Assume the following equations summarize the structure of an economy.
C = Ca + 0.7(Y - T)
Ca = 1,000 - 10r
T = 100 + 0.15Y
(M/P)d = 0.3Y - 20r
MS/P = 3,000
Ip = 3,500 - 20r
G = 3,000
NX = 2,000 - 0.4Y
a. Calculate the equilibrium real output (Y) and (r ).
b. Given the above information, compute the new equilibrium real output if government spending increases by 300.
c. What is the amount of autonomous spending that is crowded out by this expansionary fiscal policy?
The goods market equilibrium in an economy is given by:
Y = C + I + G + NX
= 1000 - 10r +0.7(0.85Y-100) + 3500 -20r + 3000 + 2000-0.4Y
Solving for Y and r, we get:
Y = 9500 -30r - 70 + 0.595Y -0.4Y
0.805Y = 9430 -30r.......(1)
The money market equilibrium us given by:
(M/P)d = MS/P
3000 = 0.3Y - 20......(2)
Solving 1 and 2 for Y and r simultaneously, we get:
Y = 11100 and r = 16.5%
If G increases by 300, equation 1 for equilibrium will now become:
0.805Y = 9730-30r
and hence from equation 1 and 2, the new equilibrkum will be:
Y = 11340 (approx.) and R= 20%
As a result of this expansionary fiscal policy (increase in G), r increases from 16.5 to 20%. Hence, autonomous spendig crowded out = C(at r=20) - C(at r=16.5)
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