Question

Suppose the production function in Netherlands can be represented by Y = [(K^(1/4)

L^(1/3)]^2

, and the production

function in Neverland is Y = [(K^4 L^3 )^(1/9)]

. Which country will experience a higher percentage

decline in national output if both capital K and labor L decrease by 25% at the same time?

(a) Neverland.

(b) Netherlands.

(c) They are the same.

(d) More information is required.

Answer 1

The correct answer is (b) Netherlands

Formula:

% change in (AB) = % change in A + % change in B

% change in (A^B) = B*% change in A

FOR NETHERLANDS

Y = [(K^1/4L^1/3]² = K^2/4L^2/3

=> Y = K^2/4L^2/3

=> % change in Y = % change in (K^2/4L^2/3)

Using above formula we get :

% change in Y = (2/4)% change in K + (2/3)% change in L

Both L and K decreases by 25%

=> %change in K = % change in L = -25

=> % change in Y = (2/4)*(-25) + (2/3)* (-25)

= -29.17

This negative sign suggest that National Output decreases

Hence, For Netherlands national output if both capital K and labor L decrease by 25% at the same time will decrease by 29.17%

FOR NEVERLAND

Y = (K⁴ L³)^1/9 = K^4/9L^3/9

=> Y = K^4/9L^3/9

=> % change in Y = % change in (K^4/9L^3/9)

Using above formula we get :

% change in Y = (4/9)*% change in K + (3/9)*% change in L

Both L and K decreases by 25%

=> %change in K = % change in L = -25

=> % change in Y = (4/9)*(-25) + (3/9)* (-25)

= -19.44

This negative sign suggest that National Output decreases

Hence, For Neverland national output if both capital K and labor L decrease by 25% at the same time will decrease by 29.17%.

So,Decline in National output is higher in Netherlands

Hence, the correct answer is (b) Netherlands