Show why a \(\$ 10\) billion reduction in government purchases of goods and
services will have a larger effect on real GDP than a \(\$ 10\) billion
reduction in government transfers by completing the accompanying table for an
economy with a marginal propensity to consume \((M P C)\) of \(0.6 .\) The first
and second rows of the table are filled in for you: on the left side of the
table, in the first row, the \(\$ 10\) billion reduction in government purchases
decreasesa. When government purchases decrease by \(\$ 10\) billion, what is the
sum of the changes in real GDP after the 10 rounds?
b. When the government reduces transfers by \(\$ 10\) billion, what is the sum
of the changes in real GDP after the 10 rounds?
c. Using the formula for the multiplier for changes in government purchases
and for changes in transfers, calculate the total change in real GDP due to
the \(\$ 10\) billion decrease in government purchases and the \(\$ 10\) billion
reduction in transfers. What explains the difference? (Hint: The multiplier
for government purchases of goods and services is \(1 /(1-M P C)\). But since
each \(\$ 1\) change in government transfers only leads to an initial change in
real GDP of \(M P C \times \$ 1\), the multiplier for government transfers is $M
P C /(1-M P C) .)$