Final answer:
When the government simultaneously increases both spending and taxes by $50 million and the MPC is 0.90, there is a net initial change of $5 million that is then amplified by the multiplier effect. This results in an increase of $50 million in aggregate demand.
Step-by-step explanation:
The question revolves around the concept of marginal propensity to consume (MPC) and its effect on the aggregate demand when the government increases spending and taxes simultaneously. The aggregate demand is expected to change based on the multiplier effect of the initial change in government spending.
Since the MPC is 0.90, for every dollar of income received, individuals will spend 90 cents and save the remaining 10 cents. When the government increases spending and taxes by $50 million, the initial increase in aggregate demand is also $50 million. However, the tax increase extracts $50 million from the economy, which would have been partly spent according to the MPC. As individuals have $50 million less to spend, they reduce their consumption by MPC × Tax Increase, which is 0.90 × $50 million = $45 million. Therefore, the net increase in aggregate demand is the initial $50 million less the $45 million that will not be spent due to higher taxes, yielding an increase of $5 million in aggregate demand.
However, because each round of spending generates further consumption based on the MPC, the final change in aggregate demand is actually more than the initial $5 million, thanks to the multiplier effect. The multiplier is calculated as 1 / (1 - MPC), which in this case is 1 / (1 - 0.90) = 10. So the final increase in aggregate demand is the initial change of $5 million times the multiplier, resulting in an increase of $50 million (5 million × 10).
Hence, the correct answer is that the aggregate demand will increase by $50 million, which corresponds to option a.