Final answer:
The equilibrium income (Ye) falls by $2000 when autonomous investment decreases by $500 with an MPC of 0.75, due to the spending multiplier effect. The same decrease would result if the change were in autonomous consumption because the multiplier applies to all autonomous spending equally.
Step-by-step explanation:
When the planned autonomous investment falls by $500 and the marginal propensity to consume (MPC) is 0.75, we utilize the multiplicative effect of the spending multiplier to determine the change in equilibrium income (Ye).
The spending multiplier is given by 1/(1 - MPC), which in this case is 1/(1 - 0.75) = 1/0.25 = 4. Therefore, the decrease in equilibrium income is 4 times $500, which amounts to a $2000 reduction.
If the change were in autonomous consumption instead of investment, the impact on Ye would be the same. This is because the spending multiplier applies to any initial change in autonomous spending, whether it comes from investment or consumption. The spending multiplier does not discriminate between different types of autonomous spending.
The answer would be different if the change were in autonomous consumption instead of investment because the multiplier effect would magnify the impact on equilibrium output. Changes in autonomous consumption have a greater impact on equilibrium output compared to changes in autonomous investment.