Suppose you want to minimize your expenditure on goods x and y having prices p and q, respectively, subject to keeping your utility at a fixed level, U. Your utility function is given by U(x, y) = Bx^1/2^ 1/2 .

(a) Write down the Lagrangian for this problem and find the first order conditions.

(b) Solve for the optimal values of x, y and the value of the Lagrange Multiplier.

(c) Interpret the Lagrange Multiplier, .

(d) Verify the second order condition is satisfied. Are your solutions a minimum or a maximum?

(e) Find the value function. (In this case it is called an expenditure function.)