Minimize the cost function such that

Question

Question

Minimize the cost function 2f+31ByVMGTo6iU1SAAAAAElFTkSuQmCC such that CsIw190J+82dHV5N0Sn5v0i72kbZ0fctbxRQbUU6

Answer 1

Answer #1

We are given that 2(KL)^0.5 = Q

Find MRTS = MPL/MPK = 2*0.5(K/L)^0.5 / 2*0.5(L/K)^0.5 or MRTS = K/L

From cost function we have w/r = 4/1.

Hence at the cost minimizing choice of K and L, MRTS = w/r

K/L = 4/1 or K = 4L

This gives the optimum labor demand function

2(KL)^0.5 = Q

2(4L*L)^0.5 = Q

L* = Q/4

K* = Q

Hence, for Q = 8 units we have L = 8/4 = 2 units and K = 8 units.

Cost is minimized at 1*8 + 4*2 = $16.

Answer 2

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