I especially need help with f) and g) but I may not have determined the correct
ID: 1193909 • Letter: I
Question
I especially need help with f) and g) but I may not have determined the correct answers for a through e.
Consider the following economy
C = Ca + 0.80 (Y – T) Ca = 400 – 10 R T = 750 + 0.2 Y (M/P)d = 0.25 Y – 25 R
(MS/P) = 2000/P. This means that Ms = 2000. Ip = 1800 – 30 R G = 2000 NX = 700 – 0.04 Y
a) Clearly define and compute the multiplier for this economy.
b) Clearly define and derive the equation of the autonomous spending Ap and the IS curves.
c) Clearly define and derive the equation of the LM curve as function of r and P. [Hint: equalize the demand and supply for money (Ms/P) = (M/P)d
d) Find the equilibrium interest rate equation for YIS = YLM. This should be a function of P.
e) Derive the equation of the aggregate demand curve AD. [Hint: Replace the equilibrium interest rate in either the IS or LM function. This should give you the AD curve in the form:
YAD= Constant + .Constant/P
f) Now consider the following aggregate supply curve YAS = 9000 - 20 W + 1000 P. For W = 31.25, derive the aggregate supply YAs.
g) Find the equilibrium levels of price and output for which YAD=YAS.
Explanation / Answer
Y = C + I + G + NX
= Ca + 0.80(Y - T) + 1800 - 30R + 2000 + 700 - 0.04Y
= 400 - 10R + 0.80(Y - 750 - 0.2Y) + 1800 - 30R + 2000 + 700 - 0.04Y
= 400 - 10R + 0.8(0.8Y - 750) + 1800 - 30R + 2000 + 700 - 0.04Y
= 400 - 10R + 0.64Y - 600 + 1800 - 30R + 2000 + 700 - 0.04Y
(1 + 0.04 - 64)Y = 4300 - 40R
0.4Y + 40R = 4300 [IS Curve]
LM: (M/P) = (MS/ P)
0.25Y – 25R = 2000 / P [LM Curve]
IS = LM
0.4Y + 40R = 4300 , or
Y + 100R = 10,750 ...... (1)
0.25Y – 25R = 2000 / P
Or,
Y - 100R = 8000 / P .... (2)
(1) + (2) gives us,
2Y = 10,750 + (8000 / P)
Y = 5,375 + (4000 / P) .... (3)
(f) YAS = 9000 - 20W + 1000P
Y = 9000 - (20 x 31.25) + 1000P
Y = 8,375 + 1000P ...... (4)
From (3) & (4)
5,375 + (4000 / P) = 8,375 + 1000P
(4000 / P) - 1000P = 3000
(4 / P) - P = 3
(4 / P) = 3 + P
4 = 3P + P2
P2 + 3P - 4 = 0
(P + 4) (P - 1) = 0
Since P cannot be negative, P = 1
Therefore, YAS = 9000 - (20 x 31.25) + (1000 x 1) = 9,375
(g)
YAD = Y = 5,375 + (4000 / P) [From (3)]
YAS = 9,375
YAD = YAS means:
5,375 + (4000 / P) = 9375
4000 / P = 4000
P = 1
YAD = YAS = 9,375
NOTE: Since you wanted help especially with (f) & (g), I've solved them by briefly touching upon & solving IS/LM. It's not possible to solve so many questions given under a single question.
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