Answer set 2 Answer 2.1 (a) For each factory with capital stock K C LwL+roy Therefore the short-run cost functions are C1(y) (y) y2+100 100 (b) The firm cares about the total profit from its two factories. The objective of firm is therefore to maximize the total profit (1+y2)-c1(y1)-c2(v) The FOCs give us the well-known equality P=MCI=MC2 We have MCi(y)=25y and MC2(v)=50y. Then p=MCi(v1)and p= MC2(32) imply that p= 25y1 and p= 5092. Thus, y=200 and 32=2. Therefore, the short-run supply function is oOu y=的+y P The labor demands for the factories are L1=+2 P 1/50p 25(2u L2=K2 v2 100(a Therefore the labor demand 12(=2) (c)The cost for each factory is cili Lwl+rKI The lagrange function is ≡uL+r+(v-VKLAnswer Set 2 Answer 2.1. (a) For each factory with capital stock K, c(y,K) ≡ min L {wL + rK | y = √ KL} = w K y2 + rK. Therefore, the short-run cost functions are c1(y) = w 25y2 + 25r, c2(y) = w 100y2 + 100r. (b) The firm cares about the total profit from its two factories. The objective of firm is therefore to maximize the total profit: π = max y1, y2 p · (y1 + y2) − c1(y1) − c2(y2). The FOCs give us the well-known equality: p = MC1 = MC2. We have MC1(y) = 2w 25 y and MC2(y) = w 50 y. Then p = MC1(y1) and p = MC2(y2) imply that p = 2w 25 y1 and p = w 50 y2. Thus, y1 = 25p 2w and y2 = 50p w . Therefore, the short-run supply function is: y = y1 + y2 =  25 2w + 50p w  p = 62.5 p w. The labor demands for the factories are: L1 = 1 K1 y2 1 = 1 25 25p 2w 2 = 25 4  p w 2 , L2 = 1 K2 y2 2 = 1 100 50p w 2 = 25  p w 2 . Therefore, the labor demand is L = L1 + L2 = 125 4  p w 2 . (c) The cost for each factory is ci(yi) ≡ min L,K {wL + rK | yi = √ KL}. The Lagrange function is L ≡ wL + rK + λ  yi − √ KL , 2—4