1.  Consider an economy in which tax collections are always $400 and in which the four components of aggregate demand are as follows:
GDP	Taxes	Disposable income	consumption	investment	gov. purchases	exports minus imports
$1360	$400	$960			$720		$200		$500		$30
1480	400	1080			810		200		500		30
1600	400	1200			900		200		500		30	
1720	400	1320			990		200		500		30
1840	400	1440			1080		200		500		30

Find the equilibrium of this economy graphically.  What is the marginal propensity to consume?  What is the multiplier?  What would happen to the equilibrium GDP if government purchases were reduced by $60 and the price level remained unchanged?

Solution:

Equilibrium is achieved where, GDP = C + I + G + NX.

When C = 990, I = 200, G = 500, NX = 30, Equilibrium is achieved.

Because, 1720 = 990 + 200 + 500 + 30.

                 1720 = 1720.

Equilibrium is shown graphically as follows.

Aggregate expenditure

Real output

45’line

C+I+G+NX

1720

Marginal propensity to consume refers to the ratio of change in consumption to change in income. 

Symbolically, MPC = dC / dY.

In the above example, MPC = 90 / 120 = 0.75.

Multiplier = 1 / (1-MPC) 

                 = 1 / (1-0.75) 

                 = 1 / 0.25 

                 = 4.

If government purchases were reduced by $60, then the equilibrium GDP will change by the multiplier times the change in government purchases.

Change in equilibrium GDP= 4 * 60 = 240.

New equilibrium GDP = 1720 – 240 = 1480.

So, equilibrium GDP will decline due to the reduction in government purchases.

2.  Consider an economy similar to that in the preceding question in which investment is also $200, purchases are also $500, net exports $30 and the price level is also fixed.  But taxes now vary with income and, as a result, the consumption schedule looks like the following:

GDp	Taxes	Disposable income	consumption
$1360	$320	$1040			$810
1480	360	1120			870
1600	400	1200			930
1720	440	1280			990
1840	480	1360			1050

Find the equilibrium graphically.  What is the marginal propensity to consume?  What is the tax rate?  Use you diagram to show the effect of a decrease of $60 in government purchases.  What is the mltiplier?  Compare this answer to your answer in Question 1.  What do you conclude

Solution:

Equilibrium is achieved where, GDP = C + I + G + NX.

When C = 990, I = 200, G = 500, NX = 30, Equilibrium is achieved.

Because, 1720 = 990 + 200 + 500 + 30.

                 1720 = 1720.

Real output

45’line

C+I+G+NX

1720

Aggregate expenditure

C+I+G’+NX

1480

MPC = dC / Dy 

   = 60 / 80 
   
 = 0.75.

Multiplier = 1 / (1-MPC) 

                 = 1 / (1-0.75) 

                 = 1 / 0.25 

                 = 4.

If government purchases were reduced by $60, then the equilibrium GDP will change by the multiplier times the change in government purchases. The expenditure line will shift downward as C+I + G’ + NX. This is shown in the above figure.

Change in equilibrium GDP= 4 * 60 = 240.

New equilibrium GDP = 1720 – 240 = 1480.

So, equilibrium GDP will decline due to the reduction in government purchases.

As the taxes are changing with the same rate i.e the taxes increase by $40 with every increase in income, the change in disposable income is also same. So, the value of MPC & the multiplier is same for both the questions. Since the MPC & multiplier are same, the changes in the equilibrium income are also the same when compared with the previous question.