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A consumer has the following utility function for goods X and Y: U(X,Y) = 5XY3 + 10
The consumer faces prices of goods X and Y given by px and py and has an income givenby I.
a. Write out the Lagrangian expression for the consumer's utility maximization problem.
b. Write out the first-order necessary conditions of the Lagrangian for maximizing utility subject to the budget constraint.
c. Show that the first order conditions imply the budget constraint and MRS=MRT condition.
d. Solve for the Demand Equations, X*(px,py,I) and Y*(px,py,I)
(Bonus). Find the expenditure function E(px,py,U) without solving the expenditure minimization problem.
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