When government expenditures fall by $500, the aggregate expenditure curve will shift downward and the equilibrium will decrease. If taxes fell by $500, the aggregate expenditure curve will shift up and the equilibrium income will increase.
When the government expenditures fall by $500, the aggregate expenditure curve will shift downward. The shift will be equal to the change in government expenditures multiplied by the marginal propensity to consume (MPC). In this case, the shift will be equal to -$500 * 0.9, which is -$450.
The equilibrium will change by the same amount as the shift in the aggregate expenditure curve. So, in this case, the equilibrium will decrease by -$450.
If taxes fell by $500, the aggregate expenditure curve will shift up by the change in taxes multiplied by the MPC. So, the shift will be $500 * 0.9, which is $450.
The equilibrium income will change by the same amount as the shift in the aggregate expenditure curve. Therefore, the equilibrium income will increase by $450.