Question

Suppose changes in autonomous consumption affect investment while changes in autonomous government spending do not. in this case, identical changes in autonomous consumption and autonomous government spending

Answer 1

 in this case, identical changes in autonomous consumption and autonomous government spending:  have different effects on equilibrium income

When a factor is implemented and have two different reaction, it is safe to assume that that factor have two different effects.
For example, an increasing interest in technology(autonomous consumption) may increased the investment for tech products. The government spending may not give as much influence in this context because it wont affect the transaction between the customers and the producer