Question

Cost minimization problem Let q=2K1/2_1/2 (Production function) let we=2 and wk=4 (capital and labor costs)

Answer 1

Answer Minimize : c = Total cost = w, L + Wkk subject to : 2x² 2 2 = q (1) =22+4K 12 12 Legrange is given by : 2= 2L+ 4 K + 2q - 2 K ² ) first Order Condition : = 0 => 2 = (24) ) al zo => 4 = 12 Dividing (2) from (3) we get 2 = x = L = 2K Putting this in (1) we get a j cast Minimizing ak 2K (2 k) = q =) K = 2 2) L = 2K = 229 2 - 9 / case of a lost in later → Cost Minimizing

Hence C = Total Cost = 2L + 4K

=> C = 2q/2^0.5 + 4(q/(2*2^0.5))

=> C = 2^0.5q + 2^0.5q

=> C = 2^1.5q ----------------------------Total Cost Function