Question

1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion for producing cars is: F(K, L) = min(2K,5L) (a) Setup the short run cost minimization problem when K = 10. (2 points) (b) Solve for the short run optimal amount of labor Lsr() and short run minimized cost Csr(w,r,q). Circle your answer. (4 points) (c) Now suppose the car factory can freely choose capital (K) and labor (L). Setup the long run cost minimization problem. (2 points)

Answer 1

a) a) FCKL) = Min (2K, 5L), ſ = 10, then F(10, L = Min (20,5 L) 80 Min WL for St F(10,41 80 since proda funcn is not differentiable, thus Lagrangian can't be formed. b) in SR, at Eqm 20 = 5 L= q L = 4 LSR = 4 CSR = WL tok = 4w+lor & Now for long run Min LOL+ ok st q = Min (2K,5L) 10 au d.) In long run, QR=q 52=9 K* = 912 LA = 915 6* = Whatok* 6 c*- q W154 82) Ang -OT Shost Run cost wir always be higher Bioz un Short Run, one input will be fixed, 80 cost Minimizing input Combination can't be obtained. con 80 elim 9