Final answer:
A 50% reduction in federal government purchases will likely shift the aggregate demand curve left and result in a new long-run equilibrium with lower output and prices, potentially leading to higher unemployment unless other economic adjustments occur.
Step-by-step explanation:
When the federal government reduces its purchases by 50%, the aggregate demand (AD) curve shifts to the left because government spending is a component of AD. In the new long-run equilibrium, the output level will be lower, and the price level is likely to decline compared to the original long-run equilibrium. This reduced output could lead to higher unemployment if the economy does not adjust through other means, such as monetary policy intervention or natural market adjustments over time.
As aggregate demand shifts left, we may initially see a move to a new short-run equilibrium with reduced output and potentially lower prices (as represented by the hypothetical move from Eo to E₁ in the figures mentioned). In the long run, the short-run aggregate supply (SRAS) may also adjust, potentially shifting to the right due to lower costs or wages, restoring the economy closer to its potential GDP.
In reference to the tax cut scenario where AD increases by 50 at every price level, this would result in an outward shift of the AD curve. The new equilibrium would reflect higher output, higher price levels, and likely an increase in employment, as businesses respond to increased demand by hiring more workers. Such a change is distinct from the situation posed by a decrease in government spending and serves as a contrast to the types of shifts we would observe in AD and SRAS in response to fiscal policies.