Assume a firm wants to minimize its cost of producing y amount using x1 and x2 as inputs, which means it wants to minimize w1x1 + w2x2 subject to x1^(1/2)x2^(1/2)= y:
(a) Using Lagrange multiplier method, find optimal x1 and x2 as functions of w1,w2 and y.
(b) What is the marginal cost of producing a higher level of y?
(c) What is the marginal cost of an increase in w1?