Question 1 (50 marks + 5 bonus marks): Skip has the following utility function: U(x, y) = x(y1), where x and y are quantities of two consumption goods whose prices are px and py respectively. Skip has a budget of B,B > py.

(5) By rearranging the indirect utility function, derive an expression for the expenditure function B = B(px, py, U). Interpret this expression. Find B/px, B/py, and B/U. (10 marks)

Skips maximization problem could be recast as the following minimization problem: min B(x,y)=pxx+pyy s.t. x(y1)=U.

(6) Write down the Lagrangian for this problem. (5 marks)

(7) Find the values of x and y that solve this minimization problem and the expenditure function. Are the optimal values, x and y, equal to the partial derivatives of the expenditure function, B/px and B/py respectively. Explain these results using the Envelope Theorem. (15 marks)

(8) Whats the relationship between the values of Lagrangian multiplier in the utility-maximization problem and the expenditure-minimization problem? Explain this relationship using their economic meanings. (Hint: Use the relationship between B and U.) (Bonus: 5 marks.)