be positively related to income and inversely related to interest rates (higher income leads to higher investment, while higher interest rates discourage investment).

Now, let's analyze the answer choices:

A. Not Exist: This option is incorrect because the Keynesian multiplier exists regardless of the factors affecting investment.

B. Equal to as compared to the case where investment is not dependent on Y: This option states that the Keynesian multiplier will remain the same as in a scenario where investment is not dependent on income. This may not be accurate because investment dependence on income is likely to impact the multiplier.

C. Smaller as compared to the case where investment is not dependent on Y: This option suggests that the Keynesian multiplier will be smaller when investment is dependent on income. This could be a plausible choice if the income dependence restricts investment spending, leading to a reduced multiplier effect.

D. Larger as compared to the case where investment is not dependent on Y: This option proposes that the Keynesian multiplier will be larger when investment is dependent on income. This is a logical possibility, as an increase in investment based on income could have a greater overall impact on economic activity.

To determine the correct answer, we would need to examine the specific relationship between investment and income in the given scenario. However, based on economic intuition, it is plausible to select option D - Larger as compared to the case where investment is not dependent on Y. This choice aligns with the idea that increased investment based on income could have a greater multiplier effect on the economy.

To definitively determine the answer, a deeper analysis and understanding of the specific investment-income relationship would be required.