Economics 576.01W Summer I, 2012 Project I I Given the basic Keynesian three-sector model Y = C + I...

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Economics 576.01W Summer I, 2012 Project I I Given the basic Keynesian three-sector model Y = C + I + G i = interest rates where C = a + bYd Y = aggregate income and I = f ??????????????????????????????f ( Y f = is a function of with G = Go and Tx = Txo 1. Assume: C = 20 + .75Yd Now assume that government spending is increased by $12 billion. That would (increase/decrease) the level of income by how much? 2. Assume: S = XXXXXXXXXX25Yd Now assume that taxes are cut by $15 billion. That would (increase/decrease) the level of income by how much? 3. Assume: C = 42 + .
	
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Summer I, 2012 
Project II

Given the basic Keynesian three-sector model 
Y = C + I + G     i = interest rates 
where C = a + bY    Y = aggregate income 
d
and I = f �XW«E,L f ( Y  f = is a function of 
with G = G 
o
and Tx = Tx 
o
 
1.  Assume:  C = 20 + .75Y
d 
Now assume that government spending is increased by $12 billion.  That would 
(increase/decrease) the level of income by how much? 
 
2.  Assume:  S = XXXXXXXXXX25Y 
d
Now assume that taxes are cut by $15 billion.  That would (increase/decrease) the 
level of income by how much? 
 
3.  Assume:  C = 42 + .8Y 
d
Now increase taxes and government spending (simultaneously) by $33 billion.  
That would lead to a (decrease/increase) of  __________ billion in the level of 
income4.  Assume:  C = XXXXXXXXXXY 
d
Now cut taxes by $20 billion.  This would have the effect of shifting the 
consumption function (upward/downward) by _________ billion.  (Think 
Keynesian cross model) 
 
5.  Assume that the current level of income in the economy is $700 billion.  It is 
determined that in order to reduce the unemployment rate to the desired level, it 
will be necessary to increase the level of aggregate income to $760 billion.  
Assume that S = XXXXXXXXXX2Yd.  How much would government spending have to be 
increased in order to accomplish the desired outcome? 
 
6.  Assume that the current level of income in the economy is $700 billion.  It is 
determined that in order to reduce the unemployment rate to the desired level, it 
will be necessary to increase the level of aggregate income to $760 billion.  
Assume that S = XXXXXXXXXX2Yd.  How much would taxes have to be cut in order to 
accomplish the desired outcome? 
  
7.  Given a saving function of S = XXXXXXXXXX2Yd, a $10 billion increase in 
government spending will bring about how many dollars of change in 
consumption?

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that Y = C + I + G + X with X = X and M = M =...

Robert · Accepted Answer

Answers: 
1. Assume C = 20 + 0.75Yd 
Y = C + I + G 
Y = 20 + 0.75(Y –T) + I + G
SINCE TX = TX0, 
(1-0.75) Y = 20 – 0.75 TX0 + I + G 
If government spending is increased by $12 billion then,
0.25∆Y = ∆G 
 ∆Y = (1/1-b) ∆G  
∆Y = (1/0.25)*12 
∆Y = $48 billion 
 Hence, if government spending is increased by $12 billion, then the level of income would 
Increase by $48 billion. 
2.   Now,   Y =  C+ S + T  
Assume S = -35 + .25Yd = -35 + 0.25(Y –TX) 
∆TX  = $15 billion 
Now,                        Y = C+ S + T  
                                  Y = C – 35 + 0.25Y – 0.25TX + TX                                 
                          0.75Y = C – 35 + 0.25TX 
                             ∆Y = ∆C + ∆S + ∆T  
                                 Since ∆C = 0 
Then                   ∆Y = ∆S + ∆T = 0 
                                  ∆Y = (-∆TX x MPC) x (1/MPS)  
                                  ∆Y = - ∆ TX x(MPC/MPS) Where MPC = 1- MPS and MPS = 0.25  
                                  ∆Y = $45 billion 
Hence, if taxes are cut by $15 billion then the level of income would increase by $45 billion. 
3.  Y = C + I + G  
Y = a + b(Y -TX) + I + G 
By rearranging the equation, we get 
      Y = 1/(1-b)[a + I + G + bTX]
Assume: C = 42 + .8Yd 
Now increase taxes and government spending (simultaneously) by $33 billion.  
                  ∆Y = 1/(1-0.8)*∆G - b∆TX] 
                  ∆Y = 5*[33 – 0.8*33] 
                  ∆Y = $33 million 
When both government spending and taxes are increased simultaneously by same amount, 
then the level of income in increased by that same amount of G and T. this means that it’s a 
balanced budget multiplier. Thus,

Economics 576.01W Summer I, 2012 Project I I Given the basic Keynesian three-sector model Y = C + I + G i = interest rates where C = a + bYd Y = aggregate income and I = f...

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