Question

W= Continuing to use the three production functions: q = h(KL) K(1/3) L(1/3) q = g(K, L) = min{:K, L}, and q = f(K, L) = K (1/4)(3/4). (h) (6 points) What is the Long Run Cost curve for each of these when r = $4 and $16? (i) (6 points) What are the Long Run Average Cost here? How about the Marginal Cost? (j) (4 points) Provide a convincing argument that a firm using with h(K, L) or 9(K, L) would select K* 128 in the Long Run given P $96, w = $16, and r = $4. (Hint: for h(K, L) try maximizing profits when K and I are adjustable.) AA

Answer 1

f = k/4 L314 curve @ h = K 13 LV3, g.zmin (k/4,45), h LR Cost for h, MRTS = W10 = 16/4.- 4 | 80 MRTS = MPLIMPI= KIL 80 at 8am KIL = 4 PK=4L from m puod" furen q = b = (AL) 3 Lla a = h = L" = (a/413 ) 32 931212 9 = 413 [2/3 (*= 9312 4112 K* = 4L" 29812 C = wkt okt 16(9812/2) + 4 (29312) 16 q° Ang 312 CA 9 forg, at eqm K14 = -4/5 5K=42 =q 80 5 k=q K-915 L = 9/4 C = Whitrk 16 (9/4) t 4 (915) for go at Eqmo K/4 = 415 = 9 L = 59 thus 80 K" 49, c = will tok" 16 (59) + 4 (49) た 16=969 Ang

for f, MRTS = 3 K = w/8= 4. L 3 K= 4L K= 413L from pluoda 1/4.L. funch q = (413 L) 1/4 2 3/4 9 = (413) L'= V/(413) 14 q (413) 114 (4/3) 314 q K' - (413) 314 a 80 C = Wltok 16 (9/413)||4) + 4 (413) c=49 A13814 + 4/(13)/4] And į LRAC, for h= c/q= 169312 q # LR AC= 16 91/2 HERMC acləq = 16 (1) 912 = 94 9"2 g, # LRAC= c/a= 96 LR MC foo f, FLRACE 4 + 4/413) V4] Aps = LR MC (413) 314 for h p=96, WH6, 9=4 T = P q- WL-ok T= 96 "3_!!8 - 161 - 4K anak 96 kl k 213 16 - O. ənlək = 96 L13. K-213 - 4 =0 3 80 from Foco 96 L"3 4 Bat3 1/8 K 213 213 = L-08)3.(6)81373 1 (62 512

696 Kt 13 こ 16 3 Lala a K'13 - 12/3 &K 13 = [(512) K z] als 2 (512)213 K 413 R13 128=K* Proved.