Question

Suppose the production function of a country is Y equals K to the power of 1 third end exponent L to the power of 2 over 3 end exponent . And its capital stock is K equals 27 and labor force is L to the power of s equals 64. Calculate the following (Enter only numbers. Round up to ONE decimal place if needed) (a) What is the labor market clearing real wage under flexible real wage? (b) What is the number of the unemployed under rigid real wage W over P equals 2 over 3?

Answer 1

(a) Y = K ^(1/3) L ^(2/3)

MPL = ΔY / ΔL

=> MPL = (2/3) * (K/L) ^(1/3)

At labor market clearing point following condition holds.

=> MPL = (W/P)

note: (W/P) is the real wage rate

=> (2/3) * (K/L) ^(1/3)= (W/P)

=> (2/3) * (27/64) ^(1/3) = (W/P)

Note: K = 27 and L s=L= 64

=> (W/P) = 0.5

Labor market clearing real wage under flexible real wage is 0.5

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(b)

At labor market clearing point following condition holds.

=> MPL = (W/P)

note: (W/P) is the real wage rate

=> (2/3) * (K/L) ^(1/3)= (W/P)

Put (W/P) = (2/3) and K = 27

=>

At labor market clearing point following condition holds.

=> MPL = (W/P)

note: (W/P) is the real wage rate

=> (2/3) * (27/L) ^(1/3)= (2/3)

=> L ^(1/3) = 27^(1/3)

=> L ^(1/3) = 3

=> L = 3³

=> L = 27

Labor demand at the rigid real wage of (2/3) is 27

Labor supply (Ls) is 64

Unemployed = Ls - L

=> Unemployed = 64 - 27

=> Unemployed = 37