Question

3. Consider the linear production function y a Br2 where aE1 and with prices w, and w respectively are inputs (a) Derive the conditional factor demands for and . (b) Derive the cost function (c) Derive the short-run cost function when input 2 is fixed at (d) Derive both short- and long-run average cost functions.

Answer 1

DE 12001 3 y = bdx + P42 ; P = wo P2 = W2 a) neue, the factors x and 2 are perfect Bu The Hene, MRS12 = 2/B and (P1/P2) - (W1/W2) Thus, is of wi xd=0; x = py Be wi xoday; X₂ d = 0 any where between x de xa - W. i. The conditional factor demands are: For X2: For i: xd = y is a <wi UB W2 = [o, y] is i [o,y] j a oko 3b) Cy, w, wa) = wry is now wy voy is wi= W2=w ij 2 B

o Bhout- run ST aor fumlton . . (y) = 102.72 if y<tr =w.ly - 7+ witz ij y *2 stay STO, LTC LTCU ws.tz d) Lag - run AC = wi average copr fun- L W2 a B I Bhout-run ang coor-fen: SAG2 (y) = w2tz ij y < 22 wo (1 - 22 ) + 02-77 [if ya W2=w W2 is voow2 W2