In: Economics
In a hypothetical economy desired consumption and desired investment are:
C^d = 184 + .6Y-500r and I^d = 200 -500r
Government purchases are 196.
Real money demand is M^d/ P = 0.5Y - 250 ( r + pi^e) where
expected inflation, pi^e, is 0.10. The nominal
money supply is 9890.
a. If full employment output is Y bar =1000, what are the general equilibrium values of the real interest rate, price level, consumption and saving?
b. What is the value of velocity in this economy?
(a)
In goods market equilibrium, Y = Cd + Id + G
1000 = 184 + 0.6 x 1000 - 500r + 200 - 500r + 196
1000 = 184 + 600 + 200 + 196 - 1000r
1000 = 1180 - 1000r
1000r = 180
r = 0.18
C = 184 + 0.6 x 1000 - 500 x 0.18 = 184 + 600 - 90 = 694
(Private) Saving = Y - C = 1000 - 694 = 306
From money market, Md/P = Ms/P
0.5 x 1000 - 250 x (0.18 + 0.1) = 9890/P
500 - 250 x 0.28 = 9890/P
500 - 70 = 9890/P
430 = 9890/P
P = 23
(b)
Velocity = (P x Y) / (Ms) = (23 x 1000) / 9890 = 2.33