Question

Determine the long-run total, average and marginal cost functions of the firms having the
production functions and facing the input prices given below:
a. ?=f(K,L)=√K+2√L,PK=1,PL=2
b. Q=f(K,L)=K+L,PK=2,PL=1
c. Q=f(K,L)=K1/2L1/2,PK=2,PL=2

Answer 1

fck L) = VK +2 VE 0410 Lok%2+242 a Q= f (K; L) = VEL Now, Q- FCK,L) - KV2+2, 's Now, marginal product of capital is.fi duct of capitat OF (K34, L Kom! JK MPK = and marginal Product of labor a of(K) ??, 2.62) 25 Flut 22 = Ľ ? / 21 20 10 o . Condition A requires t condition T THE Now, optimal MPK input min PK MPL - PL MPL -1/2 ž { Kola 1-1/2 ltou ter r ibing I 11121- (A) 76 ZR 125R L 1 Now, substituting Lk in Q = .vky + QVE = 1 => JI - VR -> L Fik [by taking square root) the production function wo are Vw IQ - VR - = √kt ark = 3 VE > Q=K Sarned, with Assanek SASUNT

Now long run total cost brition mit a renta will be P Lt Pk kietoa LEDEL ESTAD 021Q7 AUD We knool2O3p E a Te = 2Q z bogate pelle Divna Now, longlisin total lost fuction and too long run avuage-east on or friction oth wa) " Q QATA long run marginal cost function at cost ost ost ope. sa (FAN -pelle 2+2 -- 12 Q=f(k,2)=* Kthis Now, here MPK = 3F(k_) Tira and MPL = 2F (K, L 1 on here MP K = Tak buang OL. Now MPK 1 = 0.5 l Now - pk T. Pinant 8 soft output will 5 2013 MPL Thes, mort and LA MPK L Presenting more on labor and infot PK spending more on both on Capital, Huce & be produced by spending nothing K=0 Scanned with CamScanner CARL

Huse, Q= Lto Just 107 -) Q-L and Totul cost siste puctions tipi Ko ahun ku ini sering PLLT Pk K TC= tot Aidha - Q + (axo)*:! any inction "LLATC) word Hace longren totul cost ( fuction = Q long run average cost function (LATC) - LATE- IL A and long ren marginal cost function the LMLE ACTC) - 4 Q Q f(x)L) - kø, mer Now MPK = 2F(134) = { x='hL ; and MPL = 2FLK, L) 1K2 Lh Trh ,- / Now optimal input min condition will be әк and ar 22 " APKI . MPK - KYL2 eta Ž Kay KRLY "y in - 7 Ź K122-2 E ye E Scanned with CamScanner

Now, Q=K²L/ substituting K= L we get, a=2²2² As K= L, Huce K=Q Hace Long run total cost for ction LTC = PLL + Pk ka =2Q + QQ.. = 4Q and, LATC = (LTC )= 4 and LMC = d (LT(). da = 4 Scanned with CamScanner