Pkqq2 A firm uses two inputs, q and q2 to produce a single output Q, given by the produc- 25,15 tion function Q = kq"2". Let P be the price of the output Q, P1 be the price of 25 15 91, and P2 be the price of 42. The profit is given by a - P19 - P292 The inputs that maximize profits satisfy 2Pk _3,5 14,5 0 91 92 - P1 and 5 Pk 25 -415 0= 91 92 P2 5 91 and a. Show that this two equations can be used to determine the amounts of inputs 92 in terms of the prices P1, P2, and P. Show that the relevant matrix has nonzero determinant. b. Write the matrix equation for the partial derivatives of 91 and q2 with respect to P1, P2 and P in terms of the variables. c. Solve for the matrix of partial derivatives of 91 and 92 in terms of p1, p2 and P. Pkqq2 A firm uses two inputs, q and q2 to produce a single output Q, given by the produc- 25,15 tion function Q = kq"2". Let P be the price of the output Q, P1 be the price of 25 15 91, and P2 be the price of 42. The profit is given by a - P19 - P292 The inputs that maximize profits satisfy 2Pk _3,5 14,5 0 91 92 - P1 and 5 Pk 25 -415 0= 91 92 P2 5 91 and a. Show that this two equations can be used to determine the amounts of inputs 92 in terms of the prices P1, P2, and P. Show that the relevant matrix has nonzero determinant. b. Write the matrix equation for the partial derivatives of 91 and q2 with respect to P1, P2 and P in terms of the variables. c. Solve for the matrix of partial derivatives of 91 and 92 in terms of p1, p2 and P