please solve this question Consider a profit maximizing firm with production function y = f ( x 1 + x 2 ) + f ( x 2 + x 1 ) with f > 0 , f < 0 that sells its output competitively at price p = 1 . The firm obtains input x i at a competitively determined unit wage w i for all i = 1 , 2 . (i) Give an interpretation of the parameter . (ii) State the first-order conditions of profit maximization. (iii) Show that the second-order conditions are always satisfied. (iv) Let x i be the optimal choice of input i = 1 , 2 . If the choice vector ( x 1 , x 2 ) satisfies the all SOCs then show that it always exists. (v) Prove that for all i , j = 1 , 2 and i = j , (a) the sign of w i x i 0 is independent of but (b) the sign of w j x j = 0 depends on . .

1. please solve this question
Consider a profit maximizing firm with production function y = f ( x 1 + x 2 ) + f ( x 2 + x 1 )
with f > 0 , f < 0 that sells its output competitively at price p = 1 . The firm obtains input x i at a
competitively determined unit wage w i for all i = 1 , 2 . (i) Give an interpretation of the
parameter . (ii) State the first-order conditions of profit maximization. (iii) Show that the second-
order conditions are always satisfied. (iv) Let x i be the optimal choice of input i = 1 , 2 . If the
choice vector ( x 1 , x 2 ) satisfies the all SOCs then show that it always exists. (v) Prove that for
all i , j = 1 , 2 and i = j , (a) the sign of w i x i 0 is independent of but (b) the sign of w j x j = 0
depends on .