Final answer:
An increase in government purchases of $10 billion will increase aggregate demand by $100 billion due to the multiplier effect.
Step-by-step explanation:
The increase in aggregate demand can be calculated using the multiplier effect. In this case, the marginal propensity to consume is given as 0.9. The multiplier effect is calculated by dividing 1 by 1 minus the marginal propensity to consume. So, the multiplier effect is 1 / (1 - 0.9) = 10. This means that a $10 billion increase in government purchases will lead to an increase in aggregate demand of $10 billion multiplied by the multiplier effect, which equals $100 billion.