Question

3. In early 2009, economists estimated a spending multiplier m- 1.5, and they also concluded that GDP had fell 2.1 trillion dollars below the "full employment GDP". The new government then managed to pass through Congress a fiscal stimulus package amounting to about 0.75 trillion dollars of new spending composed of new government purchases and tax cuts in approximately equal parts. Would you expect this new spending to be sufficient to bridge the gap between actual and potential GDP? (In order to answer this question compute the expected increase in GDP for a stimulus package entirely composed of government purchases, and then argue whether the stimulus would be larger or smaller when it partly involves tax cuts). If the stimulus above is insufficient, propose a stimulus package that would be "exactly" sufficient to bridge the GDP gap.

Answer 1

Here spending multiplier is 1.5, it means if Government spending increases by 1 then Output ( GDP) increases by 1.5.

In order to reach/manage the Actual GDP to Potential GDP,

Case $\rightarrow$ Effect  $\downarrow$	When stimulus is partly financed by tax cuts and partly by Government Purchases.	When stimulus is entirely financed by Government Purchases.
Government spending is raised by	$ 0.375 trillion.	$0.75
Investment is raised by( through tax cuts)	$ 0.375 trillion.	-
Total fiscal stimulus	$ 0.75 trillion.	$ 0.75 trillion
Spending multiplier raises output by	0.375 x 1.5 =0.5625	0.75 x 1.5 = 1.125
Expected increase in GDP	0.375 + 0.5625 = + 0.9375	+ 1.125
Output Gap	- 1.1625	-0.975
Stimulus effect on raising GDP is	Smaller	Larger

The negative Output Gap shows that in either Case, the package is not sufficient to bridge the gap between Actual GDP and Potential GDP.

A stimulus package that will be exactly sufficient to bridge the gap between Actual GDP and Potential GDP can be any of the two package -

Case $\rightarrow$ Effect  $\downarrow$	When stimulus is partly financed by tax cuts and partly by Government Purchases.	When stimulus is entirely financed by Government Purchases.
Government spending is raised by	$ 0.84 trillion.	$1.4
Investment is raised by( through tax cuts)	$ 0.84 trillion.	-
Total fiscal stimulus	$ 2.1 trillion.	$ 2.1 trillion
Spending multiplier raises output by	0.84 x 1.5 = 1.26	1.4 x 1.5 = $2.1
Expected increase in GDP	1.26 + 0.84 = $2.1	$2.1
Output Gap	0	0
Stimulus effect	Bridges the Gap	Bridges the gap