a Which of the following sets of economic data is minimizing

(a) Which of the following sets of economic data is minimizing the cost of producing a
given level of output?

(A) MP_L = 20, MP_K = 40, w = $16, r = $32.
(B) MP_L = 20, MP_K = 40, w = $32, r = $16.
(C) MP_L = 40, MP_K = 20, w = $16, r = $32.
(D) MP_L = 40, MP_K = 40, w = $16, r = $32.

Solution

(A) MP_L = 20, MP_K = 40, w = $16, r = $32

cost minimising condition

MP_L /MP_K =w/r

MP_L /MP_K = 20/40 =1/2

w/r = 16/32 =1/2

so this economic data is minimising cost

(B) MP_L = 20, MP_K = 40, w = $32, r = $16.

cost minimising condition

MP_L /MP_K =w/r

MP_L /MP_K = 20/40 =1/2

w/r =32/16=2

above equality does not hold

so economic data does not satisfy cost minimising

(C) MP_L = 40, MP_K = 20, w = $16, r = $32.

cost minimising condition

MP_L /MP_K =w/r

MP_L /MP_K = 40/20 =2

w/r =16/32 =1/2

above equality does not hold

so economic data does not satisfy cost minimising

(D) MP_L = 40, MP_K = 40, w = $16, r = $32.

cost minimising condition

MP_L /MP_K =w/r

MP_L /MP_K = 40/40 =1

w/r =16/32 =1/2

above equality does not hold

so economic data does not satisfy cost minimising