Suppose the mpc is .75. there are no crowding out or investment accelerator effects. if the government increases expenditures by $200 billion how far does aggregate demand shift? if the government decreases taxes by $200 billion how far does aggregate demand shift?

See below.

Explanation:

The shift in aggregate demand can be computed by first identifying the multiplier,

Multiplier = 1 / (1 - marginal propensity to consume - MPC)

Multiplier = 1 / (1 - 0.75) = 4

A 200 billion spending by the government will shift the aggregate demand by 4 * 200 = $800 billion in total.

A decrease in tax has a similar effect as above, this is because a decrease in tax increases the disposable income of consumers and the net effect of increased income is as

Total change in aggregate demand = Increase in income * multiplier

Total change in aggregate income = 200 * 4 = $800 billion

An increase in income means people have more money to spend so they shift the aggregate demand to right by the above value.

Hope that helps.