An economy is described by the following equations: AD: Y = 4000 + 2(M/P) SRAS:

Question

An economy is described by the following equations: AD: Y = 4000 + 2(M/P) SRAS: Y = Y^bar + 100 (P-P^e) Okun's law: (Y-Y^bar)/Y^bar) = -2 (u-u^bar). Assume Y^bar = 6000 and u^bar = 0.05. Suppose that the nominal money supply has long been at M = 4000 and is expected by the public to remain constant forever. The equilibrium value of P is . The equilibrium value of P^e is . The equilibrium value of Y is . The equilibrium value of u is . The equilibrium value of pi^e is . A totally unexpected increase in in the money supply occurs, raising it from 4000 to 5250. [Part B is for extra credit] The short run equilibrium value of P is . The short run equilibrium value of P^e is . The short run equilibrium value of Y is . The short run equilibrium value of u is . The value of unanticipated inflation, which is defined as (P-P^e)/P^e, is . The value of the slope of the short-run Phillips curve is

Explanation / Answer

a) For long run equilibrium 6000 = 4000 + 2*4000/P so P=4 which will be same as Pe = 4, as for long run equilibrium equilibrium value of Y=6000 and unemployment rate = 0.6. As money supply is constant so inflation rate is 0

b) Now in short run with unexpected rise in M to 5250

Pe will remain 4

Y = 4000 + 2*5250/P

Y = 6000 + 100(P-4)

Now equating both the equations

5250/P = 1000+50(P-4)

105/P = P+16

P^2+16P-105=0

So P=5

Y = 6000+100(5-4) = 6100

From Okuns Law

(6100-6000) / 6000 = -2(u-0.05)

1/60 = -2u + 0.1

120u = 5

u = .04167

Unanticipated inflation = (5-4)/4 = 25%

Inf = expected inf – h(u – u(bar))

25 = 0 - h (0.04167-.05) so h=3001

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