A total income of I is given to spend on two goods x 1 and x 2
Question:
A total income of I is given to spend on two goods x1 and x2 with prices p1 and p2 respectively. Your utility function for x1 and x2 is:
U (x1, x2) = x13 x22
Using this information, solve the following questions:
(a) Using the Lagrange Method, solve for your optimal choice for x1 and x2 as functions of p1 and p2 and I
(b) What is the maximum utility you can attain given prices p1 and p2 with an income I? What is this function called?
(c) Using your result from (b), what is the minimum expenditure you need to attain a utility level u given prices p1 and p2? What is this function called?
(d) Derive the compensated demand functions h1 and h2 using the Shephard's Lemma. Use your result in (c) to solve this.
(e) Find the compensated demand functions by setting up an expenditure minimization problem. Verify that your answers are the same as in (d).
Expert Answer:
To solve the given questions lets go step by step a Using the Lagrange method we need to set up the ... View the full answer
