Question
Consider a consumer with preferences over R 4 + represented by the utility function u(x1, x2, x3, x4) = min{x1 x2, x3 x4}. All prices
Consider a consumer with preferences over R 4 + represented by the utility function u(x1, x2, x3, x4) = min{x1 x2, x3 x4}. All prices are strictly positive.
a. Argue that, at the optimum, x1x2 = x3x4
b. Argue that the budget constraint is satisfied with equality
c. Argue that there cannot be a corner solution.
d. Incorporate the results from (a) and (b) into the consumer's maximization problem. You will be left with a different but equivalent maximization problem. Hint: this new maximization problem has two constraints: the budget constraint and another one. Moreover, the objective function is different than the original one (by part (a)). e. Set up the Lagrangian and derive the Kuhn-Tucker conditions for a solution. Recall the result in (c). f. Find the solution to the consumer's optimization problem
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started