Question

3. Consider the linear production function y = ax + 3x2 where 21 and 22 are inputs with prices w; and w, respectively. (a) Derive the conditional factor demands for C and 22. (b) Derive the cost function (c) Derive the short-run cost function when input 2 is fixed at 22. (d) Derive both short and long-run average cost functions.

Answer 1

Question-3 giren Linear odution femsten ces with the bAlces of inputs are t, Soleition:- 3(a) Condlitional fautor dlemand for , ond g ara the optimal clusices of imbut faitons The conditional feitor fenctions are ,, ws) and 9 9) 11 NOw, find optimal cost whieh is the Cost funetion ot inpits C (w,,,) . , 4, y c (u,,, y.xl, ON C = his is the Conditional demanad of faitons of input t,)

Solutien-2(b) To duive the tost funition, twe ill meeol he cost as a function of Ourpet. i.e., CR) = NNOW, Solre the Constraned Dutput maximigetin Max Sub. to c,, t The Compasit function toro above equations Coith Lagsongian Mulhbler as (at + [,t C] ditferentiate wte ,, and a t9,) a =- B-A 6 diiding equ puting this valus in (

So1 W,t c t c C ( ) puting it into , value- # Gutng and (8 into gu (6 puting equ C. C C. ONE 움에+장. OrC Hence, this to the tral cost funtion hii s the fenction of output ly), thu cofficiot a,B.and t th mbutr X, 2 2

Solution!- 3(c) Derive shorlPun tost tunetion ihen mput2 Sinu, on Or Lue knous that E-R1 fixed 701al tost T vaiable (Vc) + Cost (Fc) Cost = w, , + w, TC So, -this ishe hort run tslel lost femetien Slution!-3ld) The Short Run Average costfunetien is Te ATC 뽕[보 1+313 ATC ON a