Question

Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is the output in part (a). (c) Find the unconditional labor demand function L(PL.PK 6) (d) Draw the conditional and the unconditional demand functions in one graph

Answer 1

Ang 9fuen data A im produ cas Output uSmg Punchion r (L,K)L/2 Producthon the re Butput ト3, and Paice of Mput Pacts ore pred at and the funchion (as furcdion of Sutput he Cost Ca) Rnpuds the eptmar amount of k) to marimize the prokt L and Cost P L +PK +k IL 4 6K 31/2/3-L-6k Poo Art Cost Pa For Proit delau= o f dlak d L- 1.5k/ /3 1- O 2/3 delax 2 7 1 FO 9-

Sahuing boh 2/3 6K k u 4/3 L 36k t/3 L k 3/ / Suplos wchonges Ch) Labhor demond fnetion he Con di kenal ihe L(Pey P 6& hese r POrt (a Butput output the Prfst maximi ng valuas & tnput) MRTS= (MP /oMp) 1-5ke MRTS gheuld be EQual to wr PL/P 1 this

1.5k/L-1 L/1 -5 k produchon funchon rs puthing 2/3 15/-()*(1.5)3 6/5 L IN6* e (ncon di tenal abr cerand function) CPasrt (Profst maimad outut )- %2 L O06967 Landitenal lebor demondfonchion Cenditionel and the he uncenditenel Punchions, wncendi ti&nal Rnchenal domand upecasrd shopmg menatsrilally mocogry ill be funchian whele Condstanal funchonal wl Straight hotental une be CA