macro doubt

[SoniaKapoor]

Consider the general equilibrium of the following economy
Ys = AN (production function)
W = Pe*z*ln(1/u) (wage setting)
Yd= C+I+G (goods market)
C = c0 + c1(Yd-T)
I = d0 + d1*Y –d2*i
M = P*Yd/i (Money market)
L = N + U =1 (Normalized labour force)
Derive the natural rate of output (Yn)
a) Yn = A*(1-exp[-A/(1+µ)*z)
b) Yn = A*(1-exp[-A/(1+µ))
c) Yn = A*(1-exp[A/(1+µ)*z)
d) None of the above

[L14]

I think the answer is a

Wage setting:
W = Pe*z*ln(1/u)

Price setting:
W/P=A/(1+µ)
=> W=AP/(1+µ)

Equating both
AP/(1+µ) =Pe*z*ln(1/u)

N=Ys/A
u=1-N
u=(A-Ys)/A

=> AP/(1+µ) =Pe*z*ln(A/(A-Ys))

At natural level of o/p P=Pe
=> A/z(1+µ) =ln(A/(A-Yn))
taking exponontial
exp[A/z(1+µ)]=A/(A-Yn)
A-Yn = A*exp[-A/z(1+µ)]
Yn=A*[1-exp[-A/z(1+µ)]]

[RajEco]

Hey ben,

Can we use the price setting equation involving parameter A ? Normally we use the price setting relation without A. Are you sure about it ?

Bcoz if we use the price setting equation, then we are getting a. otherwise if we use P= W(1+ mu) then , the answer is none of the above.

[L14]

@raj: i'm not 100% sure. I think you are right . If A is included in Price setting, it should be included in Wage setting too, in that case both will get cancelled and the answer will be Yn=A*[1-exp[-1/z(1+µ)]]  which is none of the above.

@sonia: can u confirm the answer

[kangkan]

Hi Ben,which chapter is this from?and which book?
Thanks :)

[SoniaKapoor]

Thanxx Ben ...The answer is a

@kangkan...this is medium run ...Chapter on labour mkt and AS n AD

[vibha chitkara]

FOR THE SAME DATA CAN ANYONE GIVE THE SOLUTION FOR THIS

Derive the Aggregate Supply (AS) schedule


a) P = Pe*(1+µ)*z*ln[A/(A-Y)]


b) P = Pe*(1+µ)*ln[A/(A-Y)]


c) P = Pe*(1+µ)*z*ln[(A-Y)/(A)]


d) None of the above