Elon Musk and Jeff Bessos are brothers. Each gets a weekly allowance of $4. Elon's prefer- ences for Tweets (good x) and News Articles (good y) can be represented by the utility function u(x, y) = x^3/4 y^1/4 . Suppose that both goods are $1 per unit. (20 points)

(a) Write down the Lagrangian Function for Elon's utility maximization problem. L(x, y, ) =

(b) Solve for Elon's optimal consumption bundle. x = y =

(c) Suppose px rises to $2. What is Elon's new optimal consumption point? x = y =

(d) How much would his parents have to increase his allowance in order to leave him exactly as well off as he was originally? How much would his parents have to decrease his allowance in order for his utility under the old prices be equal to his utility under the new prices?

(e) Jeff's preferences are represented by (x, y) = 3/ ln(x) + 1/4ln(y). Answer parts (b)-(d) for Jeff. Comment.

Answer rating: 100% (QA)

a The Lagrangian function for Elons utility maximization problem can be written as follows Lx y x34 ... View the full answer